2022-06-02_transfert-des-voix.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "tl;dr : *Inférence du transfert des voix entre candidats.*\n",
    "\n",
    "Afin d'analyser les résultats des élections, par exemple les dernières élections présidentielles de 2022 en France, et de mieux comprendre la dynamique des choix de vote entre les différents groupes de population, il peut être utile d'utiliser des outils d'apprentissage automatique pour inférer des données *a priori* cachées dans les données. En particulier, inspiré par cet [article du Monde](https://www.lemonde.fr/les-decodeurs/article/2022/05/04/election-presidentielle-2022-quels-reports-de-voix-entre-les-deux-tours_6124672_4355770.html), on peut se poser la question de savoir si on peut extraire depuis les données brutes des élections une estimation des report de voix entre les choix de vote au premier tour et ceux qui sont effectués au deuxième tour.\n",
    "\n",
    "Pour cela nous allons utiliser les outils mathématiques de l'apprentissage automatique et en particulier l'utilisation des probabilités. Cette théorie va nous permettre d'exprimer le fait que les résultats telles qu'ils sont obtenus peuvent présenter une variabilité mais que celle-ci réelle résulte de préférence de chaque individu dans la population votante. En particulier, on peut considérer que chaque individu va avoir une préférence pour chacun des candidats au premier et second tour et que les votes effectués vont correspondre à la réalisation de ces préférences (en effet, on ne peut voter que pour un candidat par scrutin). \n",
    "\n",
    "Bien sûr on a accès ni au vote de chaque individu et encore moins à ses préférences. Mais comme mais comme chaque bureau de vote présente des variabilité liée au contexte local et qui fait que la population a une préférence pour certains choix plutôt que d'autres, on peut considérer chaque bureau de vote comme une population individuelle pour lequel nous allons essayer de prédire les résultats du vote au deuxième tour. Cette prediction, si elle est efficace, peut donner une idée du transfert de vote entre les deux tours qui a lieu en fonction des préférences des votes de chaque individu.\n",
    "\n",
    "<!-- TEASER_END -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Celà se modélise mathématiquement par un [processus de Bernoulli](https://fr.wikipedia.org/wiki/Processus_de_Bernoulli) relatif à ces préférences.\n",
    "\n",
    "Grâce à l'ouverture des données (notamment pour la recherche), on peut obtenir librement les résultats des [premier](https://www.data.gouv.fr/fr/datasets/election-presidentielle-des-10-et-24-avril-2022-resultats-definitifs-du-1er-tour/) et [second](https://www.data.gouv.fr/fr/datasets/election-presidentielle-des-10-et-24-avril-2022-resultats-definitifs-du-2nd-tour/) tours. Il est intéressant de noter que ses résultats sont indiqués pour chacun des bureaux de vote. \n",
    "\n",
    "Pour cela nous allons faire deux hypothèses: \n",
    "\n",
    "Tout d'abord nous allons estimer que pour chaque individu, il existe une préférence pour les candidats du premier tour ainsi que pour les candidats du deuxieme tour. Si on note les différentes alternatives au premier tour comme $i \\in \\{ \\text{'nul'}, \\text{'abstention'}, \\ldots, \\text{'Macron'}, \\text{'Poutou'} \\}$ et au deuxième tour  $j \\in \\{ \\text{'nul'}, \\text{'abstention'}, \\ldots, \\text{'Macron'}, \\text{'Le Pen'} \\}$. Alors, on peut écrire pour chaque individu $k$ les probabilités de vote $p^k_i$ et $q^k_j$ (chacune de ces valeurs étant comprises entre $0$ et $1$ représentant un biais de probabilité pour chacune des alternatives). On pourra vérifier que $\\forall k$ (pour tout individu),  $\\sum_i p^k_i = 1$ et $\\sum_j q^k_j = 1$.\n",
    "\n",
    "Avec une telle modélisation on peut prévoir les résultats du vote car les préférences de chacun individu pour telle ou telle choix doit se révéler au niveau de la population totale suivant le théorème central limite qui indique que la moyenne observée tend vers ces probabilités avec une précision (inverse de la variance) qui augmente linéairement avec le nombre d'observations. En particulier les résultats des votes au premier et second tour seront donnés par respectivement $\\frac 1 K \\cdot \\sum_k p^k_i$ et $\\frac 1 K \\cdot \\sum_k q^k_j$ avec $K$ la taille de la population (nous vérifierons ce point plus bas)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Une deuxième hypothèse que nous allons faire et que si on considère la transition entre les préférences qui sont faites au premier tour et celles qui sont faites au second tour, les préférences évoluent avec chaque invidu mais la transition est homogène au sein de la population (par exemple \"une personne qui choisit de s'abstenir s'abstiendra\"). C'est certe une hypothèse grossière mais assez générale pour refléter les tendances au niveau de la population globale. Cette hypothèse est basée sur la modélisation de séquence d'événements aléatoires basé sur un [processus dit de Markov](https://fr.wikipedia.org/wiki/Cha%C3%AEne_de_Markov). En particulier nous allons formaliser cette hypothèse en faisant l'hypothèse de l'existence d'une matrice de transition $M$ qui permet de prédire la préférence $\\hat{q}^k_j$ d'un individu au second tour à partir de ses préférences au premier tour. En particulier, cette hypothèse peut être formulée comme un simple produit matriciel :\n",
    "\n",
    "$$\n",
    "\\hat{q}^k_j = \\sum_i M_{i, j} \\cdot p^k_i \n",
    "$$\n",
    "\n",
    "En termes plus simples, cette formule exprime que la préférence d'un individu au second tour et le mélange de ses préférences individuelles au premier tour avec des poids indiquant les affinités entre les différentes alternatives aux deux tours. Il est important de noter qu'il existe une contrainte  pour chaque colonne de cette matrice de transition de sorte que la somme des différentes éléments sur les différentes lignes de la matrice pour chaque colonne est égal à $1$ : $\\forall j$, $ \\sum_i M_{i, j} = 1$. Cette propriété découle des contraintes de représentation des préférences au premier et au deuxième tour que nous avons évoquées plus haut ($\\sum_i p^k_i = 1$ et $\\sum_j q^k_j = 1$).\n",
    "\n",
    "D'une cette certaine façon, cette matrice de transition décrit exactement les affinités de chacun des individus pour les différents choix de vote au niveau de la population globale. C'est donc un indicateur des report de vote qui vont être effectivement effectués entre les deux tours."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Collecte des données\n",
    "\n",
    "La première partie de ce travail consiste à collecter les données et elle est représenté d'une façon utile. On va utiliser les données disponibles sur https://www.data.gouv.fr en se concentrant sur les résultats définitifs par bureau de vote. \n",
    "Commençons notre procédure avec le traitement des données du premier tour. Une fois que nous aurons décortiqué cette méthode, nous passerons au deuxième tour.\n",
    "\n",
    "### Données du premier tour\n",
    "\n",
    "Pour cela nous allons utiliser deux premières librairie python : `numpy` pour le traitement de données numériques puis `pandas` pour la représentation deces données sous forme de tableau tableaux."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut directement enregistrer à partir de l'adresse des données puis extraire ses données numériques depuis le tableau Excel grâce a la [fonction suivante](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.read_excel.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
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   "source": [
    "fname = '/tmp/T1.xlsx'\n",
    "\n",
    "if not os.path.isfile(fname):\n",
    "    url = 'https://static.data.gouv.fr/resources/election-presidentielle-des-10-et-24-avril-2022-resultats-definitifs-du-1er-tour/20220414-152612/resultats-par-niveau-burvot-t1-france-entiere.xlsx' # XLSX\n",
    "    import urllib.request\n",
    "    urllib.request.urlretrieve(url, fname)\n",
    "\n",
    "T1 = pd.read_excel(fname)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut avoir une première idée de ces données et du nombre total de bureaux de vote :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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   "outputs": [
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       "      <th>Libellé de la circonscription</th>\n",
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       "      <th>Code du b.vote</th>\n",
