{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cube de données et pandas\n",
    "\n",
    "[pandas](https://pandas.pydata.org/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Un cube\n",
    "\n",
    "Les données sont disposées sous forme de table, il y a N colonnes de coordonnées et une colonne numérique. Avec ``N=4``, cela équivaut à une fonction $f(x_1,x_2,x_3,x_4)=y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X4</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C1</td>\n",
       "      <td>D1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C1</td>\n",
       "      <td>D2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C2</td>\n",
       "      <td>D1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C2</td>\n",
       "      <td>D2</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>A1</td>\n",
       "      <td>B2</td>\n",
       "      <td>C1</td>\n",
       "      <td>D1</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>A1</td>\n",
       "      <td>B2</td>\n",
       "      <td>C1</td>\n",
       "      <td>D2</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>A1</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "      <td>D1</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>A1</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "      <td>D2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "      <td>D2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   X1  X2  X3  X4  Y\n",
       "0  A1  B1  C1  D1  3\n",
       "1  A1  B1  C1  D2  4\n",
       "2  A1  B1  C2  D1  5\n",
       "3  A1  B1  C2  D2  6\n",
       "4  A1  B2  C1  D1  7\n",
       "5  A1  B2  C1  D2  8\n",
       "6  A1  B2  C2  D1  9\n",
       "7  A1  B2  C2  D2  2\n",
       "8  A2  B2  C2  D2  1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas\n",
    "\n",
    "data = [\n",
    "    {\"X1\": \"A1\", \"X2\": \"B1\", \"X3\": \"C1\", \"X4\": \"D1\", \"Y\": 3},\n",
    "    {\"X1\": \"A1\", \"X2\": \"B1\", \"X3\": \"C1\", \"X4\": \"D2\", \"Y\": 4},\n",
    "    {\"X1\": \"A1\", \"X2\": \"B1\", \"X3\": \"C2\", \"X4\": \"D1\", \"Y\": 5},\n",
    "    {\"X1\": \"A1\", \"X2\": \"B1\", \"X3\": \"C2\", \"X4\": \"D2\", \"Y\": 6},\n",
    "    {\"X1\": \"A1\", \"X2\": \"B2\", \"X3\": \"C1\", \"X4\": \"D1\", \"Y\": 7},\n",
    "    {\"X1\": \"A1\", \"X2\": \"B2\", \"X3\": \"C1\", \"X4\": \"D2\", \"Y\": 8},\n",
    "    {\"X1\": \"A1\", \"X2\": \"B2\", \"X3\": \"C2\", \"X4\": \"D1\", \"Y\": 9},\n",
    "    {\"X1\": \"A1\", \"X2\": \"B2\", \"X3\": \"C2\", \"X4\": \"D2\", \"Y\": 2},\n",
    "    {\"X1\": \"A2\", \"X2\": \"B2\", \"X3\": \"C2\", \"X4\": \"D2\", \"Y\": 1},\n",
    "]\n",
    "df = pandas.DataFrame(data)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pivot\n",
    "\n",
    "Le pivot consiste à choisir des colonnes pour les indices des lignes, et d'autres pour les colonnes. Le pivot fonctionne si chaque valeur numérique peut être identifiée de manière unique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>X3</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>X4</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">A1</th>\n",
       "      <th>B1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B2</th>\n",
       "      <td>7.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A2</th>\n",
       "      <th>B2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X3      C1        C2     \n",
       "X4      D1   D2   D1   D2\n",
       "X1 X2                    \n",
       "A1 B1  3.0  4.0  5.0  6.0\n",
       "   B2  7.0  8.0  9.0  2.0\n",
       "A2 B2  NaN  NaN  NaN  1.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.pivot(index=[\"X1\", \"X2\"], columns=[\"X3\", \"X4\"], values=\"Y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>X2</th>\n",
       "      <th colspan=\"4\" halign=\"left\">B1</th>\n",
       "      <th colspan=\"4\" halign=\"left\">B2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X3</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C2</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X4</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X1</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X2   B1                  B2               \n",
       "X3   C1        C2        C1        C2     \n",
       "X4   D1   D2   D1   D2   D1   D2   D1   D2\n",
       "X1                                        \n",
       "A1  3.0  4.0  5.0  6.0  7.0  8.0  9.0  2.0\n",
       "A2  NaN  NaN  NaN  NaN  NaN  NaN  NaN  1.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.pivot(index=[\"X1\"], columns=[\"X2\", \"X3\", \"X4\"], values=\"Y\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Index et MultiIndex\n",
    "\n",
    "A quoi correspondent les index ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MultiIndex([('B1', 'C1', 'D1'),\n",
       "            ('B1', 'C1', 'D2'),\n",
       "            ('B1', 'C2', 'D1'),\n",
       "            ('B1', 'C2', 'D2'),\n",
       "            ('B2', 'C1', 'D1'),\n",
       "            ('B2', 'C1', 'D2'),\n",
       "            ('B2', 'C2', 'D1'),\n",
       "            ('B2', 'C2', 'D2')],\n",
       "           names=['X2', 'X3', 'X4'])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv = df.pivot(index=[\"X1\"], columns=[\"X2\", \"X3\", \"X4\"], values=\"Y\")\n",
    "piv.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['A1', 'A2'], dtype='object', name='X1')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MultiIndex([('C1', 'D1'),\n",
       "            ('C1', 'D2'),\n",
       "            ('C2', 'D1'),\n",
       "            ('C2', 'D2')],\n",
       "           names=['X3', 'X4'])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv = df.pivot(index=[\"X1\", \"X2\"], columns=[\"X3\", \"X4\"], values=\"Y\")\n",
    "piv.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MultiIndex([('A1', 'B1'),\n",
       "            ('A1', 'B2'),\n",
       "            ('A2', 'B2')],\n",
