Librairies.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction au librairies Phython \n",
    "\n",
    "Une des grandes forces du langage Python réside dans le nombre important de bibliothèques logicielles externes disponibles. Une bibliothèque est un ensemble de fonctions. Celles-ci sont regroupées et mises à disposition afin de pouvoir être utilisées sans avoir à les réécrire. Celles-ci permettent de faire : du calcul numérique, du graphisme, de la programmation internet ou réseau, du formatage de texte, de la génération de documents...\n",
    "\n",
    "La distribution standard de Python contient un certain nombre de bibliothèques qui ont été considérées comme suffisamment génériques pour intéresser la majorité des utilisateurs. Dans ce notebook vous pouvez trouver les bases des librairies fondamentales en python pour la Data Science, c'est à dire pandas, numpy, matplotlib et sklearn. Ce notebook a un objectif double, d'acquérir la syntaxe de bases de ces librairies mais aussi un aide mémoire synthétique. \n",
    "\n",
    "## Pandas \n",
    "Pandas est une librairie python qui permet de manipuler facilement des données à analyser, elle permet notamment de :\n",
    "manipuler des tableaux de données avec des étiquettes de variables (colonnes) et d'individus (lignes). Ces tableaux sont appelés DataFrames, similaires aux dataframes sous R. On peut facilement lire et écrire ces dataframes à partir ou vers un fichier tabulé. Il est également assez simple de tracer des graphes à partir de ces DataFrames grâce à la librairies matplotlib.\n",
    "\n",
    "La première chose à faire est d'importer les librairies. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib as mp "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Découvertes des objets pandas \n",
    "\n",
    "### Les series \n",
    "Les series sont des vecteurs de valeurs d'une variable, soit un tableau à une dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0    0.25\n",
      "1    0.50\n",
      "2    0.75\n",
      "3    1.00\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "data = pd.Series([0.25, 0.5, 0.75, 1.0]) \n",
    "print(data) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il est possible d'effectuer plusieurs opération sur les séries tel que : \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    5.0\n",
       "b    NaN\n",
       "c    9.0\n",
       "d    NaN\n",
       "dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1 = pd.Series([1, 2, 3], ['a', 'b', 'c'])\n",
    "s2 = pd.Series([4, 5, 6], ['a', 'd', 'c'])\n",
    "s1 + s2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme on peut le voir les séries sont des objets structuré tel que : (WIP) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.25,  0.5 ,  0.75,  1.  ])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Les dataframes \n",
    "\n",
    "Un dataframe se comporte comme un dictionnaire dont les clefs sont les noms des colonnes et les valeurs sont des séries. On peut les créer à partir d'un array numpy (pas très pratique car le type des données est le même pour toutes les colonnes, ici float64)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      A     B    C     D\n",
      "a1  1.1   2.0  3.3   4.0\n",
      "a2  2.7  10.0  5.4   7.0\n",
      "a3  5.3   9.0  1.5  15.0\n"
     ]
    }
   ],
   "source": [
    "ar = np.array([[1.1, 2, 3.3, 4], [2.7, 10, 5.4, 7], [5.3, 9, 1.5, 15]])\n",
    "df = pd.DataFrame(ar, index = ['a1', 'a2', 'a3'], columns = ['A', 'B', 'C', 'D'])\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dimension d'un dataframe :\n",
    "- df.shape : renvoie la dimension du dataframe sous forme (nombre de lignes, nombre de colonnes)\n",
    "- on peut aussi faire len(df) pour avoir le nombre de lignes (ou également len(df.index)).\n",
    "- on peut aussi faire len(df.columns) pour avoir le nombre de colonnes.\n",
    "- df.memory_usage() : donne une série avec la place occupeée par chaque colonne (sum(df.memory_usage()) donne la mémoire totale occupée).\n",
    "- on peut aussi créer le dataframe avec un dictionnaire :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({'A': [1.1, 2.7, 5.3], 'B': [2, 10, 9], 'C': [3.3, 5.4, 1.5], 'D': [4, 7, 15]},\n",
    "                      index = ['a1', 'a2', 'a3'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut aussi réindexer un dataframe pour changer l'ordre des lignes et/ou des colonnes, ou n'en récupérer que certaines  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A    float64\n",
      "B      int64\n",
      "C    float64\n",
      "D      int64\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "df.reindex(columns = ['C', 'B', 'A'], index = ['a2', 'a3'])\n",
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut notamment donner un dictionnaire dont les clefs seront les index plutôt que les colonnes :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>1.1</td>\n",
       "      <td>2.7</td>\n",
       "      <td>5.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>2.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>3.3</td>\n",
       "      <td>5.4</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>4.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>15.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0     1     2\n",
       "A  1.1   2.7   5.3\n",
       "B  2.0  10.0   9.0\n",
       "C  3.3   5.4   1.5\n",
       "D  4.0   7.0  15.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame.from_dict({'A': [1.1, 2.7, 5.3], 'B': [2, 10, 9],\n",
    "    'C': [3.3, 5.4, 1.5], 'D': [4, 7, 15]}, orient = 'index')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Informations \n",
    "On peut renvoyer un dataframe donnant des statistiques sur les valeurs (nombres de valeurs, moyenne, écart-type, ...), mais uniquement sur les colonnes numériques (faire df.describe(include = 'all') pour avoir toutes les colonnes) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.033333</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>3.400000</td>\n",
       "      <td>8.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.119748</td>\n",
       "      <td>4.358899</td>\n",
       "      <td>1.951922</td>\n",
       "      <td>5.686241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.100000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>4.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.900000</td>\n",
       "      <td>5.500000</td>\n",
       "      <td>2.400000</td>\n",
       "      <td>5.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.700000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>3.300000</td>\n",
       "      <td>7.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.000000</td>\n",
       "      <td>9.500000</td>\n",
       "      <td>4.350000</td>\n",
       "      <td>11.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>5.300000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>5.400000</td>\n",
       "      <td>15.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              A          B         C          D\n",
       "count  3.000000   3.000000  3.000000   3.000000\n",
       "mean   3.033333   7.000000  3.400000   8.666667\n",
       "std    2.119748   4.358899  1.951922   5.686241\n",
       "min    1.100000   2.000000  1.500000   4.000000\n",
       "25%    1.900000   5.500000  2.400000   5.500000\n",
       "50%    2.700000   9.000000  3.300000   7.000000\n",
       "75%    4.000000   9.500000  4.350000  11.000000\n",
       "max    5.300000  10.000000  5.400000  15.000000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Indexation\n",
    "Quand on boucle sur un dataframe, on boucle sur les noms des colonnes : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A\n",
      "B\n",
      "C\n",
      "D\n"
     ]
    }
   ],
   "source": [
    "for x in df:\n",
    "  print(x) # imprime le nom de la colonne"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accèder à une colonne :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a1    1.1\n",
       "a2    2.7\n",
       "a3    5.3\n",
       "Name: A, dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['A']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Renvoyer la Series correspondant à la ligne d'index a2 :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A     2.7\n",
       "B    10.0\n",
       "C     5.4\n",
       "D     7.0\n",
       "Name: a2, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc['a2']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Renvoyer un dataframe avec un sous-ensemble des lignes et des colonnes :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a2</th>\n",
       "      <td>2.7</td>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a3</th>\n",
       "      <td>5.3</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "      A    C\n",
       "a2  2.7  5.4\n",
       "a3  5.3  1.5"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc[['a2', 'a3'], ['A', 'C']] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut avoir les opérations suivantes : \n",
    "- df.loc[:,['A', 'C']] : toutes les lignes et seulement les colonnes A et B.\n",
    "- df.loc['a2', 'C'] : accès à la valeur de la ligne a2 et de la colonne C : 5.4.\n",
    "- df.at['a2', 'C'] : autre façon recommandée d'accéder à la valeur de la ligne a2 et de la colonne C : 5.4.\n",
