10_transforms.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to DataFrames\n",
    "**[Bogumił Kamiński](http://bogumilkaminski.pl/about/), February 13, 2023**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using DataFrames"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Split-apply-combine"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grouping a data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.179636</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.856131</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.532306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.747279</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.476843</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.542538</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 2 & 2 & 0.179636 \\\\\n",
       "\t3 & 3 & 1 & 0.856131 \\\\\n",
       "\t4 & 4 & 2 & 0.532306 \\\\\n",
       "\t5 & 1 & 1 & 0.24277 \\\\\n",
       "\t6 & 2 & 2 & 0.747279 \\\\\n",
       "\t7 & 3 & 1 & 0.476843 \\\\\n",
       "\t8 & 4 & 2 & 0.542538 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     2      2  0.179636\n",
       "   3 │     3      1  0.856131\n",
       "   4 │     4      2  0.532306\n",
       "   5 │     1      1  0.24277\n",
       "   6 │     2      2  0.747279\n",
       "   7 │     3      1  0.476843\n",
       "   8 │     4      2  0.542538"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = DataFrame(id=[1,2,3,4,1,2,3,4], id2=[1,2,1,2,1,2,1,2], v=rand(8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><b>GroupedDataFrame with 4 groups based on key: id</b></p><div><div style = \"float: left;\"><span>First Group (2 rows): id = 1</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr></tbody></table></div><p>&vellip;</p><div><div style = \"float: left;\"><span>Last Group (2 rows): id = 4</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.532306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.542538</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "GroupedDataFrame with 4 groups based on key: id\n",
       "\n",
       "First Group (2 rows): id = 1\n",
       "\n",
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 1 & 1 & 0.24277 \\\\\n",
       "\\end{tabular}\n",
       "\n",
       "$\\dots$\n",
       "\n",
       "Last Group (2 rows): id = 4\n",
       "\n",
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 4 & 2 & 0.532306 \\\\\n",
       "\t2 & 4 & 2 & 0.542538 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "GroupedDataFrame with 4 groups based on key: id\n",
       "First Group (2 rows): id = 1\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     1      1  0.24277\n",
       "⋮\n",
       "Last Group (2 rows): id = 4\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     4      2  0.532306\n",
       "   2 │     4      2  0.542538"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groupby(x, :id)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><b>GroupedDataFrame with 1 group based on key: </b></p><div><div style = \"float: left;\"><span>First Group (8 rows): </span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.179636</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.856131</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.532306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.747279</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.476843</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.542538</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "GroupedDataFrame with 1 group based on key: \n",
       "\n",
       "First Group (8 rows): \n",
       "\n",
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 2 & 2 & 0.179636 \\\\\n",
       "\t3 & 3 & 1 & 0.856131 \\\\\n",
       "\t4 & 4 & 2 & 0.532306 \\\\\n",
       "\t5 & 1 & 1 & 0.24277 \\\\\n",
       "\t6 & 2 & 2 & 0.747279 \\\\\n",
       "\t7 & 3 & 1 & 0.476843 \\\\\n",
       "\t8 & 4 & 2 & 0.542538 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "GroupedDataFrame with 1 group based on key: \n",
       "First Group (8 rows): \n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     2      2  0.179636\n",
       "   3 │     3      1  0.856131\n",
       "   4 │     4      2  0.532306\n",
       "   5 │     1      1  0.24277\n",
       "   6 │     2      2  0.747279\n",
       "   7 │     3      1  0.476843\n",
       "   8 │     4      2  0.542538"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groupby(x, [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><b>GroupedDataFrame with 4 groups based on keys: id, id2</b></p><div><div style = \"float: left;\"><span>First Group (2 rows): id = 1, id2 = 1</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr></tbody></table></div><p>&vellip;</p><div><div style = \"float: left;\"><span>Last Group (2 rows): id = 4, id2 = 2</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.532306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.542538</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "GroupedDataFrame with 4 groups based on keys: id, id2\n",
       "\n",
       "First Group (2 rows): id = 1, id2 = 1\n",
       "\n",
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 1 & 1 & 0.24277 \\\\\n",
       "\\end{tabular}\n",
       "\n",
       "$\\dots$\n",
       "\n",
       "Last Group (2 rows): id = 4, id2 = 2\n",
       "\n",
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 4 & 2 & 0.532306 \\\\\n",
       "\t2 & 4 & 2 & 0.542538 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "GroupedDataFrame with 4 groups based on keys: id, id2\n",
       "First Group (2 rows): id = 1, id2 = 1\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     1      1  0.24277\n",
       "⋮\n",
       "Last Group (2 rows): id = 4, id2 = 2\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     4      2  0.532306\n",
       "   2 │     4      2  0.542538"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gx2 = groupby(x, [:id, :id2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.179636</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.856131</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.532306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.747279</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.476843</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.542538</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 2 & 2 & 0.179636 \\\\\n",
       "\t3 & 3 & 1 & 0.856131 \\\\\n",
       "\t4 & 4 & 2 & 0.532306 \\\\\n",
       "\t5 & 1 & 1 & 0.24277 \\\\\n",
       "\t6 & 2 & 2 & 0.747279 \\\\\n",
       "\t7 & 3 & 1 & 0.476843 \\\\\n",
       "\t8 & 4 & 2 & 0.542538 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     2      2  0.179636\n",
       "   3 │     3      1  0.856131\n",
       "   4 │     4      2  0.532306\n",
       "   5 │     1      1  0.24277\n",
       "   6 │     2      2  0.747279\n",
       "   7 │     3      1  0.476843\n",
       "   8 │     4      2  0.542538"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parent(gx2) # get the parent DataFrame "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.179636</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.747279</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.856131</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.476843</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.532306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.542538</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 1 & 1 & 0.24277 \\\\\n",
       "\t3 & 2 & 2 & 0.179636 \\\\\n",
       "\t4 & 2 & 2 & 0.747279 \\\\\n",
       "\t5 & 3 & 1 & 0.856131 \\\\\n",
       "\t6 & 3 & 1 & 0.476843 \\\\\n",
       "\t7 & 4 & 2 & 0.532306 \\\\\n",
       "\t8 & 4 & 2 & 0.542538 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     1      1  0.24277\n",
       "   3 │     2      2  0.179636\n",
       "   4 │     2      2  0.747279\n",
       "   5 │     3      1  0.856131\n",
       "   6 │     3      1  0.476843\n",
       "   7 │     4      2  0.532306\n",
       "   8 │     4      2  0.542538"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vcat(gx2...) # back to the DataFrame, but in a different order of rows than the original"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.179636</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.747279</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.856131</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.476843</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.532306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.542538</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 1 & 1 & 0.24277 \\\\\n",
       "\t3 & 2 & 2 & 0.179636 \\\\\n",
       "\t4 & 2 & 2 & 0.747279 \\\\\n",
       "\t5 & 3 & 1 & 0.856131 \\\\\n",
       "\t6 & 3 & 1 & 0.476843 \\\\\n",
       "\t7 & 4 & 2 & 0.532306 \\\\\n",
       "\t8 & 4 & 2 & 0.542538 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     1      1  0.24277\n",
       "   3 │     2      2  0.179636\n",
       "   4 │     2      2  0.747279\n",
       "   5 │     3      1  0.856131\n",
       "   6 │     3      1  0.476843\n",
       "   7 │     4      2  0.532306\n",
       "   8 │     4      2  0.542538"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DataFrame(gx2) # the same"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×1 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0.24277</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0.179636</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0.747279</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0.856131</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">0.476843</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">0.532306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">0.542538</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|c}\n",
       "\t& v\\\\\n",
       "\t\\hline\n",
       "\t& Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0.239786 \\\\\n",
       "\t2 & 0.24277 \\\\\n",
       "\t3 & 0.179636 \\\\\n",
       "\t4 & 0.747279 \\\\\n",
       "\t5 & 0.856131 \\\\\n",
       "\t6 & 0.476843 \\\\\n",
       "\t7 & 0.532306 \\\\\n",
       "\t8 & 0.542538 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×1 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Float64  \u001b[0m\n",
       "─────┼──────────\n",
       "   1 │ 0.239786\n",
       "   2 │ 0.24277\n",
       "   3 │ 0.179636\n",
       "   4 │ 0.747279\n",
       "   5 │ 0.856131\n",
       "   6 │ 0.476843\n",
       "   7 │ 0.532306\n",
       "   8 │ 0.542538"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DataFrame(gx2, keepkeys=false) # drop grouping columns when creating a data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Symbol}:\n",
       " :id\n",
       " :id2"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groupcols(gx2) # vector of names of grouping variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Vector{Symbol}:\n",
       " :v"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "valuecols(gx2) # and non-grouping variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8-element Vector{Union{Missing, Int64}}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groupindices(gx2) # group indices in parent(gx2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element DataFrames.GroupKeys{GroupedDataFrame{DataFrame}}:\n",
       " GroupKey: (id = 1, id2 = 1)\n",
       " GroupKey: (id = 2, id2 = 2)\n",
       " GroupKey: (id = 3, id2 = 1)\n",
       " GroupKey: (id = 4, id2 = 2)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kgx2 = keys(gx2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can index into a `GroupedDataFrame` like to a vector or to a dictionary.\n",
    "The second form acceps `GroupKey`, `NamedTuple` or a `Tuple`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><b>GroupedDataFrame with 4 groups based on keys: id, id2</b></p><div><div style = \"float: left;\"><span>First Group (2 rows): id = 1, id2 = 1</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr></tbody></table></div><p>&vellip;</p><div><div style = \"float: left;\"><span>Last Group (2 rows): id = 4, id2 = 2</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.532306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.542538</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "GroupedDataFrame with 4 groups based on keys: id, id2\n",