       "      <th>Inscrits</th>\n",
       "      <th>Abstentions</th>\n",
       "      <th>% Abs/Ins</th>\n",
       "      <th>...</th>\n",
       "      <th>Unnamed: 95</th>\n",
       "      <th>Unnamed: 96</th>\n",
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       "      <td>231</td>\n",
       "      <td>Taipei</td>\n",
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       "      <td>55.12</td>\n",
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       "      <td>Nour-Soultan</td>\n",
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       "      <td>Nicolas</td>\n",
       "      <td>1</td>\n",
       "      <td>0.85</td>\n",
       "      <td>1.96</td>\n",
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       "      <th>69680</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
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       "      <td>Monterrey</td>\n",
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       "      <td>ZZ</td>\n",
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       "      <td>2</td>\n",
       "      <td>2ème circonscription</td>\n",
       "      <td>235</td>\n",
       "      <td>Bahamas (Nassau)</td>\n",
       "      <td>0001</td>\n",
       "      <td>136</td>\n",
       "      <td>78</td>\n",
       "      <td>57.35</td>\n",
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       "      Code du département           Libellé du département  \\\n",
       "69677                  ZZ  Français établis hors de France   \n",
       "69678                  ZZ  Français établis hors de France   \n",
       "69679                  ZZ  Français établis hors de France   \n",
       "69680                  ZZ  Français établis hors de France   \n",
       "69681                  ZZ  Français établis hors de France   \n",
       "\n",
       "       Code de la circonscription Libellé de la circonscription  \\\n",
       "69677                           6          6ème circonscription   \n",
       "69678                          11         11ème circonscription   \n",
       "69679                          11         11ème circonscription   \n",
       "69680                           2          2ème circonscription   \n",
       "69681                           2          2ème circonscription   \n",
       "\n",
       "       Code de la commune Libellé de la commune Code du b.vote  Inscrits  \\\n",
       "69677                 229                Zurich           0001     24868   \n",
       "69678                 231                Taipei           0001      1709   \n",
       "69679                 233          Nour-Soultan           0001       117   \n",
       "69680                 234             Monterrey           0001       713   \n",
       "69681                 235      Bahamas (Nassau)           0001       136   \n",
       "\n",
       "       Abstentions  % Abs/Ins  ...  Unnamed: 95  Unnamed: 96  Unnamed: 97  \\\n",
       "69677        14101      56.70  ...           47         0.19         0.44   \n",
       "69678          942      55.12  ...           10         0.59         1.32   \n",
       "69679           64      54.70  ...            0         0.00         0.00   \n",
       "69680          553      77.56  ...            1         0.14         0.63   \n",
       "69681           78      57.35  ...            0         0.00         0.00   \n",
       "\n",
       "       Unnamed: 98  Unnamed: 99   Unnamed: 100  Unnamed: 101  Unnamed: 102  \\\n",
       "69677           12            M  DUPONT-AIGNAN       Nicolas           189   \n",
       "69678           12            M  DUPONT-AIGNAN       Nicolas            10   \n",
       "69679           12            M  DUPONT-AIGNAN       Nicolas             1   \n",
       "69680           12            M  DUPONT-AIGNAN       Nicolas             1   \n",
       "69681           12            M  DUPONT-AIGNAN       Nicolas             1   \n",
       "\n",
       "       Unnamed: 103  Unnamed: 104  \n",
       "69677          0.76          1.77  \n",
       "69678          0.59          1.32  \n",
       "69679          0.85          1.96  \n",
       "69680          0.14          0.63  \n",
       "69681          0.74          1.82  \n",
       "\n",
       "[5 rows x 105 columns]"
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   ],
   "source": [
    "T1.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les données sont organisées suivant des colonnes qui vont représenter les différents choix et aussi d'autres métadonnées. Il va falloir faire quelques hypothèses pour récupérer les données utiles…"
   ]
  },
  {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Code du département', 'Libellé du département',\n",
       "       'Code de la circonscription', 'Libellé de la circonscription',\n",
       "       'Code de la commune', 'Libellé de la commune', 'Code du b.vote',\n",
       "       'Inscrits', 'Abstentions', '% Abs/Ins',\n",
       "       ...\n",
       "       'Unnamed: 95', 'Unnamed: 96', 'Unnamed: 97', 'Unnamed: 98',\n",
       "       'Unnamed: 99', 'Unnamed: 100', 'Unnamed: 101', 'Unnamed: 102',\n",
       "       'Unnamed: 103', 'Unnamed: 104'],\n",
       "      dtype='object', length=105)"
      ]
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     "execution_count": 5,
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   ],
   "source": [
    "T1.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Première colonne concerne les nuls, blancs et abstention, que l'on peut enregistrer dans un nouveau tableau :"
   ]
  },
  {
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       "      <th>Blancs</th>\n",
       "      <th>Abstentions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>18</td>\n",
       "      <td>266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>15</td>\n",
       "      <td>265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>246</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Nuls  Blancs  Abstentions\n",
       "0     1      16          108\n",
       "1     1       3           38\n",
       "2     5      18          266\n",
       "3     6      15          265\n",
       "4     8      10          246"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1 = T1[['Nuls', 'Blancs', 'Abstentions']].copy()\n",
    "df_1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.852451Z",
     "iopub.status.busy": "2022-06-03T06:43:05.851134Z",
     "iopub.status.idle": "2022-06-03T06:43:05.854712Z",
     "shell.execute_reply": "2022-06-03T06:43:05.855040Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nuls</th>\n",
       "      <th>Blancs</th>\n",
       "      <th>Abstentions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>18</td>\n",
       "      <td>266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>15</td>\n",
       "      <td>265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69677</th>\n",
       "      <td>31</td>\n",
       "      <td>40</td>\n",
       "      <td>14101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69678</th>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69679</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69680</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69681</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>69682 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Nuls  Blancs  Abstentions\n",
       "0         1      16          108\n",
       "1         1       3           38\n",
       "2         5      18          266\n",
       "3         6      15          265\n",
       "4         8      10          246\n",
       "...     ...     ...          ...\n",
       "69677    31      40        14101\n",
       "69678     2       8          942\n",
       "69679     0       2           64\n",
       "69680     2       0          553\n",
       "69681     0       3           78\n",
       "\n",
       "[69682 rows x 3 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extraction des résultats de vote"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les 23 premières colonnes correspondent aux métadonnées :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.858540Z",
     "iopub.status.busy": "2022-06-03T06:43:05.858069Z",
     "iopub.status.idle": "2022-06-03T06:43:05.859986Z",
     "shell.execute_reply": "2022-06-03T06:43:05.860378Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Code du département', 'Libellé du département',\n",