    "- on peut aussi faire une affectation pour changer la valeur : df.at['a2', 'C'] = 7.\n",
    "- on peut aussi utiliser des indices numériques : df.at[0, 1] (ou même un mélange des deux).\n",
    "\n",
    "Pour accèder à un sous-ensemble du dataframe avec les numéros des lignes et colonnes :\n",
    "- df.iloc[1] : renvoie la deuxième ligne.\n",
    "- df.iloc[1:3,[0, 2]] : renvoie le dataframe avec les lignes 1 à 3 exclue, et les colonnes numéros 0 et 2.\n",
    "- df.iloc[:,2:4] : renvoie toutes les lignes et les colonnes 2 à 4 exclue.\n",
    "- df.iloc[1,2] : renvoie la valeur à la ligne 2 et la colonne 3.\n",
    "- df.iat[1,2] : renvoie la valeur à la ligne 2 et la colonne 3, mais c'est la façon recommandée d'accéder aux valeurs.\n",
    "- on peut aussi faire une affectation pour changer la valeur : df.iat[1, 2] = 7.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accèder à certaines colonnes et certaines lignes par numéros : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a1</th>\n",
       "      <td>1.1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a2</th>\n",
       "      <td>2.7</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      A  D\n",
       "a1  1.1  4\n",
       "a2  2.7  7"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc[:,['A', 'D']].iloc[0:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utiliser les conditions et renvoyer un dataframe avec seulement les lignes où la condition est vérifiée :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a2</th>\n",
       "      <td>2.7</td>\n",
       "      <td>10</td>\n",
       "      <td>5.4</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>a3</th>\n",
       "      <td>5.3</td>\n",
       "      <td>9</td>\n",
       "      <td>1.5</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      A   B    C   D\n",
       "a2  2.7  10  5.4   7\n",
       "a3  5.3   9  1.5  15"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[df['A'] > 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utiliser des condition avec booléens (AND), | (OR), ^ (XOR), - (NOT) : df2 = df[(df['A'] > 2) & - (df['B'] < 6)] (attention : parenthèses nécessaires).\n",
    "\n",
    "- Autre exemple : df2 = df[(df['A'] == 'a') & numpy.logical_not(pandas.isnull(df['b']))]\n",
    "- df[df['A'].isin([5.3, 2.7])] : renvoie un dataframe avec seulement les lignes où la valeur de A est parmi celles listées.\n",
    "- pandas.isnull(df['A']) ou aussi df['A'].isnull() : pour tester les valeurs nulles d'une colonne d'un dataframe.\n",
    "- df.query('A > 2 and B < 10') : permet d'utiliser des condtions complexes (renvoie un nouveau dataframe, le dataframe d'origine est inchangé)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Réindexation d'un dataframe :\n",
    "- df.reset_index() : renvoie un dataframe réindexé de 0 à n - 1, mais conserve une colonne index avec les anciennes valeurs de l'index !\n",
    "- df.reset_index(drop = True) : renvoie un dataframe réindexé de 0 à n - 1\n",
    "- df.reset_index(drop = True, inplace = True) : modifie le dataframe directement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Multiindexation \n",
    "\n",
    "Ce sont des index à plusieurs niveaux, qu'on peut avoir aussi bien sur les lignes que sur les colonnes.\n",
    "Attribution d'un multi-index à 2 niveaux, ici aux colonnes :\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">a</th>\n",
       "      <th colspan=\"2\" halign=\"left\">b</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   a     b    \n",
       "   A  B  A   B\n",
       "0  0  3  6   9\n",
       "1  1  4  7  10\n",
       "2  2  5  8  11"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'A': [0, 1, 2], 'B': [3, 4, 5],\n",
    "  'C': [6, 7, 8], 'D': [9, 10, 11]})\n",
    "df.columns = pd.MultiIndex(levels = [['a', 'b'], ['A', 'B']],\n",
    "  labels = [[0, 0, 1, 1], [0, 1, 0, 1]])\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "on peut alors faire des group by : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   a   b\n",
       "0  3  15\n",
       "1  5  17\n",
       "2  7  19"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(axis = 1, level = 0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Modifications de Dataframes\n",
    "\n",
    "##### Renommage des colonnes d'un dataframe :\n",
    "- on ne peut pas renommer individuellement une colonne : df.columns[0] = 'a' ne marche pas ! (non mutable)\n",
    "- par contre, on peut renommer l'ensemble des colonnes : df.columns = ['a', 'B']\n",
    "- si on veut renommer une colonne en particulier, on peut toujours faire : myList = list(df.columns); myList[0] = 'a'; df.columns = myList\n",
    "\n",
    "##### Pour réordonner les colonnes d'un dataframe df avec les colonnes 'A', 'B', C' par exemple :\n",
    "- df.reindex(columns = ['B', 'C', 'A']) renvoie le dataframe réordonné par colonne.\n",
    "- df[['B', 'C', 'A']] renvoie aussi le dataframe réordonné.\n",
    "\n",
    "##### Rajout d'une colonne à un dataframe :\n",
    "- df['E'] = pandas.Series([1, 0, 1], index = ['a1', 'a2', 'a3']) : il faut donner une Series dont les noms des individus sont les mêmes que ceux du dataframe.\n",
    "- on peut donner la Series dans un ordre différent de celui du dataframe, les données sont rajoutées dans le bon ordre : df['E'] = pandas.Series([0, 1, 1], index = ['a2', 'a1', 'a3']).\n",
    "- on peut rajouter une valeur constante sur toutes les lignes : df['E'] = 0\n",
    "- par défaut, les colonnes rajoutées le sont à la fin, mais on peut la rajouter à un autre endroit : par exemple, pour rajouter la colonne 'E' au début : df.insert(0, 'E', [1, 2, 3]).\n",
    "- df.assign(E = df['A'] + df['B'], F = 2 * df['A']) : renvoie une copie du dataframe avec deux nouvelles colonnes E et F (sans modifier le dataframe original).\n",
    "- on peut enchaîner les assign : df2 = df.assign(E = df['A'] + df['B']).assign(F = 2 * df['E'])\n",
    "\n",
    "##### Destruction de colonnes d'un dataframe :\n",
    "- del df['A'] : permet de détruire la colonne A.\n",
    "- df.drop(['A', 'C'], axis = 1, inplace = True) : permet de détruire plusieurs colonnes en même temps.\n",
    "\n",
    "##### Valeurs non définies :\n",
    "on utilise ici le dataframe : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     A     B  C\n",
       "0  1.0   NaN  7\n",
       "1  NaN  20.0  6\n",
       "2  3.0  30.0  5"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'A': [1, np.nan, 3], 'B': [np.nan, 20, 30], 'C': [7, 6, 5]})\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Gestion des NaN :\n",
    "\n",
    "On peut par exemple renvoyer un dataframe avec les lignes contenant au moins une valeur NaN supprimée (how = 'all' : supprime les lignes où toutes les valeurs sont NaN)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     A     B  C\n",
       "2  3.0  30.0  5"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dropna(how = 'any') \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut aussi effectuer les opérations suivantes : \n",
    "- df.dropna(axis = 1, how = 'any') : supprime les colonnes ayant au moins un NaN plutôt que les lignes (le défaut est axis = 0).\n",
    "- df.dropna(inplace = True) : ne renvoie rien, mais fait la modification en place.\n",
    "- df.fillna(0) : renvoie un dataframe avec toutes les valeurs NaN remplacées par 0.\n",
    "- df.isnull() : renvoie un dataframe de booléens, avec True dans toutes les cellules non définies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Copie d'un dataframe :\n",
    "df2 = df.copy() : df2 est alors un dataframe indépendant.\n",
    "par contre, si on fait : df2 = df et que l'on modifie df2, df est également modifié (df et df2 pointent vers le même objet).\n",
    "\n",
    "##### Transposition : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
       "      <td>30.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>7.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0     1     2\n",
       "A  1.0   NaN   3.0\n",
       "B  NaN  20.0  30.0\n",
       "C  7.0   6.0   5.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Opérations sur les Dataframes\n",
    "\n",
    "Lors des opérations sur les dataframes, les noms des lignes et des colonnes sont automatiquement alignés :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1 = pd.DataFrame({'A': [1, 2], 'B': [3, 4]}, index = ['a', 'c'])\n",
    "df2 = pd.DataFrame({'A': [1, 2], 'C': [7, 5]}, index = ['b', 'c'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     A   B   C\n",
       "a  NaN NaN NaN\n",
       "b  NaN NaN NaN\n",
       "c  4.0 NaN NaN"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 + df2 #addition "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   a  b\n",
       "0  9  5\n",
       "1  5  5\n",
       "2  5  6"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#si \n",
    "df1 = pd.DataFrame({'a': [1, 3, 4], 'b': [5, 3, 1]}, columns = ['a', 'b']) \n",
    "df2 = pd.DataFrame({'b': [5, 2, 0], 'a': [1, 2, 8]}, columns = ['b', 'a'], index = [2, 1, 0])\n",
    "#alors \n",
    "df1 + df2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Les opérations possibles : \n",
    "- df1 + df2\n",
    "- 2 * df + 3\n",
    "- 1 / df : opération élément par élément\n",
    "- df ** 2 : carré de chaque élément\n",