       "\n",
       "First Group (2 rows): id = 1, id2 = 1\n",
       "\n",
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 1 & 1 & 0.24277 \\\\\n",
       "\\end{tabular}\n",
       "\n",
       "$\\dots$\n",
       "\n",
       "Last Group (2 rows): id = 4, id2 = 2\n",
       "\n",
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 4 & 2 & 0.532306 \\\\\n",
       "\t2 & 4 & 2 & 0.542538 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "GroupedDataFrame with 4 groups based on keys: id, id2\n",
       "First Group (2 rows): id = 1, id2 = 1\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     1      1  0.24277\n",
       "⋮\n",
       "Last Group (2 rows): id = 4, id2 = 2\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     4      2  0.532306\n",
       "   2 │     4      2  0.542538"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gx2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GroupKey: (id = 1, id2 = 1)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = keys(gx2)[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(id = 1, id2 = 1)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ntk = NamedTuple(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 1)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tk = Tuple(k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the operations below produce the same result and are fast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×3 SubDataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 1 & 1 & 0.24277 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×3 SubDataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     1      1  0.24277"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gx2[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×3 SubDataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 1 & 1 & 0.24277 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×3 SubDataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     1      1  0.24277"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gx2[k]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×3 SubDataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 1 & 1 & 0.24277 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×3 SubDataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     1      1  0.24277"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gx2[ntk]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×3 SubDataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.239786</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.24277</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 0.239786 \\\\\n",
       "\t2 & 1 & 1 & 0.24277 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×3 SubDataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v        \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────\n",
       "   1 │     1      1  0.239786\n",
       "   2 │     1      1  0.24277"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gx2[tk]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "handling missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>5×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">1</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">2</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">3</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">5</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& id & x\\\\\n",
       "\t\\hline\n",
       "\t& Int64? & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & \\emph{missing} & 1 \\\\\n",
       "\t2 & 5 & 2 \\\\\n",
       "\t3 & 1 & 3 \\\\\n",
       "\t4 & 3 & 4 \\\\\n",
       "\t5 & \\emph{missing} & 5 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m5×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id      \u001b[0m\u001b[1m x     \u001b[0m\n",
       "     │\u001b[90m Int64?  \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼────────────────\n",
       "   1 │\u001b[90m missing \u001b[0m     1\n",
       "   2 │       5      2\n",
       "   3 │       1      3\n",
       "   4 │       3      4\n",
       "   5 │\u001b[90m missing \u001b[0m     5"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = DataFrame(id = [missing, 5, 1, 3, missing], x = 1:5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><b>GroupedDataFrame with 4 groups based on key: id</b></p><div><div style = \"float: left;\"><span>First Group (1 row): id = 1</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">3</td></tr></tbody></table></div><p>&vellip;</p><div><div style = \"float: left;\"><span>Last Group (2 rows): id = missing</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">1</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">5</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "GroupedDataFrame with 4 groups based on key: id\n",
       "\n",
       "First Group (1 row): id = 1\n",
       "\n",
       "\\begin{tabular}{r|cc}\n",
       "\t& id & x\\\\\n",
       "\t\\hline\n",
       "\t& Int64? & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 3 \\\\\n",
       "\\end{tabular}\n",
       "\n",
       "$\\dots$\n",
       "\n",
       "Last Group (2 rows): id = missing\n",
       "\n",
       "\\begin{tabular}{r|cc}\n",
       "\t& id & x\\\\\n",
       "\t\\hline\n",
       "\t& Int64? & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & \\emph{missing} & 1 \\\\\n",
       "\t2 & \\emph{missing} & 5 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "GroupedDataFrame with 4 groups based on key: id\n",
       "First Group (1 row): id = 1\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id     \u001b[0m\u001b[1m x     \u001b[0m\n",
       "     │\u001b[90m Int64? \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼───────────────\n",
       "   1 │      1      3\n",
       "⋮\n",
       "Last Group (2 rows): id = missing\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id      \u001b[0m\u001b[1m x     \u001b[0m\n",
       "     │\u001b[90m Int64?  \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼────────────────\n",
       "   1 │\u001b[90m missing \u001b[0m     1\n",
       "   2 │\u001b[90m missing \u001b[0m     5"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groupby(x, :id) # by default groups include mising values and their order is not guaranteed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><b>GroupedDataFrame with 3 groups based on key: id</b></p><div><div style = \"float: left;\"><span>First Group (1 row): id = 1</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">3</td></tr></tbody></table></div><p>&vellip;</p><div><div style = \"float: left;\"><span>Last Group (1 row): id = 5</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">2</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "GroupedDataFrame with 3 groups based on key: id\n",
       "\n",
       "First Group (1 row): id = 1\n",
       "\n",
       "\\begin{tabular}{r|cc}\n",
       "\t& id & x\\\\\n",
       "\t\\hline\n",
       "\t& Int64? & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 3 \\\\\n",
       "\\end{tabular}\n",
       "\n",
       "$\\dots$\n",
       "\n",
       "Last Group (1 row): id = 5\n",
       "\n",
       "\\begin{tabular}{r|cc}\n",
       "\t& id & x\\\\\n",
       "\t\\hline\n",
       "\t& Int64? & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 5 & 2 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "GroupedDataFrame with 3 groups based on key: id\n",
       "First Group (1 row): id = 1\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id     \u001b[0m\u001b[1m x     \u001b[0m\n",
       "     │\u001b[90m Int64? \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼───────────────\n",
       "   1 │      1      3\n",
       "⋮\n",
       "Last Group (1 row): id = 5\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id     \u001b[0m\u001b[1m x     \u001b[0m\n",
       "     │\u001b[90m Int64? \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼───────────────\n",
       "   1 │      5      2"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groupby(x, :id, sort=true, skipmissing=true) # but we can change it; now they are sorted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><b>GroupedDataFrame with 4 groups based on key: id</b></p><div><div style = \"float: left;\"><span>First Group (2 rows): id = missing</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">1</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">5</td></tr></tbody></table></div><p>&vellip;</p><div><div style = \"float: left;\"><span>Last Group (1 row): id = 3</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "GroupedDataFrame with 4 groups based on key: id\n",
       "\n",
       "First Group (2 rows): id = missing\n",
       "\n",
       "\\begin{tabular}{r|cc}\n",
       "\t& id & x\\\\\n",
       "\t\\hline\n",
       "\t& Int64? & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & \\emph{missing} & 1 \\\\\n",
       "\t2 & \\emph{missing} & 5 \\\\\n",
       "\\end{tabular}\n",
       "\n",
       "$\\dots$\n",
       "\n",
       "Last Group (1 row): id = 3\n",
       "\n",
       "\\begin{tabular}{r|cc}\n",
       "\t& id & x\\\\\n",
       "\t\\hline\n",
       "\t& Int64? & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 3 & 4 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "GroupedDataFrame with 4 groups based on key: id\n",
       "First Group (2 rows): id = missing\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id      \u001b[0m\u001b[1m x     \u001b[0m\n",
       "     │\u001b[90m Int64?  \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼────────────────\n",
       "   1 │\u001b[90m missing \u001b[0m     1\n",
       "   2 │\u001b[90m missing \u001b[0m     5\n",
       "⋮\n",
       "Last Group (1 row): id = 3\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id     \u001b[0m\u001b[1m x     \u001b[0m\n",
       "     │\u001b[90m Int64? \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼───────────────\n",
       "   1 │      3      4"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groupby(x, :id, sort=false) # and now they are in the order they appear in the source data frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performing transformations by group using `combine`, `select`, `select!`, `transform`, and `transform!`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Statistics\n",
    "using Chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>100×2 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">75 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">v</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Char\" style = \"text-align: left;\">Char</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">0.729846</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.978141</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.180073</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.264876</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.583029</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.773974</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">0.993063</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.109659</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.753735</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.540383</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.112203</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.568044</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.749729</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">89</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">0.592921</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">90</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.973998</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">91</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.814132</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">92</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.668003</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">93</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.0452986</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">94</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.0298229</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">95</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.197737</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">96</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.429591</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">97</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.726327</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">98</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.694146</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">99</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.96734</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">100</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.843926</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& id & v\\\\\n",