       "           names=['X1', 'X2'])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les [Index](https://pandas.pydata.org/docs/reference/api/pandas.Index.html) indexent les valeurs et sont équivalents à des colonnes, les [MultiIndex](https://pandas.pydata.org/docs/reference/api/pandas.MultiIndex.html) indexent les valeurs et sont équivalents à plusieurs colonnes. On récupère le nom des colonnes avec la propriété [names](https://pandas.pydata.org/docs/reference/api/pandas.MultiIndex.names.html#pandas.MultiIndex.names)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FrozenList(['X3', 'X4'])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.columns.names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FrozenList(['X1', 'X2'])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.index.names"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On récupère le nombre de colonnes avec [nlevels](https://pandas.pydata.org/docs/reference/api/pandas.MultiIndex.nlevels.html#pandas.MultiIndex.nlevels)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.columns.nlevels, piv.index.nlevels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ou encore [levels](https://pandas.pydata.org/docs/reference/api/pandas.MultiIndex.nlevels.html#pandas.MultiIndex.levels)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(FrozenList([['C1', 'C2'], ['D1', 'D2']]),\n",
       " FrozenList([['A1', 'A2'], ['B1', 'B2']]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.columns.levels, piv.index.levels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On veut accéder à un élément."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>X3</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X4</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>B1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B2</th>\n",
       "      <td>7.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X3   C1        C2     \n",
       "X4   D1   D2   D1   D2\n",
       "X2                    \n",
       "B1  3.0  4.0  5.0  6.0\n",
       "B2  7.0  8.0  9.0  2.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.loc[\"A1\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "X3  X4\n",
       "C1  D1    3.0\n",
       "    D2    4.0\n",
       "C2  D1    5.0\n",
       "    D2    6.0\n",
       "Name: (A1, B1), dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.loc[\"A1\", \"B1\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X4</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">A1</th>\n",
       "      <th>B1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B2</th>\n",
       "      <td>7.0</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A2</th>\n",
       "      <th>B2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X4      D1   D2\n",
       "X1 X2          \n",
       "A1 B1  3.0  4.0\n",
       "   B2  7.0  8.0\n",
       "A2 B2  NaN  NaN"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv[\"C1\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "X1  X2\n",
       "A1  B1    3.0\n",
       "    B2    7.0\n",
       "A2  B2    NaN\n",
       "Name: (C1, D1), dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv[\"C1\", \"D1\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Passer de l'un à l'autre\n",
    "\n",
    "Peut-on retrouver les données originales à partir du pivot?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>X3</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>X4</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">A1</th>\n",
       "      <th>B1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B2</th>\n",
       "      <td>7.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A2</th>\n",
       "      <th>B2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X3      C1        C2     \n",
       "X4      D1   D2   D1   D2\n",
       "X1 X2                    \n",
       "A1 B1  3.0  4.0  5.0  6.0\n",
       "   B2  7.0  8.0  9.0  2.0\n",
       "A2 B2  NaN  NaN  NaN  1.0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ce qui ne marche pas [reset_index](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.reset_index.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>X3</th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X4</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B2</td>\n",
       "      <td>7.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X3  X1  X2   C1        C2     \n",
       "X4           D1   D2   D1   D2\n",
       "0   A1  B1  3.0  4.0  5.0  6.0\n",
       "1   A1  B2  7.0  8.0  9.0  2.0\n",
       "2   A2  B2  NaN  NaN  NaN  1.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.reset_index(drop=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ce qui marche...\n",
    "\n",
    "* [stack](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.stack.html) : fait passer une coordonnée des colonnes aux lignes\n",
    "* [unstack](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.unstack.html) : fait passer une coordonnée des lignes aux colonnes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>X4</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">A1</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">B1</th>\n",
       "      <th>C1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">B2</th>\n",
       "      <th>C1</th>\n",
       "      <td>7.0</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>9.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">A2</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">B2</th>\n",
       "      <th>C1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X4         D1   D2\n",
       "X1 X2 X3          \n",
       "A1 B1 C1  3.0  4.0\n",
       "      C2  5.0  6.0\n",
       "   B2 C1  7.0  8.0\n",
       "      C2  9.0  2.0\n",
       "A2 B2 C1  NaN  NaN\n",
       "      C2  NaN  1.0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.stack(0, future_stack=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "X1  X2  X3  X4\n",
       "A1  B1  C1  D1    3.0\n",
       "            D2    4.0\n",
       "        C2  D1    5.0\n",