    "\n",
    "Pour des dataframes booléens comme pandas.DataFrame({'A': [1, 0, 0], 'B': [0, 1, 1]}, dtype = bool) :\n",
    "- df : not\n",
    "- df1 & df2 : et\n",
    "- df1 | df2 : ou\n",
    "- df1 ^ df2 : ou exclusif\n",
    "\n",
    "Pour ajouter une colonne à toutes les autres :\n",
    "- df.add(df['A'], axis = 'rows') (ou df.add(df['A'], axis = 'rows'))\n",
    "- idem avec sub(), mul(), div() pour les autres opérations\n",
    "- pour l'ajout d'une ligne à toutes les autres : df.add(df.iloc[0], axis = 'columns') ou df.add(df.iloc[0], axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Concaténations et jointures de dataframes \n",
    "\n",
    "##### Juxtaposition de dataframes :\n",
    "\n",
    "Pour concaténer 2 dataframes (ou plus) ayant les mêmes colonnes les uns en dessous des autres :\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
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       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A  B\n",
       "0  3  1\n",
       "1  5  2\n",
       "2  6  4\n",
       "3  7  9"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame({'A': [3, 5], 'B': [1, 2]}, index = [0, 1])\n",
    "df2 = pd.DataFrame({'A': [6, 7], 'B': [4, 9]}, index = [2, 3])\n",
    "pd.concat([df1, df2])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si les dataframes n'ont pas les mêmes colonnes, par défaut, des NaN sont mis aux endroits non définis : \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A    B    C\n",
       "0  3  1.0  NaN\n",
       "1  5  2.0  NaN\n",
       "0  6  NaN  4.0\n",
       "1  7  NaN  9.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame({'A': [3, 5], 'B': [1, 2]}) \n",
    "df2 = pd.DataFrame({'A': [6, 7], 'C': [4, 9]})\n",
    "pd.concat([df1, df2]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "si les dataframes n'ont pas les mêmes colonnes et qu'on veut conserver seulement les colonnes communes, intersection (sans avoir de NaN) : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A\n",
       "0  3\n",
       "1  5\n",
       "0  6\n",
       "1  7"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([df1, df2], join = 'inner')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "on peut rajouter un niveau hierarchique d'index en attribuant une clef à chaque dataframe de départ : \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\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>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">a</th>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">b</th>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     A  B\n",
       "a 0  3  1\n",
       "  1  5  2\n",
       "b 0  6  4\n",
       "  1  7  9"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame({'A': [3, 5], 'B': [1, 2]}) \n",
    "df2 = pd.DataFrame({'A': [6, 7], 'B': [4, 9]}) \n",
    "pd.concat([df1, df2], keys = ['a', 'b']) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "on peut concaténér des dataframes et des séries, par exemple \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A  B  C\n",
       "0  3  1  7\n",
       "1  5  2  9"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame({'A': [3, 5], 'B': [1, 2]})\n",
    "s = pd.Series([7, 9], name = 'C')\n",
    "pd.concat([df1, s], axis = 1) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Les jointures \"le même principe qu'en sql\" :\n",
    "\n",
    "Pour les jointures simple (inner) qui par défaut utilise les noms des colonnes qui sont communs : \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A  B  C\n",
       "0  3  1  2\n",
       "1  5  2  9"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame({'A': [3, 5], 'B': [1, 2]})\n",
    "df2 = pd.DataFrame({'A': [5, 3, 7], 'C': [9, 2, 0]})\n",
    "pd.merge(df1, df2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Les jointure externe : \n",
    "\n",
    "les lignes qui n'ont pas la clef commune sont quand mêmes présentes (comme en sql) : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2.0</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A    B  C\n",
       "0  3  1.0  2\n",
       "1  5  2.0  9\n",
       "2  7  NaN  0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.merge(df1, df2, how = 'outer')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- on peut aussi faire une jointure externe gauche ou droite comme en sql avec how = 'left' ou how = 'right'\n",
    "- on peut indiquer explicitement les colonnes sur lequelles on veut faire la jointure si c'est une partie seulement des colonnes de même non : \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B_x</th>\n",
       "      <th>B_y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A  B_x  B_y\n",
       "0  3    1    2\n",
       "1  5    2    9"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame({'A': [3, 5], 'B': [1, 2]}) \n",
    "df2 = pd.DataFrame({'A': [5, 3, 7], 'B': [9, 2, 0]})\n",
    "pd.merge(df1, df2, on = ['A'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B_1</th>\n",
       "      <th>B_2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A  B_1  B_2\n",
       "0  3    1    2\n",
       "1  5    2    9"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#changer les extensions rajoutées sur les colonnes de même nom non incluses dans la jointure (par défaut _x et -y) : \n",
    "pd.merge(df1, df2, on = ['A'], suffixes = ('_1', '_2'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A  B  D  E\n",
       "0  3  1  7  0\n",
       "1  5  2  3  2"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#on peut aussi faire une jointure sur l'index : \n",
    "df1 = pd.DataFrame({'A': [3, 5], 'B': [1, 2]}, index = [0, 1]); \n",
    "df2 = pd.DataFrame({'D': [5, 3, 7], 'E': [9, 2, 0]}, index = [2, 1, 0])\n",
    "df1.join(df2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- la jointure sur les index peut aussi être faite avec pandas.merge(df1, df2, left_index = True, right_index = True) au lieu de df1.join(df2)\n",
    "- pd.merge(df1, df2, sort = False) : ne trie pas les colonnes de jointure dans l'ordre (le défaut est de les trier, mais cela a un impact sur la performance)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Si \n",
    "df = pd.DataFrame({'A': ['a', 'a', 'b', 'b', 'c', 'c'], 'T': ['yes', 'no', 'yes', 'no', 'yes', 'no'], 'V': [4, 2, 5, 2, 7, 3]})\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>T</th>\n",
       "      <th>no</th>\n",
       "      <th>yes</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "T  no  yes\n",
       "A         \n",
       "a   2    4\n",
       "b   2    5\n",
       "c   3    7"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Alors\n",
    "df.pivot(index = 'A', columns = 'T', values = 'V')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- si il y a des combinaisons qui manquent, on a un NaN à ces places-là.\n",
    "- si pour certaines combinaisons on a plusieurs lignes (plusieurs valeurs) : erreur (ValueError)\n",
    "\n",
    "##### Manipuler les colonnes d'un dataframe : \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0  A    5\n",
       "   B    8\n",
       "1  A    4\n",
       "   B    9\n",
       "2  A    1\n",
       "   B    6\n",
       "dtype: int64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Si \n",
    "df = pd.DataFrame({'A': [5, 4, 1], 'B': [8, 9, 6]}) \n",
    "#alors \n",
    "df.stack() #donne "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>person</th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>c</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  person  A  B\n",
       "0      a  5  8\n",
       "1      b  4  9\n",
       "2      c  1  6"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Si on part d'un dataframe \n",
    "df = pd.DataFrame({'person': ['a', 'a', 'b', 'b', 'c', 'c'], 'condition': ['A', 'B', 'A', 'B', 'A', 'B'], 'value': [5, 8, 4, 9, 1, 6]}) \n",
    "#et que l'on veut un dataframe avec comme colonnes person, A et B :\n",
    "df = df.pivot(index = 'person', columns = 'condition', values = 'value').reset_index()\n",
    "df.columns.name = None #(pour faire passer 'person' comme colonne normale et supprimer le nom de la colonne.\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "      <td>8</td>\n",
       "      <td>x</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>4</td>\n",
       "      <td>x</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>a</td>\n",
       "      <td>5</td>\n",
       "      <td>y</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>a</td>\n",
       "      <td>10</td>\n",
       "      <td>y</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>b</td>\n",
       "      <td>8</td>\n",
       "      <td>x</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A   B  C  D\n",
       "0  a   8  x  0\n",
       "1  b   4  x  1\n",
       "2  a   5  y  2\n",
       "3  a  10  y  3\n",
       "4  b   8  x  4"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'A': ['a', 'b', 'a', 'a', 'b'], 'B': [8, 4, 5, 10, 8], 'C': ['x', 'x', 'y', 'y', 'x'], 'D': [0, 1, 2, 3, 4]}) \n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pandas.core.groupby.DataFrameGroupBy object at 0x106f37ef0>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('A') #renvoie un objet de la classe pandas.core.groupby.DataFrameGroupBy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>B</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>23</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>12</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    B  D\n",