       "\t\\hline\n",
       "\t& Char & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & a & 0.729846 \\\\\n",
       "\t2 & b & 0.978141 \\\\\n",
       "\t3 & d & 0.180073 \\\\\n",
       "\t4 & c & 0.264876 \\\\\n",
       "\t5 & d & 0.583029 \\\\\n",
       "\t6 & c & 0.773974 \\\\\n",
       "\t7 & a & 0.993063 \\\\\n",
       "\t8 & c & 0.109659 \\\\\n",
       "\t9 & d & 0.753735 \\\\\n",
       "\t10 & c & 0.540383 \\\\\n",
       "\t11 & b & 0.112203 \\\\\n",
       "\t12 & b & 0.568044 \\\\\n",
       "\t13 & b & 0.749729 \\\\\n",
       "\t14 & d & 0.728937 \\\\\n",
       "\t15 & a & 0.0685037 \\\\\n",
       "\t16 & d & 0.0125375 \\\\\n",
       "\t17 & b & 0.00380254 \\\\\n",
       "\t18 & d & 0.460973 \\\\\n",
       "\t19 & d & 0.669664 \\\\\n",
       "\t20 & b & 0.611903 \\\\\n",
       "\t21 & a & 0.792058 \\\\\n",
       "\t22 & b & 0.914439 \\\\\n",
       "\t23 & a & 0.750653 \\\\\n",
       "\t24 & d & 0.076596 \\\\\n",
       "\t25 & c & 0.492296 \\\\\n",
       "\t26 & a & 0.0964787 \\\\\n",
       "\t27 & d & 0.847667 \\\\\n",
       "\t28 & d & 0.980594 \\\\\n",
       "\t29 & c & 0.102231 \\\\\n",
       "\t30 & a & 0.958689 \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m100×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id   \u001b[0m\u001b[1m v         \u001b[0m\n",
       "     │\u001b[90m Char \u001b[0m\u001b[90m Float64   \u001b[0m\n",
       "─────┼─────────────────\n",
       "   1 │ a     0.729846\n",
       "   2 │ b     0.978141\n",
       "   3 │ d     0.180073\n",
       "   4 │ c     0.264876\n",
       "   5 │ d     0.583029\n",
       "   6 │ c     0.773974\n",
       "   7 │ a     0.993063\n",
       "   8 │ c     0.109659\n",
       "   9 │ d     0.753735\n",
       "  10 │ c     0.540383\n",
       "  11 │ b     0.112203\n",
       "  ⋮  │  ⋮        ⋮\n",
       "  91 │ c     0.814132\n",
       "  92 │ d     0.668003\n",
       "  93 │ d     0.0452986\n",
       "  94 │ d     0.0298229\n",
       "  95 │ c     0.197737\n",
       "  96 │ b     0.429591\n",
       "  97 │ d     0.726327\n",
       "  98 │ b     0.694146\n",
       "  99 │ c     0.96734\n",
       " 100 │ d     0.843926\n",
       "\u001b[36m        79 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = DataFrame(id=rand('a':'d', 100), v=rand(100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">v_mean</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Char\" style = \"text-align: left;\">Char</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.591953</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.511306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.469842</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& id & v\\_mean\\\\\n",
       "\t\\hline\n",
       "\t& Char & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & a & 0.523705 \\\\\n",
       "\t2 & b & 0.591953 \\\\\n",
       "\t3 & d & 0.511306 \\\\\n",
       "\t4 & c & 0.469842 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id   \u001b[0m\u001b[1m v_mean   \u001b[0m\n",
       "     │\u001b[90m Char \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────\n",
       "   1 │ a     0.523705\n",
       "   2 │ b     0.591953\n",
       "   3 │ d     0.511306\n",
       "   4 │ c     0.469842"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# apply a function to each group of a data frame\n",
    "# combine keeps as many rows as are returned from the function\n",
    "@chain x begin\n",
    "    groupby(:id)\n",
    "    combine(:v => mean)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Base.OneTo(100)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.id2 = axes(x, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>100×4 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">75 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">v</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v_mean</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Char\" style = \"text-align: left;\">Char</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">0.729846</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.978141</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0.591953</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.180073</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">0.511306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.264876</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.583029</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0.511306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.773974</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">0.993063</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.109659</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.753735</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0.511306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.540383</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.112203</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0.591953</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.568044</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0.591953</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.749729</td><td style = \"text-align: right;\">13</td><td style = \"text-align: right;\">0.591953</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">89</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">0.592921</td><td style = \"text-align: right;\">89</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">90</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.973998</td><td style = \"text-align: right;\">90</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">91</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.814132</td><td style = \"text-align: right;\">91</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">92</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.668003</td><td style = \"text-align: right;\">92</td><td style = \"text-align: right;\">0.511306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">93</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.0452986</td><td style = \"text-align: right;\">93</td><td style = \"text-align: right;\">0.511306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">94</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.0298229</td><td style = \"text-align: right;\">94</td><td style = \"text-align: right;\">0.511306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">95</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.197737</td><td style = \"text-align: right;\">95</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">96</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.429591</td><td style = \"text-align: right;\">96</td><td style = \"text-align: right;\">0.591953</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">97</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.726327</td><td style = \"text-align: right;\">97</td><td style = \"text-align: right;\">0.511306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">98</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.694146</td><td style = \"text-align: right;\">98</td><td style = \"text-align: right;\">0.591953</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">99</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.96734</td><td style = \"text-align: right;\">99</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">100</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.843926</td><td style = \"text-align: right;\">100</td><td style = \"text-align: right;\">0.511306</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& id & v & id2 & v\\_mean\\\\\n",
       "\t\\hline\n",
       "\t& Char & Float64 & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & a & 0.729846 & 1 & 0.523705 \\\\\n",
       "\t2 & b & 0.978141 & 2 & 0.591953 \\\\\n",
       "\t3 & d & 0.180073 & 3 & 0.511306 \\\\\n",
       "\t4 & c & 0.264876 & 4 & 0.469842 \\\\\n",
       "\t5 & d & 0.583029 & 5 & 0.511306 \\\\\n",
       "\t6 & c & 0.773974 & 6 & 0.469842 \\\\\n",
       "\t7 & a & 0.993063 & 7 & 0.523705 \\\\\n",
       "\t8 & c & 0.109659 & 8 & 0.469842 \\\\\n",
       "\t9 & d & 0.753735 & 9 & 0.511306 \\\\\n",
       "\t10 & c & 0.540383 & 10 & 0.469842 \\\\\n",
       "\t11 & b & 0.112203 & 11 & 0.591953 \\\\\n",
       "\t12 & b & 0.568044 & 12 & 0.591953 \\\\\n",
       "\t13 & b & 0.749729 & 13 & 0.591953 \\\\\n",
       "\t14 & d & 0.728937 & 14 & 0.511306 \\\\\n",
       "\t15 & a & 0.0685037 & 15 & 0.523705 \\\\\n",
       "\t16 & d & 0.0125375 & 16 & 0.511306 \\\\\n",
       "\t17 & b & 0.00380254 & 17 & 0.591953 \\\\\n",
       "\t18 & d & 0.460973 & 18 & 0.511306 \\\\\n",
       "\t19 & d & 0.669664 & 19 & 0.511306 \\\\\n",
       "\t20 & b & 0.611903 & 20 & 0.591953 \\\\\n",
       "\t21 & a & 0.792058 & 21 & 0.523705 \\\\\n",
       "\t22 & b & 0.914439 & 22 & 0.591953 \\\\\n",
       "\t23 & a & 0.750653 & 23 & 0.523705 \\\\\n",
       "\t24 & d & 0.076596 & 24 & 0.511306 \\\\\n",
       "\t25 & c & 0.492296 & 25 & 0.469842 \\\\\n",
       "\t26 & a & 0.0964787 & 26 & 0.523705 \\\\\n",
       "\t27 & d & 0.847667 & 27 & 0.511306 \\\\\n",
       "\t28 & d & 0.980594 & 28 & 0.511306 \\\\\n",
       "\t29 & c & 0.102231 & 29 & 0.469842 \\\\\n",
       "\t30 & a & 0.958689 & 30 & 0.523705 \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m100×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id   \u001b[0m\u001b[1m v         \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v_mean   \u001b[0m\n",
       "     │\u001b[90m Char \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼──────────────────────────────────\n",
       "   1 │ a     0.729846       1  0.523705\n",
       "   2 │ b     0.978141       2  0.591953\n",
       "   3 │ d     0.180073       3  0.511306\n",
       "   4 │ c     0.264876       4  0.469842\n",
       "   5 │ d     0.583029       5  0.511306\n",
       "   6 │ c     0.773974       6  0.469842\n",
       "   7 │ a     0.993063       7  0.523705\n",
       "   8 │ c     0.109659       8  0.469842\n",
       "   9 │ d     0.753735       9  0.511306\n",
       "  10 │ c     0.540383      10  0.469842\n",
       "  11 │ b     0.112203      11  0.591953\n",
       "  ⋮  │  ⋮        ⋮        ⋮       ⋮\n",
       "  91 │ c     0.814132      91  0.469842\n",
       "  92 │ d     0.668003      92  0.511306\n",
       "  93 │ d     0.0452986     93  0.511306\n",
       "  94 │ d     0.0298229     94  0.511306\n",
       "  95 │ c     0.197737      95  0.469842\n",
       "  96 │ b     0.429591      96  0.591953\n",
       "  97 │ d     0.726327      97  0.511306\n",
       "  98 │ b     0.694146      98  0.591953\n",
       "  99 │ c     0.96734       99  0.469842\n",
       " 100 │ d     0.843926     100  0.511306\n",
       "\u001b[36m                         79 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# select and transform keep as many rows as are in the source data frame and in correct order\n",
    "# additionally transform keeps all columns from the source\n",
    "@chain x begin\n",
    "    groupby(:id)\n",