       "       'Code de la circonscription', 'Libellé de la circonscription',\n",
       "       'Code de la commune', 'Libellé de la commune', 'Code du b.vote',\n",
       "       'Inscrits', 'Abstentions', '% Abs/Ins', 'Votants', '% Vot/Ins',\n",
       "       'Blancs', '% Blancs/Ins', '% Blancs/Vot', 'Nuls', '% Nuls/Ins',\n",
       "       '% Nuls/Vot', 'Exprimés', '% Exp/Ins', '% Exp/Vot', 'N°Panneau',\n",
       "       'Sexe'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T1.columns[:23]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les colonnes suivant la colonne numéro 23 vont concerner les résultats candidats par candidats :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.863454Z",
     "iopub.status.busy": "2022-06-03T06:43:05.862971Z",
     "iopub.status.idle": "2022-06-03T06:43:05.864698Z",
     "shell.execute_reply": "2022-06-03T06:43:05.865193Z"
    }
   },
   "outputs": [],
   "source": [
    "col_start = 23\n",
    "col_par_cdt = 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut extraire les noms des candidats présents au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.869418Z",
     "iopub.status.busy": "2022-06-03T06:43:05.868875Z",
     "iopub.status.idle": "2022-06-03T06:43:05.871009Z",
     "shell.execute_reply": "2022-06-03T06:43:05.871342Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Nom                   ARTHAUD\n",
       "Unnamed: 30           ROUSSEL\n",
       "Unnamed: 37            MACRON\n",
       "Unnamed: 44          LASSALLE\n",
       "Unnamed: 51            LE PEN\n",
       "Unnamed: 58           ZEMMOUR\n",
       "Unnamed: 65         MÉLENCHON\n",
       "Unnamed: 72           HIDALGO\n",
       "Unnamed: 79             JADOT\n",
       "Unnamed: 86          PÉCRESSE\n",
       "Unnamed: 93            POUTOU\n",
       "Unnamed: 100    DUPONT-AIGNAN\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "candidats = T1.iloc[0][col_start::col_par_cdt]\n",
    "candidats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut par exemple extraire les résultats pour le premier bureau de vote et donner le nombre de suffrages exprimés pour chaque candidat :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.875562Z",
     "iopub.status.busy": "2022-06-03T06:43:05.875061Z",
     "iopub.status.idle": "2022-06-03T06:43:05.877228Z",
     "shell.execute_reply": "2022-06-03T06:43:05.877711Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Voix              3\n",
       "Unnamed: 32       6\n",
       "Unnamed: 39     150\n",
       "Unnamed: 46      18\n",
       "Unnamed: 53     149\n",
       "Unnamed: 60      43\n",
       "Unnamed: 67      66\n",
       "Unnamed: 74       5\n",
       "Unnamed: 81      30\n",
       "Unnamed: 88      26\n",
       "Unnamed: 95       3\n",
       "Unnamed: 102     21\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "résultats = T1.iloc[0][(col_start+2)::col_par_cdt]\n",
    "résultats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grâce à ces connaissances, nous allons pouvoir maintenant récolter les données pour chaque candidat et pour tous les bureaux de vote en utilisant la fonction suivante :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.881530Z",
     "iopub.status.busy": "2022-06-03T06:43:05.881063Z",
     "iopub.status.idle": "2022-06-03T06:43:05.891034Z",
     "shell.execute_reply": "2022-06-03T06:43:05.891374Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# colonne 25  résultats= [3 2 4 ... 0 0 0]\n",
      "# colonne 32  résultats= [ 6  7 30 ...  1  1  1]\n",
      "# colonne 39  résultats= [150  50 159 ...  25  96  25]\n",
      "# colonne 46  résultats= [18 10 24 ...  1  1  0]\n",
      "# colonne 53  résultats= [149  23 237 ...   3   4   3]\n",
      "# colonne 60  résultats= [43 14 69 ...  7 18 17]\n",
      "# colonne 67  résultats= [ 66  41 216 ...   9  19   2]\n",
      "# colonne 74  résultats= [ 5  3 15 ...  0  2  0]\n",
      "# colonne 81  résultats= [30 10 25 ...  4 10  0]\n",
      "# colonne 88  résultats= [26  8 40 ...  0  5  6]\n",
      "# colonne 95  résultats= [3 3 8 ... 0 1 0]\n",
      "# colonne 102  résultats= [21  0 13 ...  1  1  1]\n"
     ]
    }
   ],
   "source": [
    "for i_candidat, candidat in enumerate(candidats):\n",
    "    i_col = col_start + i_candidat*col_par_cdt + 2\n",
    "    print('# colonne', i_col, ' résultats=', T1.iloc[:, i_col].values)\n",
    "    df_1[candidat] = T1.iloc[:, i_col].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous avons récolté les données utiles dans un nouveau tableau :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.894721Z",
     "iopub.status.busy": "2022-06-03T06:43:05.894250Z",
     "iopub.status.idle": "2022-06-03T06:43:05.903391Z",
     "shell.execute_reply": "2022-06-03T06:43:05.903718Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 69682 entries, 0 to 69681\n",
      "Data columns (total 15 columns):\n",
      " #   Column         Non-Null Count  Dtype\n",
      "---  ------         --------------  -----\n",
      " 0   Nuls           69682 non-null  int64\n",
      " 1   Blancs         69682 non-null  int64\n",
      " 2   Abstentions    69682 non-null  int64\n",
      " 3   ARTHAUD        69682 non-null  int64\n",
      " 4   ROUSSEL        69682 non-null  int64\n",
      " 5   MACRON         69682 non-null  int64\n",
      " 6   LASSALLE       69682 non-null  int64\n",
      " 7   LE PEN         69682 non-null  int64\n",
      " 8   ZEMMOUR        69682 non-null  int64\n",
      " 9   MÉLENCHON      69682 non-null  int64\n",
      " 10  HIDALGO        69682 non-null  int64\n",
      " 11  JADOT          69682 non-null  int64\n",
      " 12  PÉCRESSE       69682 non-null  int64\n",
      " 13  POUTOU         69682 non-null  int64\n",
      " 14  DUPONT-AIGNAN  69682 non-null  int64\n",
      "dtypes: int64(15)\n",
      "memory usage: 8.0 MB\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "print(df_1.info())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ceci nous permet par exemple d'extraire les résultats pour un candidat donné et pour tous les bureaux de vote :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.907492Z",
     "iopub.status.busy": "2022-06-03T06:43:05.907019Z",
     "iopub.status.idle": "2022-06-03T06:43:05.909335Z",
     "shell.execute_reply": "2022-06-03T06:43:05.909669Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0         3\n",
       "1         3\n",
       "2         8\n",
       "3         4\n",
       "4         3\n",
       "         ..\n",
       "69677    47\n",
       "69678    10\n",
       "69679     0\n",
       "69680     1\n",
       "69681     0\n",
       "Name: POUTOU, Length: 69682, dtype: int64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1['POUTOU']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En particulier, on a le nombre suivant de bureaux de vote :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.912788Z",
     "iopub.status.busy": "2022-06-03T06:43:05.912311Z",
     "iopub.status.idle": "2022-06-03T06:43:05.914415Z",
     "shell.execute_reply": "2022-06-03T06:43:05.914762Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69682"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et on peut calculer pour chaque alternative le nombre total de choix ainsi que le nombre total de choix dans les data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.917814Z",
     "iopub.status.busy": "2022-06-03T06:43:05.917355Z",
     "iopub.status.idle": "2022-06-03T06:43:05.923536Z",
     "shell.execute_reply": "2022-06-03T06:43:05.923864Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Nuls               247151\n",
       " Blancs             543609\n",
       " Abstentions      12824169\n",
       " ARTHAUD            197094\n",
       " ROUSSEL            802422\n",
       " MACRON            9783058\n",
       " LASSALLE          1101387\n",
       " LE PEN            8133828\n",
       " ZEMMOUR           2485226\n",
       " MÉLENCHON         7712520\n",
       " HIDALGO            616478\n",
       " JADOT             1627853\n",
       " PÉCRESSE          1679001\n",
       " POUTOU             268904\n",
       " DUPONT-AIGNAN      725176\n",
       " dtype: int64,\n",
       " 48747876)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.sum(), df_1.sum().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Par exemple, on note qu'environ 13 millions de personnes se sont abstenues, alors que environ 10 millions de personnes ont voté pour Macron."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans le reste, nous allons complétement ignorer les votes 'Nuls' et 'Abstebnsions'. En effet, des expériencesz précedentes (cf github) ont montré que ces valuers sont moins prédictibles. Pour celà, nous utilisons la fonction [`DataFrame.drop`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.drop.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.927131Z",