       "A       \n",
       "a  23  5\n",
       "b  12  5"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('A').sum() \n",
    "#groupe avec les valeurs de A et fait la somme, pour les colonnes pour lesquelles c'est possible\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\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>B</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <th>C</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">a</th>\n",
       "      <th>x</th>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>15</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <th>x</th>\n",
       "      <td>12</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      B  D\n",
       "A C       \n",
       "a x   8  0\n",
       "  y  15  5\n",
       "b x  12  5"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#on peut inclure plusieurs colonnes \n",
    "df.groupby(['A', 'C']).sum() \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>B</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>7.666667</td>\n",
       "      <td>1.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>6.000000</td>\n",
       "      <td>2.500000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          B         D\n",
       "A                    \n",
       "a  7.666667  1.666667\n",
       "b  6.000000  2.500000"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('A').mean() #calcule les moyennes pour chaque valeur de A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les fonctions classique de la statistique descriptive sont disponibles :\n",
    "- min(), max()\n",
    "- mean() : moyenne.\n",
    "- sum(), prod() : somme, produit\n",
    "- var(), std() : variance, standard deviation.\n",
    "- median() : médiane.\n",
    "- quantile(q = 0.2) : quantile\n",
    "- mad() : median absolute deviate.\n",
    "- nunique() : nombre de valeurs uniques.\n",
    "- rank() : rang dans le groupe.\n",
    "\n",
    "On peut aussi faire des groupby sur les index :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">a</th>\n",
       "      <th colspan=\"2\" halign=\"left\">b</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   a     b    \n",
       "   A  B  A   B\n",
       "0  0  3  6   9\n",
       "1  1  4  7  10\n",
       "2  2  5  8  11"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'A': [0, 1, 2], 'B': [3, 4, 5],\n",
    "  'C': [6, 7, 8], 'D': [9, 10, 11]})\n",
    "df.columns = pd.MultiIndex(levels = [['a', 'b'], ['A', 'B']],\n",
    "  labels = [[0, 0, 1, 1], [0, 1, 0, 1]])\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lecture et écriture de fichiers avec pandas\n",
    "\n",
    "#### Lecture d'un dataframe à partir d'un fichier :\n",
    "- df = pandas.read_csv('myFile.csv') : par défaut, suppose qu'il y a un header (header = 0) et qu'il n'y a pas de noms de colonne (index_col = None).\n",
    "- sep = '\\t' ou delimiter = '\\t' : indique que le séparateur est une tabulation plutôt qu'une virgule.\n",
    "- si tableau avec étiquettes de lignes et de colonnes : df = pandas.read_csv('myFile.csv', sep = '\\t', index_col = 0) (index_col est en fait le numéro de colonne contenant l'index).\n",
    "- si tableau avec étiquettes de colonnes seulement : df = pandas.read_csv('myFile.csv', sep = '\\t').\n",
    "- si tableau avec étiquettes de lignes seulement : df = pandas.read_csv('myFile.csv', sep = '\\t', header = None, index_col = 0).\n",
    "- si tableau sans étiquettes de lignes ni de colonnes : df = pandas.read_csv('myFile.csv', sep = '\\t', header = None).\n",
    "\n",
    "#### Ecriture d'un dataframe dans un fichier :\n",
    "- df.to_csv('myFile.csv', sep = '\\t') : écrit le dataframe avec une tabulation comme séparateur (le défaut est une virgule).\n",
    "- header = False : supprime le header des colonnes (défaut est de l'inclure).\n",
    "- index = False : supprime le nom des lignes (défaut est de l'inclure).\n",
    "- na_rep = '-' : imprime les valeurs NaN comme '-' (le défaut est la chaîne vide).\n",
    "- pour écrire sur stdout : df.to_csv(sys.stdout, sep = '\\t', index = False) ou alors print(df.to_csv(sep = '\\t', index = False))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy & Scipy \n",
    "\n",
    "NumPy est une librairie Python destinée à manipuler des matrices ou tableaux multidimensionnels ainsi que des fonctions mathématiques opérant sur ces tableaux.\n",
    "\n",
    "Plus précisément, cette bibliothèque logicielle libre et open source fournit de multiples fonctions permettant notamment de créer directement un tableau depuis un fichier ou au contraire de sauvegarder un tableau dans un fichier, et manipuler des vecteurs, matrices et polynômes. NumPy est la base de SciPy, regroupement de bibliothèques Python autour du calcul scientifique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "#création d'array simple\n",
    "a = np.array([[1, 2, 3], [4, 5, 6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape #renvoie les dimensions de l'array, d'abord le nombre de lignes, puis le nombre de colonnes, ici (2, 3).\n",
    "s.size #donne la taille totale d'une array numpy (le produit des tailles des differentes dimensions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.,  0.],\n",
       "       [ 0.,  0.,  1.],\n",
       "       [ 0.,  0.,  0.]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#numpy.eye permet aussi de faire des diagonales autre que la diagonale principale \n",
    "np.eye(3, 3, 1)\n",
    "#avec numpy.eye(3, 3, -1), on aurait la sous-diagonale\n",
    "#avec numpy.eye(3, 3, 2), on aurait un 1 en haut à droite.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0],\n",
       "       [0, 4]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag(np.array([1, 4])) #crée une matrice diagonale avec la diagonale indiquée :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Soit un tableau tel que \n",
    "a = np.array([[1, 2, 3], [4, 5, 6]]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [4, 5]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0:2,0:2] \n",
    "#sous-array 2d des 2 premières lignes et 2 premières colonne\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Attention, quand on fait b = a[0:2,0:2], b n'est pas une copie de a, mais une \"vue\" sur a : si on modifie b, cela modifie a (et réciproquement) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False,  True, False],\n",
       "       [False, False, False]], dtype=bool)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#on peut filtrer par valeur \n",
    "a == 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.reshape(3, 2) \n",
    "#renvoie une array2d de taille 3 x 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 7, 7])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#numpy.tile : permet de construire des arrays répétées :\n",
    "np.tile(7, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7, 8, 7, 8, 7, 8],\n",
       "       [7, 8, 7, 8, 7, 8]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#on peut combiner les deux\n",
    "np.tile([7, 8], [2, 3]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Concaténation d'arrays \n",
    "- np.concatenate([a1, a2, a3]) : concaténation d'arrays 1d\n",
    "- np.concatenate([a1, a2, a3]) : concaténation d'arrays 2d par ligne (\"les unes en dessous des autres\")\n",
    "- np.concatenate([a1, a2, a3], axis = 1) : concaténation d'arrays 2d par colonne (\"les unes à côté des autres\"). Défaut de axis est 0 (par ligne).\n",
    "Attention, il faut à chaque fois que les autres dimensions soient compatibles quand arrays à plusieurs dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Sélection d'une partie d'une array \n",
    "Si ar est une array 2d (par exemple ar = numpy.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])), alors : \n",
    "- ar[1:3,0:2] : récupère la sous-array des lignes 2 et 3, et des colonnes 1 et 2.\n",
    "- attention : l'array récupérée est une vue : si on la modifie, cela modifie l'array d'origine !\n",
    "- ar[1,:] : renvoie la 2ème ligne, mais l'array renvoyée n'a plus qu'une seule dimension ! (par contre, ar[1:2,:] renvoie aussi la 2ème ligne, mais en conservant les 2 dimensions)\n",
    "- ar[:,-1] : renvoie la dernière colonne.\n",
    "- ar[numpy.newaxis,2,:] : renvoie la 2ème ligne en conservant la première dimension (shape vaut ici (1, 3))\n",
    "- ar[:,-1,numpy.newaxis].shape : renvoie la dernière colonne en conservant la 2ème dimension (shape vaut ici (3, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Si \n",
    "a = np.array([[1, 2, 0], [4, 0, 6], [0, 0, 0]]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 0, 1, 1]), array([0, 1, 0, 2]))"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.nonzero(a) #renvoie les indices où la valeur est non nulle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2, -1],\n",
       "       [ 4, -1,  6],\n",
       "       [-1, -1, -1]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(a == 0, -1, a) #renvoie une array avec -1 si la condition est vraie, sinon la valeur de a à la même position \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- np.arange(5) #équivalent de range(5).\n",