       "            D2    6.0\n",
       "    B2  C1  D1    7.0\n",
       "            D2    8.0\n",
       "        C2  D1    9.0\n",
       "            D2    2.0\n",
       "A2  B2  C1  D1    NaN\n",
       "            D2    NaN\n",
       "        C2  D1    NaN\n",
       "            D2    1.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.stack([0, 1], future_stack=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>X3</th>\n",
       "      <th>C1</th>\n",
       "      <th>C2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X4</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">A1</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">B1</th>\n",
       "      <th>D1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D2</th>\n",
       "      <td>4.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">B2</th>\n",
       "      <th>D1</th>\n",
       "      <td>7.0</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D2</th>\n",
       "      <td>8.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">A2</th>\n",
       "      <th rowspan=\"2\" valign=\"top\">B2</th>\n",
       "      <th>D1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X3         C1   C2\n",
       "X1 X2 X4          \n",
       "A1 B1 D1  3.0  5.0\n",
       "      D2  4.0  6.0\n",
       "   B2 D1  7.0  9.0\n",
       "      D2  8.0  2.0\n",
       "A2 B2 D1  NaN  NaN\n",
       "      D2  NaN  1.0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.stack(\"X4\", future_stack=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>X3</th>\n",
       "      <th colspan=\"4\" halign=\"left\">C1</th>\n",
       "      <th colspan=\"4\" halign=\"left\">C2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X4</th>\n",
       "      <th colspan=\"2\" halign=\"left\">D1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">D2</th>\n",
       "      <th colspan=\"2\" halign=\"left\">D1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">D2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X1</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>B1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B2</th>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X3   C1                C2              \n",
       "X4   D1       D2       D1       D2     \n",
       "X1   A1  A2   A1  A2   A1  A2   A1   A2\n",
       "X2                                     \n",
       "B1  3.0 NaN  4.0 NaN  5.0 NaN  6.0  NaN\n",
       "B2  7.0 NaN  8.0 NaN  9.0 NaN  2.0  1.0"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "piv.unstack(\"X1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut changer l'ordre des index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MultiIndex([('A1', 'C1', 'D1'),\n",
       "            ('A2', 'C1', 'D1'),\n",
       "            ('A1', 'C1', 'D2'),\n",
       "            ('A2', 'C1', 'D2'),\n",
       "            ('A1', 'C2', 'D1'),\n",
       "            ('A2', 'C2', 'D1'),\n",
       "            ('A1', 'C2', 'D2'),\n",
       "            ('A2', 'C2', 'D2')],\n",
       "           names=['X1', 'X3', 'X4'])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "view = piv.unstack(\"X1\")\n",
    "new_index = view.columns.reorder_levels([\"X1\", \"X3\", \"X4\"])\n",
    "new_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>X1</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "      <th>A1</th>\n",
       "      <th>A2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X3</th>\n",
       "      <th>C1</th>\n",
       "      <th>C1</th>\n",
       "      <th>C1</th>\n",
       "      <th>C1</th>\n",
       "      <th>C2</th>\n",
       "      <th>C2</th>\n",
       "      <th>C2</th>\n",
       "      <th>C2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X4</th>\n",
       "      <th>D1</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D2</th>\n",
       "      <th>D1</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>B1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B2</th>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X1   A1  A2   A1  A2   A1  A2   A1   A2\n",
       "X3   C1  C1   C1  C1   C2  C2   C2   C2\n",
       "X4   D1  D1   D2  D2   D1  D1   D2   D2\n",
       "X2                                     \n",
       "B1  3.0 NaN  4.0 NaN  5.0 NaN  6.0  NaN\n",
       "B2  7.0 NaN  8.0 NaN  9.0 NaN  2.0  1.0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "view.columns = new_index\n",
    "view"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Un pivot aggrégé\n",
    "\n",
    "La fonction pivot suppose que la transformation conserve chaque valeur sans les aggréger ce qui permet de restaurer les données sous leurs forme initiale. Mais ce n'est pas toujours ce qu'on souhaite faire."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X4</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C1</td>\n",
       "      <td>D1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C1</td>\n",
       "      <td>D2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C2</td>\n",
       "      <td>D1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C2</td>\n",
       "      <td>D2</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>A1</td>\n",
       "      <td>B2</td>\n",
       "      <td>C1</td>\n",
       "      <td>D1</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>A1</td>\n",
       "      <td>B2</td>\n",
       "      <td>C1</td>\n",
       "      <td>D2</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>A1</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "      <td>D1</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>A1</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "      <td>D2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "      <td>D2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   X1  X2  X3  X4  Y\n",
       "0  A1  B1  C1  D1  3\n",
       "1  A1  B1  C1  D2  4\n",
       "2  A1  B1  C2  D1  5\n",
       "3  A1  B1  C2  D2  6\n",
       "4  A1  B2  C1  D1  7\n",
       "5  A1  B2  C1  D2  8\n",