    "    transform(:v => mean)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>100×3 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">75 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">id2</th><th style = \"text-align: left;\">v_mean</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Char\" style = \"text-align: left;\">Char</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">15</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">21</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">23</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">26</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">30</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">34</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">40</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">41</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">50</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">51</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">53</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">89</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">44</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">90</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">48</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">91</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">49</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">92</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">56</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">93</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">65</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">94</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">74</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">95</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">85</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">96</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">86</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">97</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">90</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">98</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">91</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">99</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">95</td><td style = \"text-align: right;\">0.469842</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">100</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">99</td><td style = \"text-align: right;\">0.469842</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & id2 & v\\_mean\\\\\n",
       "\t\\hline\n",
       "\t& Char & Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & a & 1 & 0.523705 \\\\\n",
       "\t2 & a & 7 & 0.523705 \\\\\n",
       "\t3 & a & 15 & 0.523705 \\\\\n",
       "\t4 & a & 21 & 0.523705 \\\\\n",
       "\t5 & a & 23 & 0.523705 \\\\\n",
       "\t6 & a & 26 & 0.523705 \\\\\n",
       "\t7 & a & 30 & 0.523705 \\\\\n",
       "\t8 & a & 34 & 0.523705 \\\\\n",
       "\t9 & a & 40 & 0.523705 \\\\\n",
       "\t10 & a & 41 & 0.523705 \\\\\n",
       "\t11 & a & 50 & 0.523705 \\\\\n",
       "\t12 & a & 51 & 0.523705 \\\\\n",
       "\t13 & a & 53 & 0.523705 \\\\\n",
       "\t14 & a & 57 & 0.523705 \\\\\n",
       "\t15 & a & 61 & 0.523705 \\\\\n",
       "\t16 & a & 66 & 0.523705 \\\\\n",
       "\t17 & a & 68 & 0.523705 \\\\\n",
       "\t18 & a & 69 & 0.523705 \\\\\n",
       "\t19 & a & 71 & 0.523705 \\\\\n",
       "\t20 & a & 73 & 0.523705 \\\\\n",
       "\t21 & a & 76 & 0.523705 \\\\\n",
       "\t22 & a & 77 & 0.523705 \\\\\n",
       "\t23 & a & 78 & 0.523705 \\\\\n",
       "\t24 & a & 89 & 0.523705 \\\\\n",
       "\t25 & b & 2 & 0.591953 \\\\\n",
       "\t26 & b & 11 & 0.591953 \\\\\n",
       "\t27 & b & 12 & 0.591953 \\\\\n",
       "\t28 & b & 13 & 0.591953 \\\\\n",
       "\t29 & b & 17 & 0.591953 \\\\\n",
       "\t30 & b & 20 & 0.591953 \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m100×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id   \u001b[0m\u001b[1m id2   \u001b[0m\u001b[1m v_mean   \u001b[0m\n",
       "     │\u001b[90m Char \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼───────────────────────\n",
       "   1 │ a         1  0.523705\n",
       "   2 │ a         7  0.523705\n",
       "   3 │ a        15  0.523705\n",
       "   4 │ a        21  0.523705\n",
       "   5 │ a        23  0.523705\n",
       "   6 │ a        26  0.523705\n",
       "   7 │ a        30  0.523705\n",
       "   8 │ a        34  0.523705\n",
       "   9 │ a        40  0.523705\n",
       "  10 │ a        41  0.523705\n",
       "  11 │ a        50  0.523705\n",
       "  ⋮  │  ⋮      ⋮       ⋮\n",
       "  91 │ c        49  0.469842\n",
       "  92 │ c        56  0.469842\n",
       "  93 │ c        65  0.469842\n",
       "  94 │ c        74  0.469842\n",
       "  95 │ c        85  0.469842\n",
       "  96 │ c        86  0.469842\n",
       "  97 │ c        90  0.469842\n",
       "  98 │ c        91  0.469842\n",
       "  99 │ c        95  0.469842\n",
       " 100 │ c        99  0.469842\n",
       "\u001b[36m              79 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# note that combine reorders rows by group of GroupedDataFrame\n",
    "@chain x begin\n",
    "    groupby(:id)\n",
    "    combine(:id2, :v => mean)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">res</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Char\" style = \"text-align: left;\">Char</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">0.523705</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.591953</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.511306</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.469842</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& id & res\\\\\n",
       "\t\\hline\n",
       "\t& Char & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & a & 0.523705 \\\\\n",
       "\t2 & b & 0.591953 \\\\\n",
       "\t3 & d & 0.511306 \\\\\n",
       "\t4 & c & 0.469842 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id   \u001b[0m\u001b[1m res      \u001b[0m\n",
       "     │\u001b[90m Char \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────\n",
       "   1 │ a     0.523705\n",
       "   2 │ b     0.591953\n",
       "   3 │ d     0.511306\n",
       "   4 │ c     0.469842"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we give a custom name for the result column\n",
    "@chain x begin\n",
    "    groupby(:id)\n",
    "    combine(:v => mean => :res)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×4 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">res1</th><th style = \"text-align: left;\">res2</th><th style = \"text-align: left;\">n</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Char\" style = \"text-align: left;\">Char</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">a</td><td style = \"text-align: right;\">0.523705</td><td style = \"text-align: right;\">12.5689</td><td style = \"text-align: right;\">24</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">0.591953</td><td style = \"text-align: right;\">15.9827</td><td style = \"text-align: right;\">27</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">0.511306</td><td style = \"text-align: right;\">13.8053</td><td style = \"text-align: right;\">27</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">c</td><td style = \"text-align: right;\">0.469842</td><td style = \"text-align: right;\">10.3365</td><td style = \"text-align: right;\">22</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& id & res1 & res2 & n\\\\\n",
       "\t\\hline\n",
       "\t& Char & Float64 & Float64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & a & 0.523705 & 12.5689 & 24 \\\\\n",
       "\t2 & b & 0.591953 & 15.9827 & 27 \\\\\n",
       "\t3 & d & 0.511306 & 13.8053 & 27 \\\\\n",
       "\t4 & c & 0.469842 & 10.3365 & 22 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id   \u001b[0m\u001b[1m res1     \u001b[0m\u001b[1m res2    \u001b[0m\u001b[1m n     \u001b[0m\n",
       "     │\u001b[90m Char \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼────────────────────────────────\n",
       "   1 │ a     0.523705  12.5689     24\n",
       "   2 │ b     0.591953  15.9827     27\n",
       "   3 │ d     0.511306  13.8053     27\n",
       "   4 │ c     0.469842  10.3365     22"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# you can have multiple operations\n",
    "@chain x begin\n",
    "    groupby(:id)\n",
    "    combine(:v => mean => :res1, :v => sum => :res2, nrow => :n)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additional notes:\n",
    "* `select!` and `transform!` perform operations in-place\n",
    "* The general syntax for transformation is `source_columns => function => target_column`\n",
    "* if you pass multiple columns to a function they are treated as positional arguments\n",
    "* `ByRow` and `AsTable` work exactly like discussed for operations on data frames in 05_columns.ipynb\n",
    "* you can automatically groupby again the result of `combine`, `select` etc. by passing `ungroup=false` keyword argument to them\n",
    "* similarly `keepkeys` keyword argument allows you to drop grouping columns from the resulting data frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also allowed to pass a function to all these functions (also - as a special case, as a first argument). In this case the return value can be a table. In particular it allows for an easy dropping of groups if you return an empty table from the function.\n",
    "\n",
    "If you pass a function you can use a `do` block syntax. In case of passing a function it gets a `SubDataFrame` as its argument.\n",
    "\n",
    "Here is an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">n</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Char\" style = \"text-align: left;\">Char</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">b</td><td style = \"text-align: right;\">27</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">d</td><td style = \"text-align: right;\">27</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& id & n\\\\\n",
       "\t\\hline\n",
       "\t& Char & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & b & 27 \\\\\n",
       "\t2 & d & 27 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id   \u001b[0m\u001b[1m n     \u001b[0m\n",
       "     │\u001b[90m Char \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼─────────────\n",
       "   1 │ b        27\n",
       "   2 │ d        27"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combine(groupby(x, :id)) do sdf\n",
    "    n = nrow(sdf)\n",
    "    n < 25 ? DataFrame() : DataFrame(n=n) # drop groups with low number of rows\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also produce multiple columns in a single operation, e.g.:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">val</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">2</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">4</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& id & val\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 \\\\\n",
       "\t2 & 1 & 2 \\\\\n",
       "\t3 & 2 & 3 \\\\\n",
       "\t4 & 2 & 4 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m val   \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼──────────────\n",
       "   1 │     1      1\n",
       "   2 │     1      2\n",
       "   3 │     2      3\n",
       "   4 │     2      4"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = DataFrame(id=[1,1,2,2], val=[1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">2</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & x1 & x2\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 2 \\\\\n",
       "\t2 & 2 & 3 & 4 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m x1    \u001b[0m\u001b[1m x2    \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼─────────────────────\n",
       "   1 │     1      1      2\n",
       "   2 │     2      3      4"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@chain df begin\n",
    "    groupby(:id)\n",