     "iopub.status.busy": "2022-06-03T06:43:05.926580Z",
     "iopub.status.idle": "2022-06-03T06:43:05.928930Z",
     "shell.execute_reply": "2022-06-03T06:43:05.929269Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Nuls', 'Blancs', 'Abstentions', 'ARTHAUD', 'ROUSSEL', 'MACRON',\n",
       "       'LASSALLE', 'LE PEN', 'ZEMMOUR', 'MÉLENCHON', 'HIDALGO', 'JADOT',\n",
       "       'PÉCRESSE', 'POUTOU', 'DUPONT-AIGNAN'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.932525Z",
     "iopub.status.busy": "2022-06-03T06:43:05.932032Z",
     "iopub.status.idle": "2022-06-03T06:43:05.945231Z",
     "shell.execute_reply": "2022-06-03T06:43:05.945574Z"
    }
   },
   "outputs": [],
   "source": [
    "df_1 = df_1.drop(columns=['Nuls', 'Blancs', 'Abstentions'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.949158Z",
     "iopub.status.busy": "2022-06-03T06:43:05.948681Z",
     "iopub.status.idle": "2022-06-03T06:43:05.951035Z",
     "shell.execute_reply": "2022-06-03T06:43:05.951367Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['ARTHAUD', 'ROUSSEL', 'MACRON', 'LASSALLE', 'LE PEN', 'ZEMMOUR',\n",
       "       'MÉLENCHON', 'HIDALGO', 'JADOT', 'PÉCRESSE', 'POUTOU', 'DUPONT-AIGNAN'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sous un format graphique on peut représenter ainsi les résultats du vote au premier tour et pour cela nous allons utiliser la librairie `matplotlib`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:05.954599Z",
     "iopub.status.busy": "2022-06-03T06:43:05.954118Z",
     "iopub.status.idle": "2022-06-03T06:43:06.545736Z",
     "shell.execute_reply": "2022-06-03T06:43:06.546124Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:06.550193Z",
     "iopub.status.busy": "2022-06-03T06:43:06.549713Z",
     "iopub.status.idle": "2022-06-03T06:43:06.699132Z",
     "shell.execute_reply": "2022-06-03T06:43:06.699630Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13, 5))\n",
    "k = df_1.sum()/df_1.sum().sum()\n",
    "ax = k.plot.bar(ax=ax)\n",
    "ax.set_xlabel('Choix 1er tour')\n",
    "ax.set_ylabel('Pourcentage');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque le fort taux d'abstention qui a été observé au premier tour, ainsi que les deux candidats qui se distinguent par le plus grand nombre de voix et qui sont sélectionnés pour le second tour."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Données du 2ème tour"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons maintenant répéter la même opération pour les données obtenues au deuxième tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:43:06.711288Z",
     "iopub.status.busy": "2022-06-03T06:43:06.710801Z",
     "iopub.status.idle": "2022-06-03T06:44:48.924676Z",
     "shell.execute_reply": "2022-06-03T06:44:48.925026Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Code du département</th>\n",
       "      <th>Libellé du département</th>\n",
       "      <th>Code de la circonscription</th>\n",
       "      <th>Libellé de la circonscription</th>\n",
       "      <th>Code de la commune</th>\n",
       "      <th>Libellé de la commune</th>\n",
       "      <th>Code du b.vote</th>\n",
       "      <th>Inscrits</th>\n",
       "      <th>Abstentions</th>\n",
       "      <th>% Abs/Ins</th>\n",
       "      <th>...</th>\n",
       "      <th>Voix</th>\n",
       "      <th>% Voix/Ins</th>\n",
       "      <th>% Voix/Exp</th>\n",
       "      <th>Unnamed: 28</th>\n",
       "      <th>Unnamed: 29</th>\n",
       "      <th>Unnamed: 30</th>\n",
       "      <th>Unnamed: 31</th>\n",
       "      <th>Unnamed: 32</th>\n",
       "      <th>Unnamed: 33</th>\n",
       "      <th>Unnamed: 34</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>69677</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>6</td>\n",
       "      <td>6ème circonscription</td>\n",
       "      <td>229</td>\n",
       "      <td>Zurich</td>\n",
       "      <td>0001</td>\n",
       "      <td>24867</td>\n",
       "      <td>13153</td>\n",
       "      <td>52.89</td>\n",
       "      <td>...</td>\n",
       "      <td>10166</td>\n",
       "      <td>40.88</td>\n",
       "      <td>88.88</td>\n",
       "      <td>2</td>\n",
       "      <td>F</td>\n",
       "      <td>LE PEN</td>\n",
       "      <td>Marine</td>\n",
       "      <td>1272</td>\n",
       "      <td>5.12</td>\n",
       "      <td>11.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69678</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>11</td>\n",
       "      <td>11ème circonscription</td>\n",
       "      <td>231</td>\n",
       "      <td>Taipei</td>\n",
       "      <td>0001</td>\n",
       "      <td>1703</td>\n",
       "      <td>928</td>\n",
       "      <td>54.49</td>\n",
       "      <td>...</td>\n",
       "      <td>611</td>\n",
       "      <td>35.88</td>\n",
       "      <td>82.23</td>\n",
       "      <td>2</td>\n",
       "      <td>F</td>\n",
       "      <td>LE PEN</td>\n",
       "      <td>Marine</td>\n",
       "      <td>132</td>\n",
       "      <td>7.75</td>\n",
       "      <td>17.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69679</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>11</td>\n",
       "      <td>11ème circonscription</td>\n",
       "      <td>233</td>\n",
       "      <td>Nour-Soultan</td>\n",
       "      <td>0001</td>\n",
       "      <td>117</td>\n",
       "      <td>64</td>\n",
       "      <td>54.70</td>\n",
       "      <td>...</td>\n",
       "      <td>39</td>\n",
       "      <td>33.33</td>\n",
       "      <td>78.00</td>\n",
       "      <td>2</td>\n",
       "      <td>F</td>\n",
       "      <td>LE PEN</td>\n",
       "      <td>Marine</td>\n",
       "      <td>11</td>\n",
       "      <td>9.40</td>\n",
       "      <td>22.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69680</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>2</td>\n",
       "      <td>2ème circonscription</td>\n",
       "      <td>234</td>\n",
       "      <td>Monterrey</td>\n",
       "      <td>0001</td>\n",
       "      <td>715</td>\n",
       "      <td>510</td>\n",
       "      <td>71.33</td>\n",
       "      <td>...</td>\n",
       "      <td>181</td>\n",
       "      <td>25.31</td>\n",
       "      <td>89.60</td>\n",
       "      <td>2</td>\n",
       "      <td>F</td>\n",
       "      <td>LE PEN</td>\n",
       "      <td>Marine</td>\n",
       "      <td>21</td>\n",
       "      <td>2.94</td>\n",
       "      <td>10.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69681</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>2</td>\n",
       "      <td>2ème circonscription</td>\n",
       "      <td>235</td>\n",
       "      <td>Bahamas (Nassau)</td>\n",
       "      <td>0001</td>\n",
       "      <td>137</td>\n",
       "      <td>78</td>\n",
       "      <td>56.93</td>\n",
       "      <td>...</td>\n",
       "      <td>35</td>\n",
       "      <td>25.55</td>\n",
       "      <td>68.63</td>\n",
       "      <td>2</td>\n",
       "      <td>F</td>\n",
       "      <td>LE PEN</td>\n",
       "      <td>Marine</td>\n",
       "      <td>16</td>\n",
       "      <td>11.68</td>\n",
       "      <td>31.37</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 35 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Code du département           Libellé du département  \\\n",
       "69677                  ZZ  Français établis hors de France   \n",
       "69678                  ZZ  Français établis hors de France   \n",
       "69679                  ZZ  Français établis hors de France   \n",
       "69680                  ZZ  Français établis hors de France   \n",
       "69681                  ZZ  Français établis hors de France   \n",
       "\n",
       "       Code de la circonscription Libellé de la circonscription  \\\n",
       "69677                           6          6ème circonscription   \n",
       "69678                          11         11ème circonscription   \n",
       "69679                          11         11ème circonscription   \n",
       "69680                           2          2ème circonscription   \n",
       "69681                           2          2ème circonscription   \n",