       "6  A1  B2  C2  D1  9\n",
       "7  A1  B2  C2  D2  2\n",
       "8  A2  B2  C2  D2  1"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Le pivot ne conserve pas les données.\n",
      "Index contains duplicate entries, cannot reshape\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    df.pivot(index=[\"X2\"], columns=[\"X3\", \"X4\"], values=\"Y\")\n",
    "except Exception as e:\n",
    "    print(\"Le pivot ne conserve pas les données.\")\n",
    "    print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On utlise alors [pivot_table](https://pandas.pydata.org/docs/reference/api/pandas.pivot_table.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>X3</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X4</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>B1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X3 C1    C2   \n",
       "X4 D1 D2 D1 D2\n",
       "X2            \n",
       "B1  1  1  1  1\n",
       "B2  1  1  1  2"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.pivot_table(index=[\"X2\"], columns=[\"X3\", \"X4\"], values=\"Y\", aggfunc=\"count\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>X3</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">C2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X4</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "      <th>D1</th>\n",
       "      <th>D2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>B1</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B2</th>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "X3 C1    C2   \n",
       "X4 D1 D2 D1 D2\n",
       "X2            \n",
       "B1  3  4  5  6\n",
       "B2  7  8  9  3"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.pivot_table(index=[\"X2\"], columns=[\"X3\", \"X4\"], values=\"Y\", aggfunc=\"sum\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## XArray\n",
    "\n",
    "Le package [XArray](https://docs.xarray.dev/en/stable/index.html) représente des cubes de données de façon plus efficace mais parfois moins intuitive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
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       "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
       "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
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       "  --xr-border-color: #1f1f1f;\n",
       "  --xr-disabled-color: #515151;\n",
       "  --xr-background-color: #111111;\n",
       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
       "}\n",
       "\n",
       ".xr-wrap {\n",
       "  display: block !important;\n",
       "  min-width: 300px;\n",
       "  max-width: 700px;\n",
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       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
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       "\n",
       ".xr-header {\n",
       "  padding-top: 6px;\n",
       "  padding-bottom: 6px;\n",
       "  margin-bottom: 4px;\n",
       "  border-bottom: solid 1px var(--xr-border-color);\n",
       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-obj-type {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-sections {\n",
       "  padding-left: 0 !important;\n",
       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 0 20px 0 20px;\n",
       "}\n",
       "\n",
       ".xr-section-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-section-item input {\n",
       "  display: inline-block;\n",
       "  opacity: 0;\n",
       "  height: 0;\n",
       "}\n",
       "\n",
       ".xr-section-item input + label {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label {\n",
       "  cursor: pointer;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-item input:focus + label {\n",
       "  border: 2px solid var(--xr-font-color0);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
       "}\n",
       "\n",
       ".xr-section-summary {\n",
       "  grid-column: 1;\n",
       "  color: var(--xr-font-color2);\n",
       "  font-weight: 500;\n",
       "}\n",
       "\n",
       ".xr-section-summary > span {\n",
       "  display: inline-block;\n",
       "  padding-left: 0.5em;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in + label:before {\n",
       "  display: inline-block;\n",
       "  content: \"►\";\n",
       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: \"▼\";\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: \"(\";\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: \")\";\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: \",\";\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-index-preview {\n",
       "  grid-column: 2 / 5;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data,\n",
       ".xr-index-data-in:checked ~ .xr-index-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt; Size: 192B\n",
       "Dimensions:  (X1: 2, X2: 2, X3: 2, X4: 2)\n",
       "Coordinates:\n",
       "  * X1       (X1) object 16B &#x27;A1&#x27; &#x27;A2&#x27;\n",
       "  * X2       (X2) object 16B &#x27;B1&#x27; &#x27;B2&#x27;\n",
       "  * X3       (X3) object 16B &#x27;C1&#x27; &#x27;C2&#x27;\n",
       "  * X4       (X4) object 16B &#x27;D1&#x27; &#x27;D2&#x27;\n",
       "Data variables:\n",