    "    combine(:val => (x -> [x]) => AsTable)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">c1</th><th style = \"text-align: left;\">c2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">2</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & c1 & c2\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 2 \\\\\n",
       "\t2 & 2 & 3 & 4 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m c1    \u001b[0m\u001b[1m c2    \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼─────────────────────\n",
       "   1 │     1      1      2\n",
       "   2 │     2      3      4"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@chain df begin\n",
    "    groupby(:id)\n",
    "    combine(:val => (x -> [x]) => [:c1, :c2])\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is easy to unnest the column into multiple columns, e.g."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×1 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">a</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"NamedTuple{(:p, :q), Tuple{Int64, Int64}}\" style = \"text-align: left;\">NamedTup…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">(p = 1, q = 2)</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">(p = 3, q = 4)</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|c}\n",
       "\t& a\\\\\n",
       "\t\\hline\n",
       "\t& NamedTup…\\\\\n",
       "\t\\hline\n",
       "\t1 & (p = 1, q = 2) \\\\\n",
       "\t2 & (p = 3, q = 4) \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×1 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m a              \u001b[0m\n",
       "     │\u001b[90m NamedTup…      \u001b[0m\n",
       "─────┼────────────────\n",
       "   1 │ (p = 1, q = 2)\n",
       "   2 │ (p = 3, q = 4)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = DataFrame(a=[(p=1, q=2), (p=3, q=4)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">p</th><th style = \"text-align: left;\">q</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">2</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& p & q\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 \\\\\n",
       "\t2 & 3 & 4 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m p     \u001b[0m\u001b[1m q     \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼──────────────\n",
       "   1 │     1      2\n",
       "   2 │     3      4"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select(df, :a => AsTable)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×1 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">a</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Vector{Int64}\" style = \"text-align: left;\">Array…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">[1, 2]</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">[3, 4]</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|c}\n",
       "\t& a\\\\\n",
       "\t\\hline\n",
       "\t& Array…\\\\\n",
       "\t\\hline\n",
       "\t1 & [1, 2] \\\\\n",
       "\t2 & [3, 4] \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×1 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m a      \u001b[0m\n",
       "     │\u001b[90m Array… \u001b[0m\n",
       "─────┼────────\n",
       "   1 │ [1, 2]\n",
       "   2 │ [3, 4]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = DataFrame(a=[[1, 2], [3, 4]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">2</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& x1 & x2\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 \\\\\n",
       "\t2 & 3 & 4 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1    \u001b[0m\u001b[1m x2    \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼──────────────\n",
       "   1 │     1      2\n",
       "   2 │     3      4"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select(df, :a => AsTable) # automatic column names generated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">C1</th><th style = \"text-align: left;\">C2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">2</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& C1 & C2\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 \\\\\n",
       "\t2 & 3 & 4 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m C1    \u001b[0m\u001b[1m C2    \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼──────────────\n",
       "   1 │     1      2\n",
       "   2 │     3      4"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select(df, :a => [:C1, :C2]) # custom column names generated"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, observe that one can conveniently apply multiple transformations using broadcasting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>100×3 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">75 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">101</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">102</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">103</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">104</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">105</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">106</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">107</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">108</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">109</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">110</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">111</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">112</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">13</td><td style = \"text-align: right;\">113</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">89</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">89</td><td style = \"text-align: right;\">189</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">90</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">90</td><td style = \"text-align: right;\">190</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">91</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">91</td><td style = \"text-align: right;\">191</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">92</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">92</td><td style = \"text-align: right;\">192</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">93</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">93</td><td style = \"text-align: right;\">193</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">94</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">94</td><td style = \"text-align: right;\">194</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">95</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">95</td><td style = \"text-align: right;\">195</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">96</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">96</td><td style = \"text-align: right;\">196</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">97</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">97</td><td style = \"text-align: right;\">197</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">98</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">98</td><td style = \"text-align: right;\">198</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">99</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">99</td><td style = \"text-align: right;\">199</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">100</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">100</td><td style = \"text-align: right;\">200</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & x1 & x2\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 101 \\\\\n",
       "\t2 & 2 & 2 & 102 \\\\\n",
       "\t3 & 3 & 3 & 103 \\\\\n",
       "\t4 & 4 & 4 & 104 \\\\\n",
       "\t5 & 5 & 5 & 105 \\\\\n",
       "\t6 & 6 & 6 & 106 \\\\\n",
       "\t7 & 7 & 7 & 107 \\\\\n",
       "\t8 & 8 & 8 & 108 \\\\\n",
       "\t9 & 9 & 9 & 109 \\\\\n",
       "\t10 & 10 & 10 & 110 \\\\\n",
       "\t11 & 1 & 11 & 111 \\\\\n",
       "\t12 & 2 & 12 & 112 \\\\\n",
       "\t13 & 3 & 13 & 113 \\\\\n",
       "\t14 & 4 & 14 & 114 \\\\\n",
       "\t15 & 5 & 15 & 115 \\\\\n",
       "\t16 & 6 & 16 & 116 \\\\\n",
       "\t17 & 7 & 17 & 117 \\\\\n",
       "\t18 & 8 & 18 & 118 \\\\\n",
       "\t19 & 9 & 19 & 119 \\\\\n",
       "\t20 & 10 & 20 & 120 \\\\\n",
       "\t21 & 1 & 21 & 121 \\\\\n",
       "\t22 & 2 & 22 & 122 \\\\\n",
       "\t23 & 3 & 23 & 123 \\\\\n",
       "\t24 & 4 & 24 & 124 \\\\\n",
       "\t25 & 5 & 25 & 125 \\\\\n",
       "\t26 & 6 & 26 & 126 \\\\\n",
       "\t27 & 7 & 27 & 127 \\\\\n",
       "\t28 & 8 & 28 & 128 \\\\\n",
       "\t29 & 9 & 29 & 129 \\\\\n",
       "\t30 & 10 & 30 & 130 \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m100×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m x1    \u001b[0m\u001b[1m x2    \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼─────────────────────\n",
       "   1 │     1      1    101\n",
       "   2 │     2      2    102\n",
       "   3 │     3      3    103\n",
       "   4 │     4      4    104\n",
       "   5 │     5      5    105\n",
       "   6 │     6      6    106\n",
       "   7 │     7      7    107\n",
       "   8 │     8      8    108\n",
       "   9 │     9      9    109\n",
       "  10 │    10     10    110\n",
       "  11 │     1     11    111\n",
       "  ⋮  │   ⋮      ⋮      ⋮\n",
       "  91 │     1     91    191\n",
       "  92 │     2     92    192\n",
       "  93 │     3     93    193\n",
       "  94 │     4     94    194\n",
       "  95 │     5     95    195\n",
       "  96 │     6     96    196\n",
       "  97 │     7     97    197\n",
       "  98 │     8     98    198\n",
       "  99 │     9     99    199\n",
       " 100 │    10    100    200\n",
       "\u001b[36m            79 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = DataFrame(id=repeat(1:10, 10), x1=1:100, x2=101:200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>10×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x1_minimum</th><th style = \"text-align: left;\">x2_minimum</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">101</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">102</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">103</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">104</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">105</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">106</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">107</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">108</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">109</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">110</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& id & x1\\_minimum & x2\\_minimum\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 101 \\\\\n",
       "\t2 & 2 & 2 & 102 \\\\\n",
       "\t3 & 3 & 3 & 103 \\\\\n",
       "\t4 & 4 & 4 & 104 \\\\\n",
       "\t5 & 5 & 5 & 105 \\\\\n",
       "\t6 & 6 & 6 & 106 \\\\\n",
       "\t7 & 7 & 7 & 107 \\\\\n",
       "\t8 & 8 & 8 & 108 \\\\\n",
       "\t9 & 9 & 9 & 109 \\\\\n",
       "\t10 & 10 & 10 & 110 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m10×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m x1_minimum \u001b[0m\u001b[1m x2_minimum \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64      \u001b[0m\u001b[90m Int64      \u001b[0m\n",
       "─────┼───────────────────────────────\n",
       "   1 │     1           1         101\n",
       "   2 │     2           2         102\n",
       "   3 │     3           3         103\n",
       "   4 │     4           4         104\n",
       "   5 │     5           5         105\n",
       "   6 │     6           6         106\n",
       "   7 │     7           7         107\n",
       "   8 │     8           8         108\n",
       "   9 │     9           9         109\n",
       "  10 │    10          10         110"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@chain df begin\n",
    "    groupby(:id)\n",