       "\n",
       "       Code de la commune Libellé de la commune Code du b.vote  Inscrits  \\\n",
       "69677                 229                Zurich           0001     24867   \n",
       "69678                 231                Taipei           0001      1703   \n",
       "69679                 233          Nour-Soultan           0001       117   \n",
       "69680                 234             Monterrey           0001       715   \n",
       "69681                 235      Bahamas (Nassau)           0001       137   \n",
       "\n",
       "       Abstentions  % Abs/Ins  ...   Voix  % Voix/Ins  % Voix/Exp  \\\n",
       "69677        13153      52.89  ...  10166       40.88       88.88   \n",
       "69678          928      54.49  ...    611       35.88       82.23   \n",
       "69679           64      54.70  ...     39       33.33       78.00   \n",
       "69680          510      71.33  ...    181       25.31       89.60   \n",
       "69681           78      56.93  ...     35       25.55       68.63   \n",
       "\n",
       "       Unnamed: 28  Unnamed: 29  Unnamed: 30  Unnamed: 31  Unnamed: 32  \\\n",
       "69677            2            F       LE PEN       Marine         1272   \n",
       "69678            2            F       LE PEN       Marine          132   \n",
       "69679            2            F       LE PEN       Marine           11   \n",
       "69680            2            F       LE PEN       Marine           21   \n",
       "69681            2            F       LE PEN       Marine           16   \n",
       "\n",
       "       Unnamed: 33  Unnamed: 34  \n",
       "69677         5.12        11.12  \n",
       "69678         7.75        17.77  \n",
       "69679         9.40        22.00  \n",
       "69680         2.94        10.40  \n",
       "69681        11.68        31.37  \n",
       "\n",
       "[5 rows x 35 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fname = '/tmp/T2.xlsx'\n",
    "\n",
    "if not os.path.isfile(fname):\n",
    "    url = 'https://static.data.gouv.fr/resources/election-presidentielle-des-10-et-24-avril-2022-resultats-definitifs-du-2nd-tour/20220428-142301/resultats-par-niveau-burvot-t2-france-entiere.xlsx' # XLSX\n",
    "    import urllib.request\n",
    "    urllib.request.urlretrieve(url, fname)\n",
    "\n",
    "T2 = pd.read_excel(fname)\n",
    "\n",
    "T2.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On vérifie que les données sont une nouvelle fois organisé suivant la même structure :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:48.928887Z",
     "iopub.status.busy": "2022-06-03T06:44:48.928391Z",
     "iopub.status.idle": "2022-06-03T06:44:48.930726Z",
     "shell.execute_reply": "2022-06-03T06:44:48.931061Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Code du département', 'Libellé du département',\n",
       "       'Code de la circonscription', 'Libellé de la circonscription',\n",
       "       'Code de la commune', 'Libellé de la commune', 'Code du b.vote',\n",
       "       'Inscrits', 'Abstentions', '% Abs/Ins', 'Votants', '% Vot/Ins',\n",
       "       'Blancs', '% Blancs/Ins', '% Blancs/Vot', 'Nuls', '% Nuls/Ins',\n",
       "       '% Nuls/Vot', 'Exprimés', '% Exp/Ins', '% Exp/Vot', 'N°Panneau', 'Sexe',\n",
       "       'Nom', 'Prénom', 'Voix', '% Voix/Ins', '% Voix/Exp', 'Unnamed: 28',\n",
       "       'Unnamed: 29', 'Unnamed: 30', 'Unnamed: 31', 'Unnamed: 32',\n",
       "       'Unnamed: 33', 'Unnamed: 34'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:48.934530Z",
     "iopub.status.busy": "2022-06-03T06:44:48.934050Z",
     "iopub.status.idle": "2022-06-03T06:44:48.936316Z",
     "shell.execute_reply": "2022-06-03T06:44:48.936642Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Code du département', 'Libellé du département',\n",
       "       'Code de la circonscription', 'Libellé de la circonscription',\n",
       "       'Code de la commune', 'Libellé de la commune', 'Code du b.vote',\n",
       "       'Inscrits', 'Abstentions', '% Abs/Ins', 'Votants', '% Vot/Ins',\n",
       "       'Blancs', '% Blancs/Ins', '% Blancs/Vot', 'Nuls', '% Nuls/Ins',\n",
       "       '% Nuls/Vot', 'Exprimés', '% Exp/Ins', '% Exp/Vot', 'N°Panneau',\n",
       "       'Sexe'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.columns[:23]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:48.940066Z",
     "iopub.status.busy": "2022-06-03T06:44:48.939508Z",
     "iopub.status.idle": "2022-06-03T06:44:48.941864Z",
     "shell.execute_reply": "2022-06-03T06:44:48.942193Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Nom', 'Prénom', 'Voix', '% Voix/Ins', '% Voix/Exp', 'Unnamed: 28',\n",
       "       'Unnamed: 29', 'Unnamed: 30', 'Unnamed: 31', 'Unnamed: 32',\n",
       "       'Unnamed: 33', 'Unnamed: 34'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.columns[23:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:48.946147Z",
     "iopub.status.busy": "2022-06-03T06:44:48.945613Z",
     "iopub.status.idle": "2022-06-03T06:44:48.947823Z",
     "shell.execute_reply": "2022-06-03T06:44:48.948149Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Nom              MACRON\n",
       "Prénom         Emmanuel\n",
       "Voix                237\n",
       "% Voix/Ins        36.86\n",
       "% Voix/Exp        52.67\n",
       "Unnamed: 28           2\n",
       "Unnamed: 29           F\n",
       "Unnamed: 30      LE PEN\n",
       "Unnamed: 31      Marine\n",
       "Unnamed: 32         213\n",
       "Unnamed: 33       33.13\n",
       "Unnamed: 34       47.33\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.iloc[0, 23:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:48.952272Z",
     "iopub.status.busy": "2022-06-03T06:44:48.951776Z",
     "iopub.status.idle": "2022-06-03T06:44:48.953969Z",
     "shell.execute_reply": "2022-06-03T06:44:48.954362Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Nom            MACRON\n",
       "Unnamed: 30    LE PEN\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col_start = 23\n",
    "col_par_cdt = 7\n",
    "candidats = T2.iloc[0][col_start::col_par_cdt]\n",
    "candidats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Une fois cette vérification faite nous pouvons extraire les données dans un nouveau tableau :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:48.958477Z",
     "iopub.status.busy": "2022-06-03T06:44:48.958014Z",
     "iopub.status.idle": "2022-06-03T06:44:48.962400Z",
     "shell.execute_reply": "2022-06-03T06:44:48.962728Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nuls</th>\n",
       "      <th>Blancs</th>\n",
       "      <th>Abstentions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>42</td>\n",
       "      <td>146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>23</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>71</td>\n",
       "      <td>322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18</td>\n",
       "      <td>45</td>\n",
       "      <td>313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>21</td>\n",
       "      <td>87</td>\n",
       "      <td>303</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Nuls  Blancs  Abstentions\n",
       "0     5      42          146\n",
       "1     3      23           45\n",
       "2    22      71          322\n",
       "3    18      45          313\n",
       "4    21      87          303"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_2 = T2[['Nuls', 'Blancs', 'Abstentions']].copy()\n",
    "#df_1 = df_1.rename(columns={\"Nuls\": \"1_Nuls\", \"Abstentions\": \"1_Abstentions\"})\n",
    "df_2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous vérifions aussi que nous avons le même nombre de bureaux de vote :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:48.965776Z",
     "iopub.status.busy": "2022-06-03T06:44:48.965301Z",
     "iopub.status.idle": "2022-06-03T06:44:48.967567Z",
     "shell.execute_reply": "2022-06-03T06:44:48.967958Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69682"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:48.972171Z",
     "iopub.status.busy": "2022-06-03T06:44:48.971610Z",
     "iopub.status.idle": "2022-06-03T06:44:48.973998Z",
     "shell.execute_reply": "2022-06-03T06:44:48.974328Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25 [237  94 360 ...  39 181  35]\n",
      "32 [213  48 355 ...  11  21  16]\n"
     ]
    }
   ],
   "source": [
    "for i_candidat, candidat in enumerate(candidats):\n",
    "    i_col = col_start + i_candidat*col_par_cdt + 2\n",