       "    Y        (X1, X2, X3, X4) float64 128B 3.0 4.0 5.0 6.0 ... nan nan nan 1.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-7b69a124-0024-4700-b534-d08f738f4f63' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-7b69a124-0024-4700-b534-d08f738f4f63' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>X1</span>: 2</li><li><span class='xr-has-index'>X2</span>: 2</li><li><span class='xr-has-index'>X3</span>: 2</li><li><span class='xr-has-index'>X4</span>: 2</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-39febba1-cd35-4c9b-82c8-911849a14b71' class='xr-section-summary-in' type='checkbox'  checked><label for='section-39febba1-cd35-4c9b-82c8-911849a14b71' class='xr-section-summary' >Coordinates: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>X1</span></div><div class='xr-var-dims'>(X1)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;A1&#x27; &#x27;A2&#x27;</div><input id='attrs-c045f136-fa98-4a44-90d0-dada520f9e21' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c045f136-fa98-4a44-90d0-dada520f9e21' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c4657ea3-1298-4c90-9465-0740a1b468b6' class='xr-var-data-in' type='checkbox'><label for='data-c4657ea3-1298-4c90-9465-0740a1b468b6' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;A1&#x27;, &#x27;A2&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>X2</span></div><div class='xr-var-dims'>(X2)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;B1&#x27; &#x27;B2&#x27;</div><input id='attrs-8922e367-3a95-49cb-a888-b4b8c0ae61c0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8922e367-3a95-49cb-a888-b4b8c0ae61c0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-dbe98d7f-ad89-4482-ae1e-fa126e623bbd' class='xr-var-data-in' type='checkbox'><label for='data-dbe98d7f-ad89-4482-ae1e-fa126e623bbd' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;B1&#x27;, &#x27;B2&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>X3</span></div><div class='xr-var-dims'>(X3)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;C1&#x27; &#x27;C2&#x27;</div><input id='attrs-3d466257-aaf3-4afb-bf6e-ff9065804315' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3d466257-aaf3-4afb-bf6e-ff9065804315' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-01efd02d-d9f6-4bc5-9c6f-30a3a7565b03' class='xr-var-data-in' type='checkbox'><label for='data-01efd02d-d9f6-4bc5-9c6f-30a3a7565b03' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;C1&#x27;, &#x27;C2&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>X4</span></div><div class='xr-var-dims'>(X4)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;D1&#x27; &#x27;D2&#x27;</div><input id='attrs-eb69a6f3-caa1-4ef3-a9b4-4f171870c70d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-eb69a6f3-caa1-4ef3-a9b4-4f171870c70d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bf5576d7-971a-425f-9866-d65766416156' class='xr-var-data-in' type='checkbox'><label for='data-bf5576d7-971a-425f-9866-d65766416156' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;D1&#x27;, &#x27;D2&#x27;], dtype=object)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-d098a25b-50de-4c70-a89a-503495571b58' class='xr-section-summary-in' type='checkbox'  checked><label for='section-d098a25b-50de-4c70-a89a-503495571b58' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>Y</span></div><div class='xr-var-dims'>(X1, X2, X3, X4)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.0 4.0 5.0 6.0 ... nan nan nan 1.0</div><input id='attrs-c5811283-aa18-43e4-be85-946e4ea6a27a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c5811283-aa18-43e4-be85-946e4ea6a27a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-98375a8d-dbee-42a2-bddd-fed7dff77917' class='xr-var-data-in' type='checkbox'><label for='data-98375a8d-dbee-42a2-bddd-fed7dff77917' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[[ 3.,  4.],\n",
       "         [ 5.,  6.]],\n",
       "\n",
       "        [[ 7.,  8.],\n",
       "         [ 9.,  2.]]],\n",
       "\n",
       "\n",
       "       [[[nan, nan],\n",
       "         [nan, nan]],\n",
       "\n",
       "        [[nan, nan],\n",
       "         [nan,  1.]]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-64c3e149-64dd-4df2-9c72-f9af3d67bb21' class='xr-section-summary-in' type='checkbox'  ><label for='section-64c3e149-64dd-4df2-9c72-f9af3d67bb21' class='xr-section-summary' >Indexes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>X1</div></div><div class='xr-index-preview'>PandasIndex</div><input type='checkbox' disabled/><label></label><input id='index-3881890b-1aea-402f-af80-559b01b579f2' class='xr-index-data-in' type='checkbox'/><label for='index-3881890b-1aea-402f-af80-559b01b579f2' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;A1&#x27;, &#x27;A2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;X1&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>X2</div></div><div class='xr-index-preview'>PandasIndex</div><input type='checkbox' disabled/><label></label><input id='index-aea61e45-650a-44fb-b89f-6c9585ec7204' class='xr-index-data-in' type='checkbox'/><label for='index-aea61e45-650a-44fb-b89f-6c9585ec7204' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;B1&#x27;, &#x27;B2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;X2&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>X3</div></div><div class='xr-index-preview'>PandasIndex</div><input type='checkbox' disabled/><label></label><input id='index-603fd9d1-5d4a-4b65-ae39-7940d6f91067' class='xr-index-data-in' type='checkbox'/><label for='index-603fd9d1-5d4a-4b65-ae39-7940d6f91067' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;C1&#x27;, &#x27;C2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;X3&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>X4</div></div><div class='xr-index-preview'>PandasIndex</div><input type='checkbox' disabled/><label></label><input id='index-8ae45242-e385-4692-935b-f80e8de84983' class='xr-index-data-in' type='checkbox'/><label for='index-8ae45242-e385-4692-935b-f80e8de84983' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;D1&#x27;, &#x27;D2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;X4&#x27;))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-54b0e2c6-a036-4489-8d60-dc43b1cf0f4e' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-54b0e2c6-a036-4489-8d60-dc43b1cf0f4e' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset> Size: 192B\n",
       "Dimensions:  (X1: 2, X2: 2, X3: 2, X4: 2)\n",
       "Coordinates:\n",
       "  * X1       (X1) object 16B 'A1' 'A2'\n",
       "  * X2       (X2) object 16B 'B1' 'B2'\n",
       "  * X3       (X3) object 16B 'C1' 'C2'\n",
       "  * X4       (X4) object 16B 'D1' 'D2'\n",
       "Data variables:\n",