    "    combine([:x1, :x2] .=> minimum)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>10×5 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x1_minimum</th><th style = \"text-align: left;\">x2_minimum</th><th style = \"text-align: left;\">x1_maximum</th><th style = \"text-align: left;\">x2_maximum</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">101</td><td style = \"text-align: right;\">91</td><td style = \"text-align: right;\">191</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">102</td><td style = \"text-align: right;\">92</td><td style = \"text-align: right;\">192</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">103</td><td style = \"text-align: right;\">93</td><td style = \"text-align: right;\">193</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">104</td><td style = \"text-align: right;\">94</td><td style = \"text-align: right;\">194</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">105</td><td style = \"text-align: right;\">95</td><td style = \"text-align: right;\">195</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">106</td><td style = \"text-align: right;\">96</td><td style = \"text-align: right;\">196</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">107</td><td style = \"text-align: right;\">97</td><td style = \"text-align: right;\">197</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">108</td><td style = \"text-align: right;\">98</td><td style = \"text-align: right;\">198</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">109</td><td style = \"text-align: right;\">99</td><td style = \"text-align: right;\">199</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">110</td><td style = \"text-align: right;\">100</td><td style = \"text-align: right;\">200</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& id & x1\\_minimum & x2\\_minimum & x1\\_maximum & x2\\_maximum\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Int64 & Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 1 & 101 & 91 & 191 \\\\\n",
       "\t2 & 2 & 2 & 102 & 92 & 192 \\\\\n",
       "\t3 & 3 & 3 & 103 & 93 & 193 \\\\\n",
       "\t4 & 4 & 4 & 104 & 94 & 194 \\\\\n",
       "\t5 & 5 & 5 & 105 & 95 & 195 \\\\\n",
       "\t6 & 6 & 6 & 106 & 96 & 196 \\\\\n",
       "\t7 & 7 & 7 & 107 & 97 & 197 \\\\\n",
       "\t8 & 8 & 8 & 108 & 98 & 198 \\\\\n",
       "\t9 & 9 & 9 & 109 & 99 & 199 \\\\\n",
       "\t10 & 10 & 10 & 110 & 100 & 200 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m10×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m x1_minimum \u001b[0m\u001b[1m x2_minimum \u001b[0m\u001b[1m x1_maximum \u001b[0m\u001b[1m x2_maximum \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64      \u001b[0m\u001b[90m Int64      \u001b[0m\u001b[90m Int64      \u001b[0m\u001b[90m Int64      \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────\n",
       "   1 │     1           1         101          91         191\n",
       "   2 │     2           2         102          92         192\n",
       "   3 │     3           3         103          93         193\n",
       "   4 │     4           4         104          94         194\n",
       "   5 │     5           5         105          95         195\n",
       "   6 │     6           6         106          96         196\n",
       "   7 │     7           7         107          97         197\n",
       "   8 │     8           8         108          98         198\n",
       "   9 │     9           9         109          99         199\n",
       "  10 │    10          10         110         100         200"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@chain df begin\n",
    "    groupby(:id)\n",
    "    combine([:x1, :x2] .=> [minimum maximum])\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Aggregation of a data frame using `mapcols`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>10×10 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">x5</th><th style = \"text-align: left;\">x6</th><th style = \"text-align: left;\">x7</th><th style = \"text-align: left;\">x8</th><th style = \"text-align: left;\">x9</th><th style = \"text-align: left;\">x10</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0.793935</td><td style = \"text-align: right;\">0.45687</td><td style = \"text-align: right;\">0.907089</td><td style = \"text-align: right;\">0.351164</td><td style = \"text-align: right;\">0.468913</td><td style = \"text-align: right;\">0.438825</td><td style = \"text-align: right;\">0.680173</td><td style = \"text-align: right;\">0.39229</td><td style = \"text-align: right;\">0.0923248</td><td style = \"text-align: right;\">0.11396</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0.387642</td><td style = \"text-align: right;\">0.881526</td><td style = \"text-align: right;\">0.776264</td><td style = \"text-align: right;\">0.295657</td><td style = \"text-align: right;\">0.629058</td><td style = \"text-align: right;\">0.57288</td><td style = \"text-align: right;\">0.751462</td><td style = \"text-align: right;\">0.504253</td><td style = \"text-align: right;\">0.813727</td><td style = \"text-align: right;\">0.0109507</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0.0588001</td><td style = \"text-align: right;\">0.448813</td><td style = \"text-align: right;\">0.811436</td><td style = \"text-align: right;\">0.0117327</td><td style = \"text-align: right;\">0.424192</td><td style = \"text-align: right;\">0.420064</td><td style = \"text-align: right;\">0.122655</td><td style = \"text-align: right;\">0.596486</td><td style = \"text-align: right;\">0.389178</td><td style = \"text-align: right;\">0.987284</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0.0149787</td><td style = \"text-align: right;\">0.55115</td><td style = \"text-align: right;\">0.864966</td><td style = \"text-align: right;\">0.23952</td><td style = \"text-align: right;\">0.598431</td><td style = \"text-align: right;\">0.919414</td><td style = \"text-align: right;\">0.0160189</td><td style = \"text-align: right;\">0.916821</td><td style = \"text-align: right;\">0.935497</td><td style = \"text-align: right;\">0.0557498</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0.393852</td><td style = \"text-align: right;\">0.263755</td><td style = \"text-align: right;\">0.457996</td><td style = \"text-align: right;\">0.122174</td><td style = \"text-align: right;\">0.152931</td><td style = \"text-align: right;\">0.0982895</td><td style = \"text-align: right;\">0.926354</td><td style = \"text-align: right;\">0.134069</td><td style = \"text-align: right;\">0.498688</td><td style = \"text-align: right;\">0.677689</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">0.825976</td><td style = \"text-align: right;\">0.112791</td><td style = \"text-align: right;\">0.3081</td><td style = \"text-align: right;\">0.000525589</td><td style = \"text-align: right;\">0.909336</td><td style = \"text-align: right;\">0.340167</td><td style = \"text-align: right;\">0.228858</td><td style = \"text-align: right;\">0.464665</td><td style = \"text-align: right;\">0.147053</td><td style = \"text-align: right;\">0.361095</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">0.553853</td><td style = \"text-align: right;\">0.689573</td><td style = \"text-align: right;\">0.15967</td><td style = \"text-align: right;\">0.856762</td><td style = \"text-align: right;\">0.518455</td><td style = \"text-align: right;\">0.675691</td><td style = \"text-align: right;\">0.538844</td><td style = \"text-align: right;\">0.522398</td><td style = \"text-align: right;\">0.110538</td><td style = \"text-align: right;\">0.884335</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">0.825157</td><td style = \"text-align: right;\">0.8904</td><td style = \"text-align: right;\">0.481969</td><td style = \"text-align: right;\">0.0589375</td><td style = \"text-align: right;\">0.0665701</td><td style = \"text-align: right;\">0.858516</td><td style = \"text-align: right;\">0.157013</td><td style = \"text-align: right;\">0.938286</td><td style = \"text-align: right;\">0.875335</td><td style = \"text-align: right;\">0.451671</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">0.839455</td><td style = \"text-align: right;\">0.564254</td><td style = \"text-align: right;\">0.178448</td><td style = \"text-align: right;\">0.727648</td><td style = \"text-align: right;\">0.483625</td><td style = \"text-align: right;\">0.903504</td><td style = \"text-align: right;\">0.459634</td><td style = \"text-align: right;\">0.928908</td><td style = \"text-align: right;\">0.0244351</td><td style = \"text-align: right;\">0.0397077</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">0.3542</td><td style = \"text-align: right;\">0.488556</td><td style = \"text-align: right;\">0.468679</td><td style = \"text-align: right;\">0.691836</td><td style = \"text-align: right;\">0.448638</td><td style = \"text-align: right;\">0.872127</td><td style = \"text-align: right;\">0.69638</td><td style = \"text-align: right;\">0.39555</td><td style = \"text-align: right;\">0.633463</td><td style = \"text-align: right;\">0.209026</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& x1 & x2 & x3 & x4 & x5 & x6 & x7 & x8 & \\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & 0.793935 & 0.45687 & 0.907089 & 0.351164 & 0.468913 & 0.438825 & 0.680173 & 0.39229 & $\\dots$ \\\\\n",
       "\t2 & 0.387642 & 0.881526 & 0.776264 & 0.295657 & 0.629058 & 0.57288 & 0.751462 & 0.504253 & $\\dots$ \\\\\n",
       "\t3 & 0.0588001 & 0.448813 & 0.811436 & 0.0117327 & 0.424192 & 0.420064 & 0.122655 & 0.596486 & $\\dots$ \\\\\n",
       "\t4 & 0.0149787 & 0.55115 & 0.864966 & 0.23952 & 0.598431 & 0.919414 & 0.0160189 & 0.916821 & $\\dots$ \\\\\n",
       "\t5 & 0.393852 & 0.263755 & 0.457996 & 0.122174 & 0.152931 & 0.0982895 & 0.926354 & 0.134069 & $\\dots$ \\\\\n",
       "\t6 & 0.825976 & 0.112791 & 0.3081 & 0.000525589 & 0.909336 & 0.340167 & 0.228858 & 0.464665 & $\\dots$ \\\\\n",
       "\t7 & 0.553853 & 0.689573 & 0.15967 & 0.856762 & 0.518455 & 0.675691 & 0.538844 & 0.522398 & $\\dots$ \\\\\n",
       "\t8 & 0.825157 & 0.8904 & 0.481969 & 0.0589375 & 0.0665701 & 0.858516 & 0.157013 & 0.938286 & $\\dots$ \\\\\n",
       "\t9 & 0.839455 & 0.564254 & 0.178448 & 0.727648 & 0.483625 & 0.903504 & 0.459634 & 0.928908 & $\\dots$ \\\\\n",
       "\t10 & 0.3542 & 0.488556 & 0.468679 & 0.691836 & 0.448638 & 0.872127 & 0.69638 & 0.39555 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m10×10 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1        \u001b[0m\u001b[1m x2       \u001b[0m\u001b[1m x3       \u001b[0m\u001b[1m x4          \u001b[0m\u001b[1m x5        \u001b[0m\u001b[1m x6        \u001b[0m\u001b[1m x7   \u001b[0m ⋯\n",
       "     │\u001b[90m Float64   \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64     \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ 0.793935   0.45687   0.907089  0.351164     0.468913   0.438825   0.680 ⋯\n",
       "   2 │ 0.387642   0.881526  0.776264  0.295657     0.629058   0.57288    0.751\n",
       "   3 │ 0.0588001  0.448813  0.811436  0.0117327    0.424192   0.420064   0.122\n",
       "   4 │ 0.0149787  0.55115   0.864966  0.23952      0.598431   0.919414   0.016\n",
       "   5 │ 0.393852   0.263755  0.457996  0.122174     0.152931   0.0982895  0.926 ⋯\n",
       "   6 │ 0.825976   0.112791  0.3081    0.000525589  0.909336   0.340167   0.228\n",
       "   7 │ 0.553853   0.689573  0.15967   0.856762     0.518455   0.675691   0.538\n",
       "   8 │ 0.825157   0.8904    0.481969  0.0589375    0.0665701  0.858516   0.157\n",
       "   9 │ 0.839455   0.564254  0.178448  0.727648     0.483625   0.903504   0.459 ⋯\n",
       "  10 │ 0.3542     0.488556  0.468679  0.691836     0.448638   0.872127   0.696\n",