    "    print(i_col, T2.iloc[:, i_col].values)\n",
    "    df_2[candidat] = T2.iloc[:, i_col].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:48.979911Z",
     "iopub.status.busy": "2022-06-03T06:44:48.976812Z",
     "iopub.status.idle": "2022-06-03T06:44:48.982150Z",
     "shell.execute_reply": "2022-06-03T06:44:48.982472Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nuls</th>\n",
       "      <th>Blancs</th>\n",
       "      <th>Abstentions</th>\n",
       "      <th>MACRON</th>\n",
       "      <th>LE PEN</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>42</td>\n",
       "      <td>146</td>\n",
       "      <td>237</td>\n",
       "      <td>213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>23</td>\n",
       "      <td>45</td>\n",
       "      <td>94</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>71</td>\n",
       "      <td>322</td>\n",
       "      <td>360</td>\n",
       "      <td>355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18</td>\n",
       "      <td>45</td>\n",
       "      <td>313</td>\n",
       "      <td>426</td>\n",
       "      <td>327</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>21</td>\n",
       "      <td>87</td>\n",
       "      <td>303</td>\n",
       "      <td>449</td>\n",
       "      <td>353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69677</th>\n",
       "      <td>49</td>\n",
       "      <td>227</td>\n",
       "      <td>13153</td>\n",
       "      <td>10166</td>\n",
       "      <td>1272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69678</th>\n",
       "      <td>6</td>\n",
       "      <td>26</td>\n",
       "      <td>928</td>\n",
       "      <td>611</td>\n",
       "      <td>132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69679</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>64</td>\n",
       "      <td>39</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69680</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>510</td>\n",
       "      <td>181</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69681</th>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>78</td>\n",
       "      <td>35</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>69682 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Nuls  Blancs  Abstentions  MACRON  LE PEN\n",
       "0         5      42          146     237     213\n",
       "1         3      23           45      94      48\n",
       "2        22      71          322     360     355\n",
       "3        18      45          313     426     327\n",
       "4        21      87          303     449     353\n",
       "...     ...     ...          ...     ...     ...\n",
       "69677    49     227        13153   10166    1272\n",
       "69678     6      26          928     611     132\n",
       "69679     0       3           64      39      11\n",
       "69680     1       2          510     181      21\n",
       "69681     1       7           78      35      16\n",
       "\n",
       "[69682 rows x 5 columns]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De la même façon que pour le premier tour, nous pouvons représenter les résultats totaux obtenus au second tour de façon graphique :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.019405Z",
     "iopub.status.busy": "2022-06-03T06:44:49.017123Z",
     "iopub.status.idle": "2022-06-03T06:44:49.108585Z",
     "shell.execute_reply": "2022-06-03T06:44:49.108940Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13, 5))\n",
    "k = df_2.sum()/df_2.sum().sum()\n",
    "ax = k.plot.bar(ax=ax)\n",
    "ax.set_xlabel('Candidat')\n",
    "#ax.set_xlim(1, 10)\n",
    "#ax.set_xticks(np.arange(1, 10)+.5)\n",
    "#ax.set_xticklabels(np.arange(1, 10)) , rotation=45\n",
    "ax.set_ylabel('pourcentage');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.112833Z",
     "iopub.status.busy": "2022-06-03T06:44:49.112309Z",
     "iopub.status.idle": "2022-06-03T06:44:49.116369Z",
     "shell.execute_reply": "2022-06-03T06:44:49.116696Z"
    }
   },
   "outputs": [],
   "source": [
    "df_2 = df_2.drop(columns=['Nuls', 'Blancs', 'Abstentions'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nettoyage des données (non aux nans)\n",
    "\n",
    "Certains bureaux de vote n'ont pas de votants au premier ou au deuxieme. Ceci peut engendrer des problèmes numériques en générant des divisions par zéro, des `Not a Number (NaN)` dans le jargon informatique. Comme ceux-ci représentent un nombre très faible d'électeurs nous allons les ignorer par rapport au reste de la population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons d'abord compter le nombre de bureaux de vote qui n'ont aucun suffrage enregistré:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.120303Z",
     "iopub.status.busy": "2022-06-03T06:44:49.119834Z",
     "iopub.status.idle": "2022-06-03T06:44:49.124146Z",
     "shell.execute_reply": "2022-06-03T06:44:49.124481Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70, 97)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(df_1.sum(axis=1)==0).sum(), (df_2.sum(axis=1)==0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons \"effacer\" ces bureaux du vote en commençant par filtrer ceux qui n'ont aucun suffrage enregistré au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.128260Z",
     "iopub.status.busy": "2022-06-03T06:44:49.127767Z",
     "iopub.status.idle": "2022-06-03T06:44:49.136821Z",
     "shell.execute_reply": "2022-06-03T06:44:49.137162Z"
    }
   },
   "outputs": [],
   "source": [
    "df_2.drop(df_2.loc[df_1.sum(axis=1)==0].index, inplace=True)\n",
    "df_1.drop(df_1.loc[df_1.sum(axis=1)==0].index, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.140842Z",
     "iopub.status.busy": "2022-06-03T06:44:49.140338Z",
     "iopub.status.idle": "2022-06-03T06:44:49.144395Z",
     "shell.execute_reply": "2022-06-03T06:44:49.144727Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 58)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(df_1.sum(axis=1)==0).sum(), (df_2.sum(axis=1)==0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et maintenant répéter la même procédure sur les bureaux de vote qui n'ont aucun suffrage enregistré au second tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.148187Z",
     "iopub.status.busy": "2022-06-03T06:44:49.147679Z",
     "iopub.status.idle": "2022-06-03T06:44:49.157134Z",
     "shell.execute_reply": "2022-06-03T06:44:49.157482Z"
    }
   },
   "outputs": [],
   "source": [
    "df_1.drop(df_1.loc[df_2.sum(axis=1)==0].index, inplace=True)\n",
    "df_2.drop(df_2.loc[df_2.sum(axis=1)==0].index, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.160889Z",
     "iopub.status.busy": "2022-06-03T06:44:49.160415Z",
     "iopub.status.idle": "2022-06-03T06:44:49.164613Z",
     "shell.execute_reply": "2022-06-03T06:44:49.164946Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(df_1.sum(axis=1)==0).sum(), (df_2.sum(axis=1)==0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistiques de second ordre\n",
    "\n",
    "Comme cela est montré dans l'[article du Monde](https://www.lemonde.fr/les-decodeurs/article/2022/05/04/election-presidentielle-2022-quels-reports-de-voix-entre-les-deux-tours_6124672_4355770.html) on peut montrer la dépendance entre les choix qui sont effectués au premier tour et ceux qui sont effectués au deuxième tour. On va utiliser des représentations graphiques similaires à ceux de l'article pour d'une première part les répliquer et vérifier que la méthode est correct et d'un autre côté pour mieux comprendre comment nous pouvons tirer dans ses enseignements depuis ces observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.168401Z",
     "iopub.status.busy": "2022-06-03T06:44:49.167906Z",
     "iopub.status.idle": "2022-06-03T06:44:49.169680Z",
     "shell.execute_reply": "2022-06-03T06:44:49.170003Z"
    }
   },
   "outputs": [],
   "source": [
    "df_12 = pd.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.175280Z",
     "iopub.status.busy": "2022-06-03T06:44:49.172684Z",
     "iopub.status.idle": "2022-06-03T06:44:49.178188Z",
     "shell.execute_reply": "2022-06-03T06:44:49.178542Z"
    }
   },
   "outputs": [],
   "source": [
    "df_12['1_MÉLENCHON'] = df_1['MÉLENCHON'].copy()\n",
    "df_12['MACRON'] = df_2['MACRON'].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.181878Z",
     "iopub.status.busy": "2022-06-03T06:44:49.181308Z",
     "iopub.status.idle": "2022-06-03T06:44:49.187267Z",