       "    Y        (X1, X2, X3, X4) float64 128B 3.0 4.0 5.0 6.0 ... nan nan nan 1.0"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import xarray as xr\n",
    "\n",
    "cube = xr.Dataset.from_dataframe(df.set_index([\"X1\", \"X2\", \"X3\", \"X4\"]))\n",
    "cube"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modifier une valeur existante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
       "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
       "</symbol>\n",
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       "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
       "</symbol>\n",
       "</defs>\n",
       "</svg>\n",
       "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
       " *\n",
       " */\n",
       "\n",
       ":root {\n",
       "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
       "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
       "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
       "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "}\n",
       "\n",
       "html[theme=\"dark\"],\n",
       "html[data-theme=\"dark\"],\n",
       "body[data-theme=\"dark\"],\n",
       "body.vscode-dark {\n",
       "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
       "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
       "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
       "  --xr-border-color: #1f1f1f;\n",
       "  --xr-disabled-color: #515151;\n",
       "  --xr-background-color: #111111;\n",
       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
       "}\n",
       "\n",
       ".xr-wrap {\n",
       "  display: block !important;\n",
       "  min-width: 300px;\n",
       "  max-width: 700px;\n",
       "}\n",
       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-header {\n",
       "  padding-top: 6px;\n",
       "  padding-bottom: 6px;\n",
       "  margin-bottom: 4px;\n",
       "  border-bottom: solid 1px var(--xr-border-color);\n",
       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-obj-type {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-sections {\n",
       "  padding-left: 0 !important;\n",
       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 0 20px 0 20px;\n",
       "}\n",
       "\n",
       ".xr-section-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-section-item input {\n",
       "  display: inline-block;\n",
       "  opacity: 0;\n",
       "  height: 0;\n",
       "}\n",
       "\n",
       ".xr-section-item input + label {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label {\n",
       "  cursor: pointer;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-item input:focus + label {\n",
       "  border: 2px solid var(--xr-font-color0);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
       "}\n",
       "\n",
       ".xr-section-summary {\n",
       "  grid-column: 1;\n",
       "  color: var(--xr-font-color2);\n",
       "  font-weight: 500;\n",
       "}\n",
       "\n",
       ".xr-section-summary > span {\n",
       "  display: inline-block;\n",
       "  padding-left: 0.5em;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in + label:before {\n",
       "  display: inline-block;\n",
       "  content: \"►\";\n",
       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: \"▼\";\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: \"(\";\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: \")\";\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: \",\";\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
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       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
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       "\n",
       ".xr-var-name {\n",
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       "\n",
       ".xr-var-dims {\n",
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       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
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       "\n",
       ".xr-var-preview {\n",
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       "\n",
       ".xr-index-preview {\n",
       "  grid-column: 2 / 5;\n",
       "  color: var(--xr-font-color2);\n",
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       "\n",
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       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
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       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
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       "  width: auto;\n",
       "  z-index: 1;\n",
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       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
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       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data,\n",
       ".xr-index-data-in:checked ~ .xr-index-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt; Size: 192B\n",
       "Dimensions:  (X1: 2, X2: 2, X3: 2, X4: 2)\n",
       "Coordinates:\n",
       "  * X1       (X1) object 16B &#x27;A1&#x27; &#x27;A2&#x27;\n",
       "  * X2       (X2) object 16B &#x27;B1&#x27; &#x27;B2&#x27;\n",
       "  * X3       (X3) object 16B &#x27;C1&#x27; &#x27;C2&#x27;\n",
       "  * X4       (X4) object 16B &#x27;D1&#x27; &#x27;D2&#x27;\n",
       "Data variables:\n",