    "- np.arange(5, dtype = numpy.float16) #avec des floats.\n",
    "- np.arange(2, 7) #entiers de 2 à 6.\n",
    "- np.arange(2, 7, 0.5) #nombres avec incrément de 0.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2 3]\n",
      " [0 1 2 3]\n",
      " [0 1 2 3]]\n",
      "[[0 0 0 0]\n",
      " [1 1 1 1]\n",
      " [2 2 2 2]]\n"
     ]
    }
   ],
   "source": [
    "#Un meshgrid permet de générer deux matrices, l'une avec des colonnes constantes, l'autre avec des lignes constantes afin de pouvoir évaluer une fonction sur une matrice de valeurs \n",
    "(x, y) = np.meshgrid([0, 1, 2, 3], [0, 1, 2])\n",
    "print(x)\n",
    "print(y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Les fonctions \n",
    "- np.negative(a1) : pareil que -a1\n",
    "- np.sign(a1) : -1, 0 ou 1 selon le signe.\n",
    "- np.exp, numpy.log : exponentielle, logarithme (base e).\n",
    "- np.exp2, numpy.log2 : exponentielle en base 2 (i.e. 2 puissance n), logarithme en base 2.\n",
    "- np.log10 : logarithme en base 10.\n",
    "- np.sqrt : racine carrée.\n",
    "- np.square : carrés.\n",
    "- np.reciprocal : l'inverse.\n",
    "- np.sin, numpy.cos, numpy.tan, numpy.arcsin, numpy.arccos, numpy.arctan, numpy.sinh, numpy.cosh, numpy.tanh\n",
    "- np.arcsinh, numpy.arccosh, numpy.arctanh : fonctions trigonométriques classiques, avec argument en radians.\n",
    "- np.deg2rad, numpy.rad2deg : conversion de degrés en radians et vice-versa.\n",
    "- a = np.add(a1, a2) et a = a1 + a2 sont équivalents.\n",
    "- a = np.subtract(a1, a2) : comme a1 - a2\n",
    "- a = np.multiply(a1, a2) : comme a1 * a2. C'est la multiplication terme à terme.\n",
    "- a = np.divide(a1, a2) : comme a1 / a2 : c'est la division entière si ce sont des entiers, sinon, c'est la division normale.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Vectorization d'une fonction \n",
    "\n",
    "Elle peut être appliqu&é à un numpy array. On définit par exemple la fonction :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def myFunc(x, y):\n",
    "    return x + y / 2.0 if y > 0 else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "#on définit ensuite une version vectorisée par \n",
    "myFuncV = np.vectorize(myFunc)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 4, 5])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Application de la fonction \n",
    "myFuncV(np.array([1, 2, 3]), np.array([-1, 4, 5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Générations aléatoires simples  \n",
    "- np.random.randn(10) : array 1d de 10 nombres d'une distribution gaussienne standard (moyenne 0, écart-type 1).\n",
    "- np.random.randn(10, 10) : array 2d de 10 x 10 nombres d'une distribution gaussienne standard.\n",
    "- np.random.randint(1, 5, 10) : une array 1d de 10 nombres entiers entre 1 et 5, 5 exclus.\n",
    "- np.random.random_integers(1, 5, 10) : une array 1d de 10 nombres entiers entre 1 et 5, 5 inclus.\n",
    "- np.random.random_sample(7) : renvoie 7 valeurs aléatoires dans l'intervalle [0,1[."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Permutations \n",
    "- a = np.array([1, 2, 3, 4, 5, 6]); np.random.shuffle(a) : fait une permutation aléatoire en place de a.\n",
    "- a = np.array([1, 2, 3, 4, 5, 6]); b = np.random.permutation(a) : renvoie une permutation aléatoire, sans affecter a."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Variables aléatoires de différentes distributions \n",
    "- np.seed(5) : pour donner la graine, afin d'avoir des valeurs reproductibles d'un lancement du programme à un autre.\n",
    "- np.random.binomial(10, 0.3, 7) : une array de 7 valeurs d'une loi binomiale de 10 tirages avec probabilité de succès de 0.3.\n",
    "- np.random.poisson(1, 7) : une array de 7 valeurs issues d'une loi de Poisson de paramètre 1.\n",
    "- np.random.standard_normal(7) : une array de 7 valeurs issues d'une loi normale standard (moyenne 0, écart-type 1).\n",
    "- np.random.normal(5, 2, 7) : une array de 7 valeurs issues d'une loi normale de moyenne 5 et écart-type 2.\n",
    "- np.random.uniform(0, 2, 7): une array de 7 valeurs issues d'une loi uniforme entre 0 et 2.\n",
    "- np.random.standard_t(2, 7): une array de 7 valeurs issues d'une loi standard t de Student à 2 degrés de liberté.\n",
    "- np.random.chisquare(2, 7) : une array de 7 valeurs issues d'une loi du chi 2 à 2 degrés de liberté.\n",
    "- np.random.f(2, 3, 7) : une array de 7 valeurs issues d'une loi F de Fisher à 2 et 3 degrés de liberté."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Minimum et maximum "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[1, 2, 3], [4, 5, 6]]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- np.amin(a) ou numpy.min(a) ou aussi a.min() : renvoie la valeur minimum de l'array (sur toute l'array si à plusieurs dimensions).\n",
    "- np.amin(a, 0) : la ligne des minima par colonne, donc renvoie array([1, 2, 3]).\n",
    "- np.amin(a, 1) : la ligne des minima par ligne, donc renvoie array([1, 4]).\n",
    "- np.amax : pareil pour le maximum.\n",
    "- nanmin et nanmax : pareil en ignorant les valeurs non définies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Valeurs statistiques de base \n",
    "- a.mean() : renvoie la moyenne sur toute l'array.\n",
    "- np.mean(a, 0) : la ligne des moyennes, c'est à dire array([ 2.5, 3.5, 4.5]).\n",
    "- np.median(a, 0) : la ligne des médiane, c'est à dire aussi ici array([ 2.5, 3.5, 4.5]) (cas particulier).\n",
    "- np.std(a, 0) : la ligne des déviations standard par colonne au sens mathématique, c'est à dire divisé par racine de n, ici array([ 1.5, 1.5, 1.5]).\n",
    "- np.std(a, 0, ddof = 1) : la ligne des déviations standard par colonne au sens statistique, c'est à dire divisé par racine de n - 1 (ddof : degrés of freedom), ici array([ 2.12132034, 2.12132034, 2.12132034]).\n",
    "- np.var(a, 0) : la lignes des variances par colonne, donc ici : array([ 1.5, 1.5, 1.5]).\n",
    "- np.percentile(a, 10) : valeur du premier décile.\n",
    "\n",
    "##### Coefficient de corrélation de Pearson \n",
    "On peut utiliser la fonction corrcoef "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.77685086],\n",
       "       [ 0.77685086,  1.        ]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat = np.corrcoef([2, 4, 6, 2, 9], [3, 5, 9, 4, 7]) \n",
    "#renvoie une matrice 2 x 2 symétrique avec tous les coefficients, en l'occurence 1 sur la diagonale, et la valeur recherchée ailleurs.\n",
    "mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.57655666, -0.98198051],\n",
       "       [ 0.57655666,  1.        , -0.72057669],\n",
       "       [-0.98198051, -0.72057669,  1.        ]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#on peut aussi donner une matrice en input pour avoir la matrice des coefficients de corrélations des lignes 2 à 2 : \n",
    "mat = np.array([[6, 4, 3], [7, 9, 1], [2, 5, 8]])\n",
    "np.corrcoef(mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Attention donc, np.corrcoef procéde par défaut par ligne, chaque ligne représentant une variable !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Test  de Student \n",
    "\n",
    "- scipy.stats.ttest_ind([3, 5, 7], [6, 9, 10, 11]) : test t standard pour comparer les valeurs de 2 échantillons et renvoie une paire (statistique t, p-value), ici (-2.4967511357294372, 0.054707113913075575). Le test fait l'hypothèse d'une variance égale, sinon, rajouter equal_var = False.\n",
    "- scipy.stats.ttest_rel([3, 5, 7], [6, 9, 10]) : test t apparié (il doit y avoir autant de valeurs dans les 2 vecteurs). Renvoie une paire (statistique t, p-value), ici (-10.0, 0.0098524570233256923).\n",
    "\n",
    "\n",
    "##### Régression polynomiale \n",
    "\n",
    "- fit = numpy.polyfit([3, 4, 6, 8], [6.5, 4.2, 11.8, 15.7], 1) : fait une régression polynomiale de degré 1 et renvoie les coefficients, d'abord celui de poids le plus élevé. Donc ici [a, b] si y = ax + b. Renvoie ici array([2.17966102, -1.89322034]).\n",
    "- on peut alors après construire la fonction polynôme correspondante : poly = numpy.poly1d(fit) (renvoie une fonction), et évaluer cette fonction sur une valeur de x : poly(7.0) donne 13.364406779661021.\n",
    "- cette fonction peut être évaluée directement sur une liste : poly([2, 3, 4, 5]) donne array([2.46610169, 4.64576271, 6.82542373, 9.00508475]).\n",
    "\n",
    "##### Regression linéaire \n",
    "- on peut aussi faire lr = scipy.stats.linregress([3, 4, 6, 8], [6.5, 4.2, 11.8, 15.7]).\n",
    "\n",
    "np.linalg.lstsq : permet de résoudre l'équation **y = mx + c** avec **y** et **x** des matrices par la méthode des moindres carrés où le système d'équation peut être sur-déterminé, sous-déterminé ou exactement déterminé :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "x = np.array([0, 1, 2, 3])\n",
    "y = np.array([-1, 0.2, 0.9, 2.1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut réecrire l'équation tel que **y = Ap** ,ou A = [[x 1]] et p = [[m], [c]].  \n",
    "On va pouvoir utiliser lstsq pour trouver p:\n",
    "(Voir le notebook RegressionSimple.ipynb pour plus de détails) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.],\n",
       "       [ 1.,  1.],\n",
       "       [ 2.,  1.],\n",