       "\u001b[36m                                                               4 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = DataFrame(rand(10, 10), :auto)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>1×10 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">x5</th><th style = \"text-align: left;\">x6</th><th style = \"text-align: left;\">x7</th><th style = \"text-align: left;\">x8</th><th style = \"text-align: left;\">x9</th><th style = \"text-align: left;\">x10</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0.504785</td><td style = \"text-align: right;\">0.534769</td><td style = \"text-align: right;\">0.541462</td><td style = \"text-align: right;\">0.335596</td><td style = \"text-align: right;\">0.470015</td><td style = \"text-align: right;\">0.609948</td><td style = \"text-align: right;\">0.457739</td><td style = \"text-align: right;\">0.579373</td><td style = \"text-align: right;\">0.452024</td><td style = \"text-align: right;\">0.379147</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& x1 & x2 & x3 & x4 & x5 & x6 & x7 & x8 & \\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & 0.504785 & 0.534769 & 0.541462 & 0.335596 & 0.470015 & 0.609948 & 0.457739 & 0.579373 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m1×10 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1       \u001b[0m\u001b[1m x2       \u001b[0m\u001b[1m x3       \u001b[0m\u001b[1m x4       \u001b[0m\u001b[1m x5       \u001b[0m\u001b[1m x6       \u001b[0m\u001b[1m x7       \u001b[0m\u001b[1m x\u001b[0m ⋯\n",
       "     │\u001b[90m Float64  \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m F\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ 0.504785  0.534769  0.541462  0.335596  0.470015  0.609948  0.457739  0 ⋯\n",
       "\u001b[36m                                                               3 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mapcols(mean, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mapping rows and columns using `eachcol` and `eachrow`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Vector{Float64}:\n",
       " 0.504784841417523\n",
       " 0.5347688352920631\n",
       " 0.5414617940852021\n",
       " 0.3355955804813384\n",
       " 0.4700149148775635\n",
       " 0.6099479022673252\n",
       " 0.4577392326685229\n",
       " 0.57937264963089\n",
       " 0.45202385337967466\n",
       " 0.3791468806271661"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "map(mean, eachcol(x)) # map a function over each column and return a vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1: 0.504784841417523\n",
      "x2: 0.5347688352920631\n",
      "x3: 0.5414617940852021\n",
      "x4: 0.3355955804813384\n",
      "x5: 0.4700149148775635\n",
      "x6: 0.6099479022673252\n",
      "x7: 0.4577392326685229\n",
      "x8: 0.57937264963089\n",
      "x9: 0.45202385337967466\n",
      "x10: 0.3791468806271661\n"
     ]
    }
   ],
   "source": [
    "# an iteration returns a Pair with column name and values\n",
    "foreach(c -> println(c[1], \": \", mean(c[2])), pairs(eachcol(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Vector{Float64}:\n",
       " 1.737770179560276\n",
       " 0.4397392873188234\n",
       " 0.13101271017638122\n",
       " 0.027177156050721477\n",
       " 1.4932473184688198\n",
       " 7.323092180729385\n",
       " 0.8031817580079057\n",
       " 0.9267256635293967\n",
       " 1.4877250440295864\n",
       " 0.7249933549150893"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now the returned value is DataFrameRow which works as a NamedTuple but is a view to a parent DataFrame\n",
    "map(r -> r.x1/r.x2, eachrow(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>10×10 DataFrameRows</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">x5</th><th style = \"text-align: left;\">x6</th><th style = \"text-align: left;\">x7</th><th style = \"text-align: left;\">x8</th><th style = \"text-align: left;\">x9</th><th style = \"text-align: left;\">x10</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0.793935</td><td style = \"text-align: right;\">0.45687</td><td style = \"text-align: right;\">0.907089</td><td style = \"text-align: right;\">0.351164</td><td style = \"text-align: right;\">0.468913</td><td style = \"text-align: right;\">0.438825</td><td style = \"text-align: right;\">0.680173</td><td style = \"text-align: right;\">0.39229</td><td style = \"text-align: right;\">0.0923248</td><td style = \"text-align: right;\">0.11396</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0.387642</td><td style = \"text-align: right;\">0.881526</td><td style = \"text-align: right;\">0.776264</td><td style = \"text-align: right;\">0.295657</td><td style = \"text-align: right;\">0.629058</td><td style = \"text-align: right;\">0.57288</td><td style = \"text-align: right;\">0.751462</td><td style = \"text-align: right;\">0.504253</td><td style = \"text-align: right;\">0.813727</td><td style = \"text-align: right;\">0.0109507</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0.0588001</td><td style = \"text-align: right;\">0.448813</td><td style = \"text-align: right;\">0.811436</td><td style = \"text-align: right;\">0.0117327</td><td style = \"text-align: right;\">0.424192</td><td style = \"text-align: right;\">0.420064</td><td style = \"text-align: right;\">0.122655</td><td style = \"text-align: right;\">0.596486</td><td style = \"text-align: right;\">0.389178</td><td style = \"text-align: right;\">0.987284</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0.0149787</td><td style = \"text-align: right;\">0.55115</td><td style = \"text-align: right;\">0.864966</td><td style = \"text-align: right;\">0.23952</td><td style = \"text-align: right;\">0.598431</td><td style = \"text-align: right;\">0.919414</td><td style = \"text-align: right;\">0.0160189</td><td style = \"text-align: right;\">0.916821</td><td style = \"text-align: right;\">0.935497</td><td style = \"text-align: right;\">0.0557498</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0.393852</td><td style = \"text-align: right;\">0.263755</td><td style = \"text-align: right;\">0.457996</td><td style = \"text-align: right;\">0.122174</td><td style = \"text-align: right;\">0.152931</td><td style = \"text-align: right;\">0.0982895</td><td style = \"text-align: right;\">0.926354</td><td style = \"text-align: right;\">0.134069</td><td style = \"text-align: right;\">0.498688</td><td style = \"text-align: right;\">0.677689</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">0.825976</td><td style = \"text-align: right;\">0.112791</td><td style = \"text-align: right;\">0.3081</td><td style = \"text-align: right;\">0.000525589</td><td style = \"text-align: right;\">0.909336</td><td style = \"text-align: right;\">0.340167</td><td style = \"text-align: right;\">0.228858</td><td style = \"text-align: right;\">0.464665</td><td style = \"text-align: right;\">0.147053</td><td style = \"text-align: right;\">0.361095</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">0.553853</td><td style = \"text-align: right;\">0.689573</td><td style = \"text-align: right;\">0.15967</td><td style = \"text-align: right;\">0.856762</td><td style = \"text-align: right;\">0.518455</td><td style = \"text-align: right;\">0.675691</td><td style = \"text-align: right;\">0.538844</td><td style = \"text-align: right;\">0.522398</td><td style = \"text-align: right;\">0.110538</td><td style = \"text-align: right;\">0.884335</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">0.825157</td><td style = \"text-align: right;\">0.8904</td><td style = \"text-align: right;\">0.481969</td><td style = \"text-align: right;\">0.0589375</td><td style = \"text-align: right;\">0.0665701</td><td style = \"text-align: right;\">0.858516</td><td style = \"text-align: right;\">0.157013</td><td style = \"text-align: right;\">0.938286</td><td style = \"text-align: right;\">0.875335</td><td style = \"text-align: right;\">0.451671</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">0.839455</td><td style = \"text-align: right;\">0.564254</td><td style = \"text-align: right;\">0.178448</td><td style = \"text-align: right;\">0.727648</td><td style = \"text-align: right;\">0.483625</td><td style = \"text-align: right;\">0.903504</td><td style = \"text-align: right;\">0.459634</td><td style = \"text-align: right;\">0.928908</td><td style = \"text-align: right;\">0.0244351</td><td style = \"text-align: right;\">0.0397077</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">0.3542</td><td style = \"text-align: right;\">0.488556</td><td style = \"text-align: right;\">0.468679</td><td style = \"text-align: right;\">0.691836</td><td style = \"text-align: right;\">0.448638</td><td style = \"text-align: right;\">0.872127</td><td style = \"text-align: right;\">0.69638</td><td style = \"text-align: right;\">0.39555</td><td style = \"text-align: right;\">0.633463</td><td style = \"text-align: right;\">0.209026</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& x1 & x2 & x3 & x4 & x5 & x6 & x7 & x8 & \\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & 0.793935 & 0.45687 & 0.907089 & 0.351164 & 0.468913 & 0.438825 & 0.680173 & 0.39229 & $\\dots$ \\\\\n",
       "\t2 & 0.387642 & 0.881526 & 0.776264 & 0.295657 & 0.629058 & 0.57288 & 0.751462 & 0.504253 & $\\dots$ \\\\\n",
       "\t3 & 0.0588001 & 0.448813 & 0.811436 & 0.0117327 & 0.424192 & 0.420064 & 0.122655 & 0.596486 & $\\dots$ \\\\\n",
       "\t4 & 0.0149787 & 0.55115 & 0.864966 & 0.23952 & 0.598431 & 0.919414 & 0.0160189 & 0.916821 & $\\dots$ \\\\\n",
       "\t5 & 0.393852 & 0.263755 & 0.457996 & 0.122174 & 0.152931 & 0.0982895 & 0.926354 & 0.134069 & $\\dots$ \\\\\n",
       "\t6 & 0.825976 & 0.112791 & 0.3081 & 0.000525589 & 0.909336 & 0.340167 & 0.228858 & 0.464665 & $\\dots$ \\\\\n",
       "\t7 & 0.553853 & 0.689573 & 0.15967 & 0.856762 & 0.518455 & 0.675691 & 0.538844 & 0.522398 & $\\dots$ \\\\\n",
       "\t8 & 0.825157 & 0.8904 & 0.481969 & 0.0589375 & 0.0665701 & 0.858516 & 0.157013 & 0.938286 & $\\dots$ \\\\\n",
       "\t9 & 0.839455 & 0.564254 & 0.178448 & 0.727648 & 0.483625 & 0.903504 & 0.459634 & 0.928908 & $\\dots$ \\\\\n",
       "\t10 & 0.3542 & 0.488556 & 0.468679 & 0.691836 & 0.448638 & 0.872127 & 0.69638 & 0.39555 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m10×10 DataFrameRows\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1        \u001b[0m\u001b[1m x2       \u001b[0m\u001b[1m x3       \u001b[0m\u001b[1m x4          \u001b[0m\u001b[1m x5        \u001b[0m\u001b[1m x6        \u001b[0m\u001b[1m x7   \u001b[0m ⋯\n",
       "     │\u001b[90m Float64   \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64     \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ 0.793935   0.45687   0.907089  0.351164     0.468913   0.438825   0.680 ⋯\n",
       "   2 │ 0.387642   0.881526  0.776264  0.295657     0.629058   0.57288    0.751\n",
       "   3 │ 0.0588001  0.448813  0.811436  0.0117327    0.424192   0.420064   0.122\n",
       "   4 │ 0.0149787  0.55115   0.864966  0.23952      0.598431   0.919414   0.016\n",
       "   5 │ 0.393852   0.263755  0.457996  0.122174     0.152931   0.0982895  0.926 ⋯\n",
       "   6 │ 0.825976   0.112791  0.3081    0.000525589  0.909336   0.340167   0.228\n",
       "   7 │ 0.553853   0.689573  0.15967   0.856762     0.518455   0.675691   0.538\n",
       "   8 │ 0.825157   0.8904    0.481969  0.0589375    0.0665701  0.858516   0.157\n",
       "   9 │ 0.839455   0.564254  0.178448  0.727648     0.483625   0.903504   0.459 ⋯\n",
       "  10 │ 0.3542     0.488556  0.468679  0.691836     0.448638   0.872127   0.696\n",
       "\u001b[36m                                                               4 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# it prints like a data frame, only the caption is different so that you know the type of the object\n",
    "er = eachrow(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Vector{Float64}:\n",
       " 0.793935382423837\n",
       " 0.38764175810388546\n",
       " 0.058800146945729326\n",
       " 0.014978679608386947\n",
       " 0.3938518572622478\n",
       " 0.8259762402778601\n",
       " 0.5538525731101662\n",
       " 0.8251566133725446\n",
       " 0.8394550502957067\n",