       "    Y        (X1, X2, X3, X4) float64 128B 3.0 4.0 5.0 6.0 ... nan nan nan 1.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-cc371cff-60f0-4cfe-a094-978d46b62650' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-cc371cff-60f0-4cfe-a094-978d46b62650' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>X1</span>: 2</li><li><span class='xr-has-index'>X2</span>: 2</li><li><span class='xr-has-index'>X3</span>: 2</li><li><span class='xr-has-index'>X4</span>: 2</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-24d14a27-e8f5-4f30-a5aa-108208575b92' class='xr-section-summary-in' type='checkbox'  checked><label for='section-24d14a27-e8f5-4f30-a5aa-108208575b92' class='xr-section-summary' >Coordinates: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>X1</span></div><div class='xr-var-dims'>(X1)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;A1&#x27; &#x27;A2&#x27;</div><input id='attrs-1c949d47-9880-495d-9de7-5ec9b5c3b014' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1c949d47-9880-495d-9de7-5ec9b5c3b014' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-de70013b-bcee-4de7-bb23-b19506710e8d' class='xr-var-data-in' type='checkbox'><label for='data-de70013b-bcee-4de7-bb23-b19506710e8d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;A1&#x27;, &#x27;A2&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>X2</span></div><div class='xr-var-dims'>(X2)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;B1&#x27; &#x27;B2&#x27;</div><input id='attrs-8f7aa74a-5c71-445e-a354-ac4acbb6f5ee' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8f7aa74a-5c71-445e-a354-ac4acbb6f5ee' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ad119a2f-9d4c-4be5-8f90-933037630148' class='xr-var-data-in' type='checkbox'><label for='data-ad119a2f-9d4c-4be5-8f90-933037630148' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;B1&#x27;, &#x27;B2&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>X3</span></div><div class='xr-var-dims'>(X3)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;C1&#x27; &#x27;C2&#x27;</div><input id='attrs-b2f9426a-a202-4c34-a40b-cc2a8bb9a345' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b2f9426a-a202-4c34-a40b-cc2a8bb9a345' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4d4fe1d1-e0f1-43fa-b47a-8f0162fc17d0' class='xr-var-data-in' type='checkbox'><label for='data-4d4fe1d1-e0f1-43fa-b47a-8f0162fc17d0' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;C1&#x27;, &#x27;C2&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>X4</span></div><div class='xr-var-dims'>(X4)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;D1&#x27; &#x27;D2&#x27;</div><input id='attrs-a95e7bb0-5b0c-47ac-a235-52309bb285dd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a95e7bb0-5b0c-47ac-a235-52309bb285dd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bf0a2792-60f6-4e89-a0bc-f4800ae35a05' class='xr-var-data-in' type='checkbox'><label for='data-bf0a2792-60f6-4e89-a0bc-f4800ae35a05' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;D1&#x27;, &#x27;D2&#x27;], dtype=object)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-dcf00f4a-05e9-4d64-b4cf-84471d778639' class='xr-section-summary-in' type='checkbox'  checked><label for='section-dcf00f4a-05e9-4d64-b4cf-84471d778639' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>Y</span></div><div class='xr-var-dims'>(X1, X2, X3, X4)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.0 4.0 5.0 6.0 ... nan nan nan 1.0</div><input id='attrs-845eb377-ca0b-416d-ad6d-f2683961f358' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-845eb377-ca0b-416d-ad6d-f2683961f358' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-688a8daa-93af-4e29-862a-0c3429189db8' class='xr-var-data-in' type='checkbox'><label for='data-688a8daa-93af-4e29-862a-0c3429189db8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[[  3.,   4.],\n",
       "         [  5.,   6.]],\n",
       "\n",
       "        [[  7.,   8.],\n",
       "         [100.,   2.]]],\n",
       "\n",
       "\n",
       "       [[[ nan,  nan],\n",
       "         [ nan,  nan]],\n",
       "\n",
       "        [[ nan,  nan],\n",
       "         [ nan,   1.]]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-e86c966c-f486-483e-8fe5-2bd0f95de2ab' class='xr-section-summary-in' type='checkbox'  ><label for='section-e86c966c-f486-483e-8fe5-2bd0f95de2ab' class='xr-section-summary' >Indexes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>X1</div></div><div class='xr-index-preview'>PandasIndex</div><input type='checkbox' disabled/><label></label><input id='index-281cffbe-47cd-4ebd-a83b-d65056f0aca3' class='xr-index-data-in' type='checkbox'/><label for='index-281cffbe-47cd-4ebd-a83b-d65056f0aca3' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;A1&#x27;, &#x27;A2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;X1&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>X2</div></div><div class='xr-index-preview'>PandasIndex</div><input type='checkbox' disabled/><label></label><input id='index-a18b71b7-3ec0-4bf2-826f-3e464ca5f6b8' class='xr-index-data-in' type='checkbox'/><label for='index-a18b71b7-3ec0-4bf2-826f-3e464ca5f6b8' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;B1&#x27;, &#x27;B2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;X2&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>X3</div></div><div class='xr-index-preview'>PandasIndex</div><input type='checkbox' disabled/><label></label><input id='index-835e215f-6f31-41ee-8d5a-48b25574fc46' class='xr-index-data-in' type='checkbox'/><label for='index-835e215f-6f31-41ee-8d5a-48b25574fc46' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;C1&#x27;, &#x27;C2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;X3&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>X4</div></div><div class='xr-index-preview'>PandasIndex</div><input type='checkbox' disabled/><label></label><input id='index-679b61f7-3900-48a2-b9b6-db6bb0cadc3f' class='xr-index-data-in' type='checkbox'/><label for='index-679b61f7-3900-48a2-b9b6-db6bb0cadc3f' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;D1&#x27;, &#x27;D2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;X4&#x27;))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-aa04ec41-a0af-47d9-85d0-7e16f6c828be' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-aa04ec41-a0af-47d9-85d0-7e16f6c828be' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset> Size: 192B\n",
       "Dimensions:  (X1: 2, X2: 2, X3: 2, X4: 2)\n",
       "Coordinates:\n",
       "  * X1       (X1) object 16B 'A1' 'A2'\n",
       "  * X2       (X2) object 16B 'B1' 'B2'\n",
       "  * X3       (X3) object 16B 'C1' 'C2'\n",