       "       [ 3.,  1.]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.vstack([x, np.ones(len(x))]).T\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 -0.95\n"
     ]
    }
   ],
   "source": [
    "m, c = np.linalg.lstsq(A, y)[0]\n",
    "print(m, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107f768d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o', label='Donées de base', markersize=10)\n",
    "plt.plot(x, m*x + c, 'r', label='Regression')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matplotlib\n",
    "\n",
    "Matplotlib est une librairie qui permet de tracer des graphes (dans le sens graphiques), grandement inspiré de Matlab au départ. Elle peut être utilisé de 2 façons :\n",
    "- soit avec une approche objet : plus compliquée et plus verbeuse, mais plus évoluée.\n",
    "- soit via des appels de fonctions, avec pyplot : plus simple. pyplot fournit ainsi des raccourcis qui évitent la formulation objet plus longue à écrire.\n",
    "\n",
    "Elle permet notamment de faire des graphes qui peuvent être comlètement adaptés si besoin. Sur une figure, on peut tracer plusieurs graphes.\n",
    "\n",
    "#### Notions principales pour les graphes sous matplotlib \n",
    "- figure : une figure qui peut être sauvée dans un fichier.\n",
    "- axe : un graphe (graphique) individuel appartenant à une figure qui peut en compter plusieurs. Attention, ce n'est pas un axe de coordonnées !\n",
    "- axis : un axe de coordonnées appartenant à un objet axe.\n",
    "- divers objets graphiques qui dérivent de la classe Artist et qui participent au graphe. Ce sont par exemple des rectangles, des lignes, du texte. Ces différents objets peuvent être totalement configurés (y compris individuellement) pour adapter le graphe aux besoins en appelant dessus des méthodes pour modifier leurs propriétés !\n",
    "\n",
    "#### Pyplot généralités : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106f98a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Importer la librairie \n",
    "from matplotlib import pyplot\n",
    "#graphique de base \n",
    "pyplot.plot([1, 2, 3, 6], [1, 4, 9, 36])\n",
    "#Montrer le graphique \n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1081d6668>]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106f98d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(x, y, 'bo') #bleu et avec des ronds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1083142e8>]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108267358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(x, y, color = 'green', linestyle = 'dashed', linewidth = 2, marker = 'o', markerfacecolor = 'blue', markersize = 5) \n",
    "#symboles ronds en bleu avec une taille de 5 et traits pointillés en vert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1080db320>,\n",
       " <matplotlib.lines.Line2D at 0x1080db198>]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nu/XLgJs2QU3vBj4xht+p3wTOB+5ZYf8lwJeAABcCt22Sui4C/nEMx2sncH63/mzgP5f5fznyY3aSdY38mHXH4Fnd+hnAbcCFS/ps2Otxy5z51ya7mfwiu4Hru/Xrgbds8HgncjI//+J6PwO8ITl2n8ex1TQWVfUN4LETdNkN3FB9twLPTbJzE9Q1FlV1pKru6NZ/TP/+HUvv1z3yY3aSdY1cdwye6DbP6JalH8Ju2Otxy4T/SRrZzeQXeWFVHenWvw+8cIV+z+zuX3xrko16gziZn/8Xfap/I57HgRdsUD0nWxPA27ppgs8kOWeZ/eMwjt+nk/XabjrhS0leMerBu+mJV9M/m11srMfsBHXBGI5ZktOS3Ak8Any5qlY8XsN+Pa56D9/NJMlXgBcts2tvVX1h1PUcc6K6Fm9UVSVZ6fKqyao6nOSlwNeS3F1V3xt2raeoLwI3VtVPk/w+/TOh3xpzTZvZHfR/n55IcgnweeDcUQ2e5FnAZ4EPVtWPRjXualapayzHrKp+DrwqyXOBf0jyq1W17Gc5w3ZKhX+N8Gbya3GiupL8IMnOqjrS/fP2kRWe43D3+ECSr9M/Oxl2+J/Mz3+sz6EkpwPPAR4dch1rqqmqFo9/Lf3PUTaDDfl9GtTiYKuqA0n+MsmOqtrwv2GT5Az6ATtXVZ9bpstYjtlqdY3zmHVj/neSW4CLgcXhv2Gvx9amfUZ2M/lF9gOXd+uXA0/7F0qS5yV5Rre+A3g9cN8G1HIyP//iet8OfK26T5s2yKo1LZkTvpT+nO1msB94V3cFy4XA44um+MYmyYuOzQsnuYD+63wj38CPjRvgU8D9VfWxFbqN/JidTF3jOGZJJrozfpL8EvAm4D+WdNu41+MoP93eyAV4K/35w58CPwBu7tpfDBxY1O8S+p/2f4/+dNFG1/UC4KvAd4GvAM/v2nvAtd3664C76V/pcjfwng2s52k/P/Bh4NJu/ZnA3wMHgW8CLx3BMVqtpj8F7u2Ozy3Ar4zod+pG4Ajwv93v1nuA9wHv6/YHuKar+25WuMpsDHVdseh43Qq8bkR1/Qb9DyzvAu7slkvGfcxOsq6RHzPglcC/d3XdA3yoax/J69Fv+EpSg1qb9pEkYfhLUpMMf0lqkOEvSQ0y/CWpQYa/JDXI8JekBhn+ktSg/wdS5SaYjNsqgAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1082f94e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#on peut tracer plusieurs courbes sur le même graphe \n",
    "pyplot.plot(x, y, 'r+', y, y, 'bo')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Un exemple')"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1080c06a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Tracer un graphe d'une liste de valeurs en fonction du numéro d'ordre \n",
    "pyplot.plot([1, 2, 4, 4, 2, 1], color = 'red', linestyle = 'dashed', linewidth = 2, markerfacecolor = 'blue', markersize = 5)\n",
    "pyplot.ylim(0, 5)\n",
    "pyplot.title('Un exemple')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0,0,'lab0'),\n",
       " Text(0,0,'lab10'),\n",
       " Text(0,0,'lab20'),\n",
       " Text(0,0,'lab30'),\n",
       " Text(0,0,'lab40'),\n",
       " Text(0,0,'lab50'),\n",
       " Text(0,0,'lab60'),\n",
       " Text(0,0,'lab70'),\n",
       " Text(0,0,'lab80'),\n",
       " Text(0,0,'lab90')]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10813a860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Si on veut mettre des etiquettes tous les n valeurs   \n",
    "import math\n",
    "val = [math.log(i + 1) for i in range(100)]\n",
    "lab = ['lab' + str(i) for i in range(100)]\n",
    "pyplot.plot(val, linestyle = 'none', marker = '+')\n",
    "pyplot.gca().get_xaxis().set_ticks([i for i in range(len(lab)) if i % 10 == 0])\n",
    "pyplot.gca().get_xaxis().set_ticklabels([lab[i] for i in range(len(lab)) if i % 10 == 0], fontsize = 8, rotation = 90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Sauvegarde de l'image dans un fichier  \n",
    "- pyplot.savefig('image.png'); pyplot.close().\n",
    "- pyplot.savefig('image.png', dpi = 600) : fixe la résolution.\n",
    "- pyplot.savefig('image.png', transparent = True) : fond transparent.\n",
    "- pyplot.savefig('image, format = 'pdf') : indique le format. Les formats supportés sont : png, pdf, eps, svg, sinon le format est deviné d'après l'extension du fichier.\n",
    "\n",
    "##### Les Graphiques en bar "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.XTick at 0x1082a29b0>,\n",
       "  <matplotlib.axis.XTick at 0x1082a7e48>,\n",
       "  <matplotlib.axis.XTick at 0x1082c7208>,\n",
       "  <matplotlib.axis.XTick at 0x1083c9898>,\n",
       "  <matplotlib.axis.XTick at 0x1083c9f28>],\n",
       " <a list of 5 Text xticklabel objects>)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108048c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.bar(range(5), [1, 3, 3, 5, 4], width = 0.6, color = 'yellow', edgecolor = 'blue', linewidth = 2, yerr = [0.5, 1, 2, 1, 2], ecolor = 'magenta', capsize = 10)\n",
    "pyplot.xticks([x + 0.6 / 2 for x in range(5)], ['A', 'B', 'C', 'D', 'E'], rotation = 45)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Exemple de barplot avec 2 séries superposées "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.XTick at 0x1083f6b38>,\n",
       "  <matplotlib.axis.XTick at 0x1083f6f98>,\n",
       "  <matplotlib.axis.XTick at 0x1083fb5c0>,\n",
       "  <matplotlib.axis.XTick at 0x108731fd0>],\n",
       " <a list of 4 Text xticklabel objects>)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083e3588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "barWidth = 0.8\n",
    "y1 = [1, 2, 4, 3]\n",
    "y2 = [3, 4, 4, 3]\n",
    "r = range(len(y1))\n",
    "pyplot.bar(r, y1, width = barWidth, color = ['yellow' for i in y1],\n",
    "           edgecolor = ['blue' for i in y1], linestyle = 'solid', hatch ='/',\n",
    "           linewidth = 3)\n",
    "pyplot.bar(r, y2, width = barWidth, bottom = y1, color = ['pink' for i in y1],\n",
    "           edgecolor = ['green' for i in y1], linestyle = 'dotted', hatch = 'o',\n",
    "           linewidth = 3)\n",
    "pyplot.xticks([r + barWidth / 2 for r in range(len(y1))], ['A', 'B', 'C', 'D'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.YTick at 0x10871b438>,\n",
       "  <matplotlib.axis.YTick at 0x1087f3c88>,\n",
       "  <matplotlib.axis.YTick at 0x108808358>,\n",
       "  <matplotlib.axis.YTick at 0x10883bba8>],\n",
       " <a list of 4 Text yticklabel objects>)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083fb0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# passer à l'horizontale \n",
    "pyplot.barh(r, y1, height = barWidth, color = ['yellow' for i in y1],\n",
    "           edgecolor = ['blue' for i in y1], linestyle = 'solid', hatch ='/',\n",
    "           linewidth = 3)\n",
    "pyplot.barh(r, y2, height = barWidth, left = y1, color = ['pink' for i in y1],\n",
    "           edgecolor = ['green' for i in y1], linestyle = 'dotted', hatch = 'o',\n",
    "           linewidth = 3)\n",
    "pyplot.yticks([r + barWidth / 2 for r in range(len(y1))], ['A', 'B', 'C', 'D'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### On peut rajouter des barres d'erreur à un barplot \n",
    "- pyplot.errorbar(range(len(values)), values, yerr = errorValues, fmt = 'none')\n",
    "- capsize = 10 : permet de rajouter des traits horizontaux aux extremités des barres d'erreur.\n",
    "- ecolor = 'red' : pour choisir la couleur de la barre d'erreur.\n",
    "- elinewidth = 5 : l'épaisseur du trait vertical\n",