     "shell.execute_reply": "2022-06-03T06:44:49.187656Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 69554 entries, 0 to 69681\n",
      "Data columns (total 2 columns):\n",
      " #   Column       Non-Null Count  Dtype\n",
      "---  ------       --------------  -----\n",
      " 0   1_MÉLENCHON  69554 non-null  int64\n",
      " 1   MACRON       69554 non-null  int64\n",
      "dtypes: int64(2)\n",
      "memory usage: 1.6 MB\n"
     ]
    }
   ],
   "source": [
    "df_12.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.190904Z",
     "iopub.status.busy": "2022-06-03T06:44:49.190400Z",
     "iopub.status.idle": "2022-06-03T06:44:49.194705Z",
     "shell.execute_reply": "2022-06-03T06:44:49.195030Z"
    }
   },
   "outputs": [],
   "source": [
    "df_12['1_MÉLENCHON'] = df_12['1_MÉLENCHON']/df_1.sum(axis=1)\n",
    "df_12['MACRON'] = df_12['MACRON']/df_2.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:44:49.198125Z",
     "iopub.status.busy": "2022-06-03T06:44:49.197627Z",
     "iopub.status.idle": "2022-06-03T06:45:01.663017Z",
     "shell.execute_reply": "2022-06-03T06:45:01.663465Z"
    }
   },
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:01.669219Z",
     "iopub.status.busy": "2022-06-03T06:45:01.667970Z",
     "iopub.status.idle": "2022-06-03T06:45:02.255870Z",
     "shell.execute_reply": "2022-06-03T06:45:02.256225Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.jointplot(x=df_12['1_MÉLENCHON'], y=df_12['MACRON'], kind='hist', height=8);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque effectivement une dépendance entre le choix. Un premier candidat effectué au premier tour et celui qui est effectué au second tour. Nous allons essayer d'inférer de façon plus précise cette dépendance grâce au modèle de transition que nous avons exposer au début de cet article."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modèle de prédiction du transfert des voix\n",
    "\n",
    "Tenant que nous avons récolté toutes les données pour les deux tours, et que nous avons une idée qu'il existe une dépendance entre les choix qui sont faits entre un tour et le suivant, nous allons pouvoir utiliser des librairies de tes apprentissage automatique machine Learning en anglais pour pouvoir insérer le report de voix entre les deux tours :. Pour cela nous allons utiliser un travail précédemment effectué appliquer à l'[exploration du comportement humain](https://laurentperrinet.github.io/sciblog/posts/2020-04-08-fitting-a-psychometric-curve-using-pytorch.html) ou alors pour [l'épidémiologie du Covid](https://laurentperrinet.github.io/sciblog/posts/2020-10-10-fitting-covid-data.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Formatage des données au format de la librairie `torch`\n",
    "\n",
    "Pendant un aperçu des résultats au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:02.263656Z",
     "iopub.status.busy": "2022-06-03T06:45:02.263058Z",
     "iopub.status.idle": "2022-06-03T06:45:02.265452Z",
     "shell.execute_reply": "2022-06-03T06:45:02.265786Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ARTHAUD</th>\n",
       "      <th>ROUSSEL</th>\n",
       "      <th>MACRON</th>\n",
       "      <th>LASSALLE</th>\n",
       "      <th>LE PEN</th>\n",
       "      <th>ZEMMOUR</th>\n",
       "      <th>MÉLENCHON</th>\n",
       "      <th>HIDALGO</th>\n",
       "      <th>JADOT</th>\n",
       "      <th>PÉCRESSE</th>\n",
       "      <th>POUTOU</th>\n",
       "      <th>DUPONT-AIGNAN</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>150</td>\n",
       "      <td>18</td>\n",
       "      <td>149</td>\n",
       "      <td>43</td>\n",
       "      <td>66</td>\n",
       "      <td>5</td>\n",
       "      <td>30</td>\n",
       "      <td>26</td>\n",
       "      <td>3</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>50</td>\n",
       "      <td>10</td>\n",
       "      <td>23</td>\n",
       "      <td>14</td>\n",
       "      <td>41</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>30</td>\n",
       "      <td>159</td>\n",
       "      <td>24</td>\n",
       "      <td>237</td>\n",
       "      <td>69</td>\n",
       "      <td>216</td>\n",
       "      <td>15</td>\n",
       "      <td>25</td>\n",
       "      <td>40</td>\n",
       "      <td>8</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>13</td>\n",
       "      <td>201</td>\n",
       "      <td>19</td>\n",
       "      <td>210</td>\n",
       "      <td>68</td>\n",
       "      <td>194</td>\n",
       "      <td>19</td>\n",
       "      <td>46</td>\n",
       "      <td>42</td>\n",
       "      <td>4</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>18</td>\n",
       "      <td>229</td>\n",
       "      <td>28</td>\n",
       "      <td>227</td>\n",
       "      <td>74</td>\n",
       "      <td>227</td>\n",
       "      <td>16</td>\n",
       "      <td>65</td>\n",
       "      <td>35</td>\n",
       "      <td>3</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ARTHAUD  ROUSSEL  MACRON  LASSALLE  LE PEN  ZEMMOUR  MÉLENCHON  HIDALGO  \\\n",
       "0        3        6     150        18     149       43         66        5   \n",
       "1        2        7      50        10      23       14         41        3   \n",
       "2        4       30     159        24     237       69        216       15   \n",
       "3        6       13     201        19     210       68        194       19   \n",
       "4        8       18     229        28     227       74        227       16   \n",
       "\n",
       "   JADOT  PÉCRESSE  POUTOU  DUPONT-AIGNAN  \n",
       "0     30        26       3             21  \n",
       "1     10         8       3              0  \n",
       "2     25        40       8             13  \n",
       "3     46        42       4             20  \n",
       "4     65        35       3             19  "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous avons donc comptabilisé ces différentes alternatives au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:02.269096Z",
     "iopub.status.busy": "2022-06-03T06:45:02.268547Z",
     "iopub.status.idle": "2022-06-03T06:45:02.270791Z",
     "shell.execute_reply": "2022-06-03T06:45:02.271117Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_1.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De sorte que sur les bureaux de vote que nous avons validé nous avons les deux tableaux suivants :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:02.274637Z",
     "iopub.status.busy": "2022-06-03T06:45:02.274151Z",
     "iopub.status.idle": "2022-06-03T06:45:02.276365Z",
     "shell.execute_reply": "2022-06-03T06:45:02.276694Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((69554, 12), (69554, 2))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.values.shape, df_2.values.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons maintenant utiliser la librairie `torch` pour enregistrer ses données sous la forme d'une matrice (ou tenseur dans le jargon de cette librairie) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:02.279975Z",
     "iopub.status.busy": "2022-06-03T06:45:02.279504Z",
     "iopub.status.idle": "2022-06-03T06:45:03.204676Z",
     "shell.execute_reply": "2022-06-03T06:45:03.205156Z"
    }
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "\n",
    "X_1, X_2 = df_1.values, df_2.values\n",
    "x_1, x_2 = torch.Tensor(X_1), torch.Tensor(X_2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.208895Z",
     "iopub.status.busy": "2022-06-03T06:45:03.208337Z",
     "iopub.status.idle": "2022-06-03T06:45:03.210695Z",
     "shell.execute_reply": "2022-06-03T06:45:03.211047Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([69554, 12])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_1.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ainsi nous allons très facilement pouvoir représenter les données pour pouvoir les apprendre. Une pratique extrêmement importante dans l'apprentissage automatique et de séparer les données qui sont utilisés pour apprendre le modèle, avec celles qui sont utilisés pour tester ce modèle :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.215346Z",
     "iopub.status.busy": "2022-06-03T06:45:03.214761Z",
     "iopub.status.idle": "2022-06-03T06:45:03.220409Z",
     "shell.execute_reply": "2022-06-03T06:45:03.220738Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch.utils.data import TensorDataset, DataLoader\n",
    "\n",
    "dataset = TensorDataset(x_1, x_2)\n",
    "\n",
    "# Random split\n",
    "train_set_size = int(len(dataset) * 0.8)\n",