       "  * X4       (X4) object 16B 'D1' 'D2'\n",
       "Data variables:\n",
       "    Y        (X1, X2, X3, X4) float64 128B 3.0 4.0 5.0 6.0 ... nan nan nan 1.0"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cube[\"Y\"].loc[{\"X1\": \"A1\", \"X2\": \"B2\", \"X3\": \"C2\", \"X4\": \"D1\"}] = 100\n",
    "cube"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
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       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-index-preview {\n",
       "  grid-column: 2 / 5;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data,\n",
       ".xr-index-data-in:checked ~ .xr-index-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt; Size: 64B\n",
       "Dimensions:  (X1: 2, X4: 2)\n",
       "Coordinates:\n",
       "  * X1       (X1) object 16B &#x27;A1&#x27; &#x27;A2&#x27;\n",
       "  * X4       (X4) object 16B &#x27;D1&#x27; &#x27;D2&#x27;\n",
       "Data variables:\n",
       "    Y        (X1, X4) float64 32B 28.75 5.0 nan 1.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-dd7156df-c073-4498-a733-d1e42adfceee' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-dd7156df-c073-4498-a733-d1e42adfceee' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>X1</span>: 2</li><li><span class='xr-has-index'>X4</span>: 2</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-8a7118f8-eafa-473a-a4b3-5c7b5f923e91' class='xr-section-summary-in' type='checkbox'  checked><label for='section-8a7118f8-eafa-473a-a4b3-5c7b5f923e91' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>X1</span></div><div class='xr-var-dims'>(X1)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;A1&#x27; &#x27;A2&#x27;</div><input id='attrs-7bf6acdf-ad12-475c-87a4-4308d01faff9' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7bf6acdf-ad12-475c-87a4-4308d01faff9' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-9f334924-150c-42d7-9ccf-cbf0e6a157fe' class='xr-var-data-in' type='checkbox'><label for='data-9f334924-150c-42d7-9ccf-cbf0e6a157fe' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;A1&#x27;, &#x27;A2&#x27;], dtype=object)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>X4</span></div><div class='xr-var-dims'>(X4)</div><div class='xr-var-dtype'>object</div><div class='xr-var-preview xr-preview'>&#x27;D1&#x27; &#x27;D2&#x27;</div><input id='attrs-70e008dc-4099-4dc2-967c-d953a53c1d81' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-70e008dc-4099-4dc2-967c-d953a53c1d81' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4a8770e7-4848-45e3-93f3-fe478d6fea1c' class='xr-var-data-in' type='checkbox'><label for='data-4a8770e7-4848-45e3-93f3-fe478d6fea1c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;D1&#x27;, &#x27;D2&#x27;], dtype=object)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f68bdf46-f9eb-440c-8816-1fdb0040e19a' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f68bdf46-f9eb-440c-8816-1fdb0040e19a' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>Y</span></div><div class='xr-var-dims'>(X1, X4)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>28.75 5.0 nan 1.0</div><input id='attrs-862254a2-51b5-4f1f-b4d8-0b4018e2241a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-862254a2-51b5-4f1f-b4d8-0b4018e2241a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-090d5ab5-40af-4a13-92c7-bc8d36b4e635' class='xr-var-data-in' type='checkbox'><label for='data-090d5ab5-40af-4a13-92c7-bc8d36b4e635' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[28.75,  5.  ],\n",
       "       [  nan,  1.  ]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c0b6a30e-9f24-456f-8368-111485be222b' class='xr-section-summary-in' type='checkbox'  ><label for='section-c0b6a30e-9f24-456f-8368-111485be222b' class='xr-section-summary' >Indexes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>X1</div></div><div class='xr-index-preview'>PandasIndex</div><input type='checkbox' disabled/><label></label><input id='index-55f2c3fd-7671-4b17-b4f2-90b1b309c14d' class='xr-index-data-in' type='checkbox'/><label for='index-55f2c3fd-7671-4b17-b4f2-90b1b309c14d' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;A1&#x27;, &#x27;A2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;X1&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>X4</div></div><div class='xr-index-preview'>PandasIndex</div><input type='checkbox' disabled/><label></label><input id='index-a5ebd02e-b956-44d9-bc31-ea86c4a878c7' class='xr-index-data-in' type='checkbox'/><label for='index-a5ebd02e-b956-44d9-bc31-ea86c4a878c7' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([&#x27;D1&#x27;, &#x27;D2&#x27;], dtype=&#x27;object&#x27;, name=&#x27;X4&#x27;))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-dfaa7e16-3919-42c8-8aff-1bb2ac26ce9e' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-dfaa7e16-3919-42c8-8aff-1bb2ac26ce9e' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset> Size: 64B\n",
       "Dimensions:  (X1: 2, X4: 2)\n",
       "Coordinates:\n",
       "  * X1       (X1) object 16B 'A1' 'A2'\n",
       "  * X4       (X4) object 16B 'D1' 'D2'\n",
       "Data variables:\n",
       "    Y        (X1, X4) float64 32B 28.75 5.0 nan 1.0"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cube.mean(dim=(\"X2\", \"X3\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "                 Y\n",
       "X1 X2 X3 X4       \n",
       "A1 B1 C1 D1    3.0\n",
       "         D2    4.0\n",
       "      C2 D1    5.0\n",
       "         D2    6.0\n",
       "   B2 C1 D1    7.0\n",
       "         D2    8.0\n",
       "      C2 D1  100.0\n",
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       "A2 B1 C1 D1    NaN\n",
       "         D2    NaN\n",
       "      C2 D1    NaN\n",
       "         D2    NaN\n",
       "   B2 C1 D1    NaN\n",
       "         D2    NaN\n",
       "      C2 D1    NaN\n",
       "         D2    1.0"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cube.to_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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