    "- capthick = 5 : l'épaisseur du petit trait horizontal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 3 artists>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6ACRBoQNAEhQ6ACTx/wwOqTq6EnjEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083c9be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "values = [5, 3, 7, 9]\n",
    "errorValues = [1, 0.5, 2.5, 3]\n",
    "pyplot.bar(range(len(values)), values, color = 'skyblue')\n",
    "pyplot.errorbar(range(len(values)), values, yerr = errorValues,\n",
    "    fmt = 'none', capsize = 10, ecolor = 'red', elinewidth = 2, capthick = 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Les histogrammes "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,\"Exemple d' histogramme simple\")"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108902f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [1, 2, 2, 3, 4, 4, 4, 4, 4, 5, 5]\n",
    "pyplot.hist(x, range = (0, 5), bins = 5, color = 'yellow',\n",
    "            edgecolor = 'red')\n",
    "pyplot.xlabel('valeurs')\n",
    "pyplot.ylabel('nombres')\n",
    "\n",
    "pyplot.title('Exemple d\\' histogramme simple')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x108b37978>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108a13ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Affichage de l'histogramme de 2 séries (les 2 couleurs sont obligatoires, par contre la couleur des bordures et les rayures ne sont communs)\n",
    "x1 = [1, 2, 2, 3, 4, 4, 4, 4, 4, 5, 5]\n",
    "x2 = [1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5]\n",
    "bins = [x + 0.5 for x in range(0, 6)]\n",
    "pyplot.hist([x1, x2], bins = bins, color = ['yellow', 'green'],\n",
    "            edgecolor = 'red', hatch = '/', label = ['x1', 'x2'],\n",
    "            histtype = 'bar') # bar est le defaut\n",
    "pyplot.ylabel('valeurs')\n",
    "pyplot.xlabel('nombres')\n",
    "pyplot.title('2 series')\n",
    "pyplot.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x108c56358>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108b1c0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Affichage de l'histogramme de 2 séries, mais sous forme superposées, l'un au dessus de l'autre\n",
    "x1 = [1, 2, 2, 3, 4, 4, 4, 4, 4, 5, 5]\n",
    "x2 = [1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5]\n",
    "bins = [x + 0.5 for x in range(0, 6)]\n",
    "pyplot.hist([x1, x2], bins = bins, color = ['yellow', 'green'],\n",
    "            edgecolor = 'red', hatch = '/', label = ['x1', 'x2'],\n",
    "            histtype = 'barstacked')\n",
    "pyplot.ylabel('valeurs')\n",
    "pyplot.xlabel('nombres')\n",
    "pyplot.title('2 series superposees')\n",
    "pyplot.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Les boites à moustaches \n",
    "La boîte à moustaches résume quelques caractéristiques de position du caractère étudié (médiane, quartiles, minimum, maximum ou déciles). Ce diagramme est utilisé principalement pour comparer un même caractère dans deux populations de tailles différentes.\n",
    "\n",
    "Il s'agit de tracer un rectangle allant du premier quartile au troisième quartile et coupé par la médiane. Ce rectangle suffit pour le diagramme en boîte. On ajoute alors des segments aux extrémités menant jusqu'aux valeurs extrêmes, ou jusqu'aux premier et neuvième déciles. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'boxplot avec array 2d')"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108c39e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.subplot(121)\n",
    "pyplot.boxplot([[1, 2, 3, 4, 5, 13], [6, 7, 8, 10, 10, 11, 12], [1, 2, 3]])\n",
    "pyplot.ylim(0, 14)\n",
    "pyplot.title('boxplot avec sequence')\n",
    "\n",
    "pyplot.subplot(122)\n",
    "pyplot.boxplot(np.array([[1, 2, 3], [2, 7, 8], [1, 3, 10], [2, 5, 12]]))\n",
    "pyplot.ylim(0, 14)\n",
    "pyplot.title('boxplot avec array 2d')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Les camemberts "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x106faafd0>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108a934a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize = (8, 8))\n",
    "x = [1, 2, 3, 4, 10]\n",
    "pyplot.pie(x, labels = ['A', 'B', 'C', 'D', 'E'])\n",
    "pyplot.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x108d33978>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107e222e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plus complet \n",
    "pyplot.figure(figsize = (8, 8))\n",
    "x = [1, 2, 3, 4, 10]\n",
    "pyplot.pie(x, labels = ['A', 'B', 'C', 'D', 'E'],\n",
    "           colors = ['red', 'green', 'yellow'],\n",
    "           explode = [0, 0.2, 0, 0, 0],\n",
    "           autopct = lambda x: str(round(x, 2)) + '%',\n",
    "           pctdistance = 0.7, labeldistance = 1.4,\n",
    "           shadow = True)\n",
    "pyplot.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Les Heatmap \n",
    "\n",
    "On peut représenter une matrice sous forme de heatmap (un carré par valeur, et une couleur qui dépend de cette valeur) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1.05,'exemple de matrice avec couleurs par defaut')"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10845f5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mat = [[1, 2, 3, 1], [4, 5, 6, 4], [7, 7, 10, 10]]\n",
    "\n",
    "pyplot.matshow(mat)\n",
    "pyplot.title('exemple de matrice avec couleurs par defaut')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 5 artists>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1091cab00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Exemple de figure avec des graphes multiples \n",
    "pyplot.figure(1)\n",
    "pyplot.subplot(1, 2, 1)\n",
    "pyplot.scatter(range(5), [x ** 2 for x in range(5)], color = 'blue')\n",
    "pyplot.subplot(2, 2, 2)\n",
    "pyplot.plot(range(5), color = 'red')\n",
    "pyplot.subplot(2, 2, 4)\n",
    "pyplot.bar(range(5), range(5), color = 'green')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bokeh \n",
    "\n",
    "Bokeh est une bibliothèque de visualisation interactive qui cible les navigateurs Web afin de faire de la datavisualisation. Son objectif est de fournir une construction élégante et concise de graphiques variés interactifs de hautes performances sur des jeux de données très volumineux ou en flux continu. Bokeh peut aider tous ceux qui souhaitent créer rapidement et facilement des graphiques interactifs, des tableaux de bord et des applications de \n",
    "données.\n",
    "\n",
    "### Installation via pip \n",
    "```python \n",
    "pip install bokeh\n",
    "```\n",
    "\n",
    "### Quickstart"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Importer la librairies \n",
    "from bokeh.plotting import figure, output_file, show\n",
    "#déclaration du fichier de sortie \n",
    "output_file(\"test.html\")\n",
    "#figure \n",
    "p = figure()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "#data random\n",
    "p.line([1, 2, 3, 4, 5], [6, 7, 2, 4, 5], line_width=2)\n",
    "#affichage du plot\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Afficher plus d'informations "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "#d'autre data random \n",
    "x = [0.1, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0]\n",
    "y0 = [i**2 for i in x]\n",
    "y1 = [10**i for i in x]\n",
    "y2 = [10**(i**2) for i in x]\n",
    "\n",
    "#output\n",
    "output_file(\"log_lines.html\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "# créer un nouveau plot dans une figure \n",
    "p = figure(\n",
    "   tools=\"pan,box_zoom,reset,save\",\n",
    "   y_axis_type=\"log\", y_range=[0.001, 10**11], title=\"log axis example\",\n",
    "   x_axis_label='sections', y_axis_label='particles'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ajouter les data\n",
    "p.line(x, x, legend=\"y=x\")\n",
    "p.circle(x, x, legend=\"y=x\", fill_color=\"white\", size=8)\n",
    "p.line(x, y0, legend=\"y=x^2\", line_width=3)\n",
    "p.line(x, y1, legend=\"y=10^x\", line_color=\"red\")\n",
    "p.circle(x, y1, legend=\"y=10^x\", fill_color=\"red\", line_color=\"red\", size=6)\n",
    "p.line(x, y2, legend=\"y=10^x^2\", line_color=\"orange\", line_dash=\"4 4\")\n",
    "\n",
    "# affichier la figure \n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Jouer avec les vecteurs "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "# prepare d'autres random data\n",
    "N = 4000\n",
    "x = np.random.random(size=N) * 100\n",
    "y = np.random.random(size=N) * 100\n",
    "radii = np.random.random(size=N) * 1.5\n",
    "#configurer les couleurs \n",
    "colors = [\n",
    "    \"#%02x%02x%02x\" % (int(r), int(g), 150) for r, g in zip(50+2*x, 30+2*y)\n",
    "]\n",
    "\n",
    "#output\n",
    "output_file(\"color_scatter.html\", title=\"color_scatter.py example\", mode=\"cdn\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "TOOLS = \"crosshair,pan,wheel_zoom,box_zoom,reset,box_select,lasso_select\"\n",
    "#figure avec les paramètres ci-dessus \n",
    "p = figure(tools=TOOLS, x_range=(0, 100), y_range=(0, 100))\n",
    "#ajouter les points en fonction des couleurs et tailles \n",