       " 0.3542001127748666"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "er.x1 # you can access columns of a parent data frame directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>10×10 DataFrameColumns</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">x5</th><th style = \"text-align: left;\">x6</th><th style = \"text-align: left;\">x7</th><th style = \"text-align: left;\">x8</th><th style = \"text-align: left;\">x9</th><th style = \"text-align: left;\">x10</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0.793935</td><td style = \"text-align: right;\">0.45687</td><td style = \"text-align: right;\">0.907089</td><td style = \"text-align: right;\">0.351164</td><td style = \"text-align: right;\">0.468913</td><td style = \"text-align: right;\">0.438825</td><td style = \"text-align: right;\">0.680173</td><td style = \"text-align: right;\">0.39229</td><td style = \"text-align: right;\">0.0923248</td><td style = \"text-align: right;\">0.11396</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0.387642</td><td style = \"text-align: right;\">0.881526</td><td style = \"text-align: right;\">0.776264</td><td style = \"text-align: right;\">0.295657</td><td style = \"text-align: right;\">0.629058</td><td style = \"text-align: right;\">0.57288</td><td style = \"text-align: right;\">0.751462</td><td style = \"text-align: right;\">0.504253</td><td style = \"text-align: right;\">0.813727</td><td style = \"text-align: right;\">0.0109507</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0.0588001</td><td style = \"text-align: right;\">0.448813</td><td style = \"text-align: right;\">0.811436</td><td style = \"text-align: right;\">0.0117327</td><td style = \"text-align: right;\">0.424192</td><td style = \"text-align: right;\">0.420064</td><td style = \"text-align: right;\">0.122655</td><td style = \"text-align: right;\">0.596486</td><td style = \"text-align: right;\">0.389178</td><td style = \"text-align: right;\">0.987284</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0.0149787</td><td style = \"text-align: right;\">0.55115</td><td style = \"text-align: right;\">0.864966</td><td style = \"text-align: right;\">0.23952</td><td style = \"text-align: right;\">0.598431</td><td style = \"text-align: right;\">0.919414</td><td style = \"text-align: right;\">0.0160189</td><td style = \"text-align: right;\">0.916821</td><td style = \"text-align: right;\">0.935497</td><td style = \"text-align: right;\">0.0557498</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0.393852</td><td style = \"text-align: right;\">0.263755</td><td style = \"text-align: right;\">0.457996</td><td style = \"text-align: right;\">0.122174</td><td style = \"text-align: right;\">0.152931</td><td style = \"text-align: right;\">0.0982895</td><td style = \"text-align: right;\">0.926354</td><td style = \"text-align: right;\">0.134069</td><td style = \"text-align: right;\">0.498688</td><td style = \"text-align: right;\">0.677689</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">0.825976</td><td style = \"text-align: right;\">0.112791</td><td style = \"text-align: right;\">0.3081</td><td style = \"text-align: right;\">0.000525589</td><td style = \"text-align: right;\">0.909336</td><td style = \"text-align: right;\">0.340167</td><td style = \"text-align: right;\">0.228858</td><td style = \"text-align: right;\">0.464665</td><td style = \"text-align: right;\">0.147053</td><td style = \"text-align: right;\">0.361095</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">0.553853</td><td style = \"text-align: right;\">0.689573</td><td style = \"text-align: right;\">0.15967</td><td style = \"text-align: right;\">0.856762</td><td style = \"text-align: right;\">0.518455</td><td style = \"text-align: right;\">0.675691</td><td style = \"text-align: right;\">0.538844</td><td style = \"text-align: right;\">0.522398</td><td style = \"text-align: right;\">0.110538</td><td style = \"text-align: right;\">0.884335</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">0.825157</td><td style = \"text-align: right;\">0.8904</td><td style = \"text-align: right;\">0.481969</td><td style = \"text-align: right;\">0.0589375</td><td style = \"text-align: right;\">0.0665701</td><td style = \"text-align: right;\">0.858516</td><td style = \"text-align: right;\">0.157013</td><td style = \"text-align: right;\">0.938286</td><td style = \"text-align: right;\">0.875335</td><td style = \"text-align: right;\">0.451671</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">0.839455</td><td style = \"text-align: right;\">0.564254</td><td style = \"text-align: right;\">0.178448</td><td style = \"text-align: right;\">0.727648</td><td style = \"text-align: right;\">0.483625</td><td style = \"text-align: right;\">0.903504</td><td style = \"text-align: right;\">0.459634</td><td style = \"text-align: right;\">0.928908</td><td style = \"text-align: right;\">0.0244351</td><td style = \"text-align: right;\">0.0397077</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">0.3542</td><td style = \"text-align: right;\">0.488556</td><td style = \"text-align: right;\">0.468679</td><td style = \"text-align: right;\">0.691836</td><td style = \"text-align: right;\">0.448638</td><td style = \"text-align: right;\">0.872127</td><td style = \"text-align: right;\">0.69638</td><td style = \"text-align: right;\">0.39555</td><td style = \"text-align: right;\">0.633463</td><td style = \"text-align: right;\">0.209026</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& x1 & x2 & x3 & x4 & x5 & x6 & x7 & x8 & \\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & 0.793935 & 0.45687 & 0.907089 & 0.351164 & 0.468913 & 0.438825 & 0.680173 & 0.39229 & $\\dots$ \\\\\n",
       "\t2 & 0.387642 & 0.881526 & 0.776264 & 0.295657 & 0.629058 & 0.57288 & 0.751462 & 0.504253 & $\\dots$ \\\\\n",
       "\t3 & 0.0588001 & 0.448813 & 0.811436 & 0.0117327 & 0.424192 & 0.420064 & 0.122655 & 0.596486 & $\\dots$ \\\\\n",
       "\t4 & 0.0149787 & 0.55115 & 0.864966 & 0.23952 & 0.598431 & 0.919414 & 0.0160189 & 0.916821 & $\\dots$ \\\\\n",
       "\t5 & 0.393852 & 0.263755 & 0.457996 & 0.122174 & 0.152931 & 0.0982895 & 0.926354 & 0.134069 & $\\dots$ \\\\\n",
       "\t6 & 0.825976 & 0.112791 & 0.3081 & 0.000525589 & 0.909336 & 0.340167 & 0.228858 & 0.464665 & $\\dots$ \\\\\n",
       "\t7 & 0.553853 & 0.689573 & 0.15967 & 0.856762 & 0.518455 & 0.675691 & 0.538844 & 0.522398 & $\\dots$ \\\\\n",
       "\t8 & 0.825157 & 0.8904 & 0.481969 & 0.0589375 & 0.0665701 & 0.858516 & 0.157013 & 0.938286 & $\\dots$ \\\\\n",
       "\t9 & 0.839455 & 0.564254 & 0.178448 & 0.727648 & 0.483625 & 0.903504 & 0.459634 & 0.928908 & $\\dots$ \\\\\n",
       "\t10 & 0.3542 & 0.488556 & 0.468679 & 0.691836 & 0.448638 & 0.872127 & 0.69638 & 0.39555 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m10×10 DataFrameColumns\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1        \u001b[0m\u001b[1m x2       \u001b[0m\u001b[1m x3       \u001b[0m\u001b[1m x4          \u001b[0m\u001b[1m x5        \u001b[0m\u001b[1m x6        \u001b[0m\u001b[1m x7   \u001b[0m ⋯\n",
       "     │\u001b[90m Float64   \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64     \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ 0.793935   0.45687   0.907089  0.351164     0.468913   0.438825   0.680 ⋯\n",
       "   2 │ 0.387642   0.881526  0.776264  0.295657     0.629058   0.57288    0.751\n",
       "   3 │ 0.0588001  0.448813  0.811436  0.0117327    0.424192   0.420064   0.122\n",
       "   4 │ 0.0149787  0.55115   0.864966  0.23952      0.598431   0.919414   0.016\n",
       "   5 │ 0.393852   0.263755  0.457996  0.122174     0.152931   0.0982895  0.926 ⋯\n",
       "   6 │ 0.825976   0.112791  0.3081    0.000525589  0.909336   0.340167   0.228\n",
       "   7 │ 0.553853   0.689573  0.15967   0.856762     0.518455   0.675691   0.538\n",
       "   8 │ 0.825157   0.8904    0.481969  0.0589375    0.0665701  0.858516   0.157\n",
       "   9 │ 0.839455   0.564254  0.178448  0.727648     0.483625   0.903504   0.459 ⋯\n",
       "  10 │ 0.3542     0.488556  0.468679  0.691836     0.448638   0.872127   0.696\n",
       "\u001b[36m                                                               4 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# it prints like a data frame, only the caption is different so that you know the type of the object\n",
    "ec = eachcol(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Vector{Float64}:\n",
       " 0.793935382423837\n",
       " 0.38764175810388546\n",
       " 0.058800146945729326\n",
       " 0.014978679608386947\n",
       " 0.3938518572622478\n",
       " 0.8259762402778601\n",
       " 0.5538525731101662\n",
       " 0.8251566133725446\n",
       " 0.8394550502957067\n",
       " 0.3542001127748666"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ec.x1 # you can access columns of a parent data frame directly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transposing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "you can transpose a data frame using `permutedims`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>3×4 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">x4</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">10</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">11</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">12</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& x1 & x2 & x3 & x4\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 4 & 7 & 10 \\\\\n",
       "\t2 & 2 & 5 & 8 & 11 \\\\\n",
       "\t3 & 3 & 6 & 9 & 12 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m3×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1    \u001b[0m\u001b[1m x2    \u001b[0m\u001b[1m x3    \u001b[0m\u001b[1m x4    \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼────────────────────────────\n",
       "   1 │     1      4      7     10\n",
       "   2 │     2      5      8     11\n",
       "   3 │     3      6      9     12"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = DataFrame(reshape(1:12, 3, 4), :auto)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">6</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">9</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">12</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& x1 & x2 & x3\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 2 & 3 \\\\\n",
       "\t2 & 4 & 5 & 6 \\\\\n",
       "\t3 & 7 & 8 & 9 \\\\\n",
       "\t4 & 10 & 11 & 12 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1    \u001b[0m\u001b[1m x2    \u001b[0m\u001b[1m x3    \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼─────────────────────\n",
       "   1 │     1      2      3\n",
       "   2 │     4      5      6\n",
       "   3 │     7      8      9\n",
       "   4 │    10     11     12"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutedims(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{String}:\n",
       " \"a\"\n",
       " \"b\"\n",
       " \"c\""
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.names = [\"a\", \"b\", \"c\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×4 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">names</th><th style = \"text-align: left;\">a</th><th style = \"text-align: left;\">b</th><th style = \"text-align: left;\">c</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String\" style = \"text-align: left;\">String</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">x1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">x2</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">6</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">x3</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">9</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">x4</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">12</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& names & a & b & c\\\\\n",
       "\t\\hline\n",
       "\t& String & Int64 & Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & x1 & 1 & 2 & 3 \\\\\n",
       "\t2 & x2 & 4 & 5 & 6 \\\\\n",
       "\t3 & x3 & 7 & 8 & 9 \\\\\n",
       "\t4 & x4 & 10 & 11 & 12 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m names  \u001b[0m\u001b[1m a     \u001b[0m\u001b[1m b     \u001b[0m\u001b[1m c     \u001b[0m\n",
       "     │\u001b[90m String \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼─────────────────────────────\n",
       "   1 │ x1          1      2      3\n",
       "   2 │ x2          4      5      6\n",
       "   3 │ x3          7      8      9\n",
       "   4 │ x4         10     11     12"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permutedims(df, :names)"
   ]
  }
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