    "p.circle(x, y, radius=radii, fill_color=colors, fill_alpha=0.6, line_color=None)\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Afficher les Datetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using data directory: /Users/benjamindallard/.bokeh/data\n",
      "Downloading: CGM.csv (1589982 bytes)\n",
      "   1589982 [100.00%]\n",
      "Downloading: US_Counties.zip (3182088 bytes)\n",
      "   3182088 [100.00%]\n",
      "Unpacking: US_Counties.csv\n",
      "Downloading: us_cities.json (713565 bytes)\n",
      "    713565 [100.00%]\n",
      "Downloading: unemployment09.csv (253301 bytes)\n",
      "    253301 [100.00%]\n",
      "Downloading: AAPL.csv (166698 bytes)\n",
      "    166698 [100.00%]\n",
      "Downloading: FB.csv (9706 bytes)\n",
      "      9706 [100.00%]\n",
      "Downloading: GOOG.csv (113894 bytes)\n",
      "    113894 [100.00%]\n",
      "Downloading: IBM.csv (165625 bytes)\n",
      "    165625 [100.00%]\n",
      "Downloading: MSFT.csv (161614 bytes)\n",
      "    161614 [100.00%]\n",
      "Downloading: WPP2012_SA_DB03_POPULATION_QUINQUENNIAL.zip (5148539 bytes)\n",
      "   5148539 [100.00%]\n",
      "Unpacking: WPP2012_SA_DB03_POPULATION_QUINQUENNIAL.csv\n",
      "Downloading: gapminder_fertility.csv (64346 bytes)\n",
      "     64346 [100.00%]\n",
      "Downloading: gapminder_population.csv (94509 bytes)\n",
      "     94509 [100.00%]\n",
      "Downloading: gapminder_life_expectancy.csv (73243 bytes)\n",
      "     73243 [100.00%]\n",
      "Downloading: gapminder_regions.csv (7781 bytes)\n",
      "      7781 [100.00%]\n",
      "Downloading: world_cities.zip (646858 bytes)\n",
      "    646858 [100.00%]\n",
      "Unpacking: world_cities.csv\n",
      "Downloading: airports.json (6373 bytes)\n",
      "      6373 [100.00%]\n",
      "Downloading: movies.db.zip (5067833 bytes)\n",
      "   5067833 [100.00%]\n",
      "Unpacking: movies.db\n",
      "Downloading: airports.csv (203190 bytes)\n",
      "    203190 [100.00%]\n",
      "Downloading: routes.csv (377280 bytes)\n",
      "    377280 [100.00%]\n"
     ]
    }
   ],
   "source": [
    "import bokeh.sampledata\n",
    "#télécharger les dataset de bokeh \n",
    "bokeh.sampledata.download()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "from bokeh.plotting import figure, output_file, show\n",
    "from bokeh.sampledata.stocks import AAPL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "#préparer d'autre random data\n",
    "aapl = np.array(AAPL['adj_close'])\n",
    "aapl_dates = np.array(AAPL['date'], dtype=np.datetime64)\n",
    "#paramétrage\n",
    "window_size = 30\n",
    "window = np.ones(window_size)/float(window_size)\n",
    "aapl_avg = np.convolve(aapl, window, 'same')\n",
    "\n",
    "#output \n",
    "output_file(\"stocks.html\", title=\"stocks.py example\")\n",
    "#créer un nouveau plot avec un axis datetime\n",
    "p = figure(width=800, height=350, x_axis_type=\"datetime\")\n",
    "\n",
    "#ajouter les data \n",
    "p.circle(aapl_dates, aapl, size=4, color='darkgrey', alpha=0.2, legend='close')\n",
    "p.line(aapl_dates, aapl_avg, color='navy', legend='avg')\n",
    "\n",
    "#Customiser les attribues \n",
    "p.title.text = \"AAPL One-Month Average\"\n",
    "p.legend.location = \"top_left\"\n",
    "p.grid.grid_line_alpha = 0\n",
    "p.xaxis.axis_label = 'Date'\n",
    "p.yaxis.axis_label = 'Price'\n",
    "p.ygrid.band_fill_color = \"olive\"\n",
    "p.ygrid.band_fill_alpha = 0.1\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Pour aller plus loin \n",
    "Pour explorer plus en détail bokeh nous vous invitons à consulter la documentation officiel <https://bokeh.pydata.org/en/latest/index.html> ainsi que l'activité Map.ipynb qui met en application des API. On utilisera durant les ateliers la librairie seaborn <https://seaborn.pydata.org> qui fonctionne sur le même principe. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scikit-learn \n",
    "\n",
    "Scikit-learn est une bibliothèque libre Python destinée à l'apprentissage automatique. Elle est développée par de nombreux contributeurs notamment dans le monde académique par des instituts français d'enseignement supérieur et de recherche comme *Inria3* et *Télécom ParisTech*. Elle est conçue pour s'harmoniser avec d'autres bibliothèques libres Python, notamment NumPy et SciPy. \n",
    "\n",
    "### Importer un dataset exemple "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 8, 8)\n",
      "[[  0.   0.   5. ...,   0.   0.   0.]\n",
      " [  0.   0.   0. ...,  10.   0.   0.]\n",
      " [  0.   0.   0. ...,  16.   9.   0.]\n",
      " ..., \n",
      " [  0.   0.   1. ...,   6.   0.   0.]\n",
      " [  0.   0.   2. ...,  12.   0.   0.]\n",
      " [  0.   0.  10. ...,  12.   1.   0.]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "#iris et digits datasets d'images 8x8\n",
    "iris = datasets.load_iris()\n",
    "digits = datasets.load_digits()\n",
    "#taille de l'image\n",
    "print(digits.images.shape)\n",
    "print(digits.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 ..., 8 9 8]\n"
     ]
    }
   ],
   "source": [
    "#nombre correpondant aux images\n",
    "print(digits.target)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Les estimateurs \n",
    "\n",
    "Tous les objets estimateur exposent une méthode d’ajustement *fit(X, y)* qui prend un jeu de données (généralement un tableau à 2 dimensions numpy). \n",
    "Les estimateurs ont aussi des paramètres tel que : \n",
    "```python\n",
    "estimator = Estimator(param1=1, param2=2)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Le SVM \n",
    "Le support vecteurs machines ou séparateurs à vaste marge (en anglais support vector machine, SVM) sont un ensemble de techniques d'apprentissage supervisé destinées à résoudre des problèmes de régréssions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import svm\n",
    "#nous verrons comment choisir les paramètres plus tard \n",
    "clf = svm.SVC(gamma=0.001, C=100.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=100.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape='ovr', degree=3, gamma=0.001, kernel='rbf',\n",
       "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "  tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.fit(digits.data[:-1], digits.target[:-1]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x10f04f630>"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f0160b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#voir la prédiction\n",
    "clf.predict(digits.data[-1:])\n",
    "#voir à quoi cela ressemble : 8\n",
    "pyplot.imshow(digits.images[-1], cmap=pyplot.cm.gray_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### La régréssion linéaire \n",
    "Voir le notebook *StatBasics.ipynb* ou les repo Atelier3 et Atelier4. L'exemple ci-dessous est effectué à l'aire du dataset diabetes qui regrouppe 10 variables physiologiques (âge, sexe, poids, pression artérielle,...) sur 442 patients ainsi qu'une indication de la progression de la maladie après un an. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "#chargement des données\n",
    "diabetes = datasets.load_diabetes()\n",
    "#définitions des ensembles de test et de train\n",
    "diabetes_X_train = diabetes.data[:-20]\n",
    "diabetes_X_test  = diabetes.data[-20:]\n",
    "diabetes_y_train = diabetes.target[:-20]\n",
    "diabetes_y_test  = diabetes.target[-20:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  3.03499549e-01  -2.37639315e+02   5.10530605e+02   3.27736980e+02\n",
      "  -8.14131709e+02   4.92814588e+02   1.02848452e+02   1.84606489e+02\n",
      "   7.43519617e+02   7.60951722e+01]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(diabetes_X_train, diabetes_y_train)\n",
    "print(regr.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Les arbre\n",
    "\n",
    "Un arbre de décision est un outil d'aide à la décision représentant un ensemble de choix sous la forme graphique d'un arbre. Les différentes décisions possibles sont situées aux extrémités des branches (les « feuilles » de l'arbre), et sont atteints en fonction de décisions prises à chaque étape. L'arbre de décision est un outil utilisé dans des domaines variés tels que la sécurité, la fouille de données, la médecine, etc. Il a l'avantage d'être lisible et rapide à exécuter. Il s'agit de plus d'une représentation calculable automatiquement par des algorithmes d'apprentissage supervisé."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a888128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#données d'apprentissage random\n",
    "rng = np.random.RandomState(1)\n",
    "X = np.sort(5 * rng.rand(80, 1), axis=0)\n",
    "y = np.sin(X).ravel()\n",
    "y[::5] += 3 * (0.5 - rng.rand(16))\n",
    "\n",
    "#le modèle \n",
    "regr_1 = DecisionTreeRegressor(max_depth=2)\n",
    "regr_1.fit(X, y)\n",
    "\n",
    "#la prédiction\n",
    "X_test = np.arange(0.0, 5.0, 0.01)[:, np.newaxis]\n",
    "y_1 = regr_1.predict(X_test)\n",
    "\n",
    "# Affichage des résultats\n",
    "plt.figure()\n",
    "plt.scatter(X, y, c=\"darkorange\", label=\"data\")\n",
    "plt.plot(X_test, y_1, color=\"cornflowerblue\", label=\"max_depth=2\", linewidth=2)\n",
    "plt.xlabel(\"data\")\n",
    "plt.ylabel(\"target\")\n",
    "plt.title(\"Decision Tree Regression\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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