    "test_set_size = len(dataset) - train_set_size\n",
    "train_set, test_set = torch.utils.data.random_split(dataset, [train_set_size, test_set_size])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ainsi nous pourrons utiliser l'ensemble d'apprentissage au cours des différentes époques d'apprentissage utilisé plus bas :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.223953Z",
     "iopub.status.busy": "2022-06-03T06:45:03.223472Z",
     "iopub.status.idle": "2022-06-03T06:45:03.225178Z",
     "shell.execute_reply": "2022-06-03T06:45:03.225562Z"
    }
   },
   "outputs": [],
   "source": [
    "train_loader = DataLoader(train_set, batch_size=32, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.229026Z",
     "iopub.status.busy": "2022-06-03T06:45:03.228458Z",
     "iopub.status.idle": "2022-06-03T06:45:03.237428Z",
     "shell.execute_reply": "2022-06-03T06:45:03.237768Z"
    }
   },
   "outputs": [],
   "source": [
    "for n_1, n_2 in train_loader:\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En particulier nous allons couper les données de façon aléatoire puis il est représenté sous la forme de différents « paquet » dont la taille est fixé ici à 32, et nous verrons plus tard que si cette procédure permet d'accélérer l'apprentissage la taille du paquet n'a plus d'influence sur le résultat final."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.241125Z",
     "iopub.status.busy": "2022-06-03T06:45:03.240565Z",
     "iopub.status.idle": "2022-06-03T06:45:03.242882Z",
     "shell.execute_reply": "2022-06-03T06:45:03.243209Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([32, 12]), torch.Size([32, 2]))"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_1.shape, n_2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans chaque paquet nous pouvons compter le nombre de votes pour les différentes alternatives :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.246984Z",
     "iopub.status.busy": "2022-06-03T06:45:03.246475Z",
     "iopub.status.idle": "2022-06-03T06:45:03.250136Z",
     "shell.execute_reply": "2022-06-03T06:45:03.250488Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([173., 184., 744., 679., 844., 434., 774., 394., 725., 676., 979., 153.,\n",
       "          46., 815., 258., 760.,  70., 489.,  77., 765., 155., 296., 695., 759.,\n",
       "         698., 217., 564., 458.,  59., 700.,  58., 681.]),\n",
       " tensor([161., 184., 693., 636., 777., 414., 704., 353., 711., 588., 842., 136.,\n",
       "          24., 702., 257., 727.,  71., 447.,  72., 724., 143., 260., 632., 674.,\n",
       "         642., 187., 484., 411.,  50., 612.,  62., 629.]))"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_1, sum_2 = n_1.sum(axis=1), n_2.sum(axis=1)\n",
    "sum_1, sum_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons aussi vérifier que parmi toutes les et les alternatives on peut calculer des fréquences d'occurrence, et que comme chaque individu peut faire un seul un choix est un seul, la somme de ses fréquences d'occurrence pour chacun des paquets est égal à $1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.253789Z",
     "iopub.status.busy": "2022-06-03T06:45:03.253310Z",
     "iopub.status.idle": "2022-06-03T06:45:03.256074Z",
     "shell.execute_reply": "2022-06-03T06:45:03.256480Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,\n",
       "        1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,\n",
       "        1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,\n",
       "        1.0000, 1.0000, 1.0000, 1.0000, 1.0000])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(n_1/sum_1[:, None]).sum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pourrons aussi aisément utiliser les données qui sont représentés dans l'ensemble de test :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.260370Z",
     "iopub.status.busy": "2022-06-03T06:45:03.259583Z",
     "iopub.status.idle": "2022-06-03T06:45:03.264457Z",
     "shell.execute_reply": "2022-06-03T06:45:03.264874Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([13911, 12]), torch.Size([13911, 2]))"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_1, n_2 = dataset[test_set.indices]\n",
    "n_1.shape, n_2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modèle `torch` de transition de probabilités\n",
    "\n",
    "\n",
    "Maintenant que nous avons correctement formater les données, nous allons exprimer dans le langage de la librairie torche le modèle qui nous permet d'exprimer la transition entre les préférences au premier tour et les préférences au premier second tour. En particulier la matrice de transition sera définie par une matric `self.M` de telle sorte que quand on l'utilise, la contrainte qui fait que la somme des éléments colonne par colonne est bien égal à $1$ (utilisation de `torch.softmax(self.M, axis=0)`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.269475Z",
     "iopub.status.busy": "2022-06-03T06:45:03.268979Z",
     "iopub.status.idle": "2022-06-03T06:45:03.270781Z",
     "shell.execute_reply": "2022-06-03T06:45:03.271119Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch.utils.data import TensorDataset, DataLoader, random_split\n",
    "import torch.nn.functional as F\n",
    "\n",
    "torch.set_default_tensor_type(\"torch.FloatTensor\")\n",
    "\n",
    "class TransfertVoix(torch.nn.Module):\n",
    "    def __init__(self, N_1er, N_2eme):\n",
    "        super(TransfertVoix, self).__init__()\n",
    "        self.lin = torch.nn.Linear(N_1er, N_2eme, bias=False)\n",
    "\n",
    "    def forward(self, p_2):\n",
    "        M = torch.softmax(self.lin.weight, axis=1)\n",
    "        p_1_pred = torch.matmul(p_2, M)\n",
    "        return p_1_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ce modèle va utiliser comme dimension le nombre de différentes alternatives au premier et deuxième tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.274484Z",
     "iopub.status.busy": "2022-06-03T06:45:03.273895Z",
     "iopub.status.idle": "2022-06-03T06:45:03.276137Z",
     "shell.execute_reply": "2022-06-03T06:45:03.276466Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12, 2)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N_1er, N_2eme = len(df_1.columns), len(df_2.columns)\n",
    "N_1er, N_2eme"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De telle sorte que nous allons pouvoir instancier un tel modèle, sachant que la matrice de transition sera choisi de façon totalement aléatoire et donc déconnecté des données à l'initialisation de cet apprentissage :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.279467Z",
     "iopub.status.busy": "2022-06-03T06:45:03.278992Z",
     "iopub.status.idle": "2022-06-03T06:45:03.281009Z",
     "shell.execute_reply": "2022-06-03T06:45:03.281483Z"
    }
   },
   "outputs": [],
   "source": [
    "trans = TransfertVoix(N_1er, N_2eme)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.284719Z",
     "iopub.status.busy": "2022-06-03T06:45:03.284258Z",
     "iopub.status.idle": "2022-06-03T06:45:03.286682Z",
     "shell.execute_reply": "2022-06-03T06:45:03.287025Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[-0.0981,  0.0304,  0.0021, -0.1506, -0.0572,  0.2719, -0.2644, -0.1255,\n",
      "          0.1123,  0.1804, -0.0747,  0.2480],\n",
      "        [ 0.0022,  0.0837,  0.2663, -0.0088,  0.0346, -0.2831, -0.0974, -0.1426,\n",
      "         -0.2109, -0.0489,  0.1639, -0.0108]], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "for p in trans.parameters():print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.290412Z",
     "iopub.status.busy": "2022-06-03T06:45:03.289747Z",
     "iopub.status.idle": "2022-06-03T06:45:03.292112Z",
     "shell.execute_reply": "2022-06-03T06:45:03.292440Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 12])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans.lin.weight.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.295689Z",
     "iopub.status.busy": "2022-06-03T06:45:03.295146Z",
     "iopub.status.idle": "2022-06-03T06:45:03.298464Z",
     "shell.execute_reply": "2022-06-03T06:45:03.298795Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.4749, 0.4867, 0.4343, 0.4646, 0.4771, 0.6353, 0.4583, 0.5043, 0.5801,\n",
       "         0.5571, 0.4406, 0.5643],\n",
       "        [0.5251, 0.5133, 0.5657, 0.5354, 0.5229, 0.3647, 0.5417, 0.4957, 0.4199,\n",
       "         0.4429, 0.5594, 0.4357]], grad_fn=<SoftmaxBackward0>)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.softmax(trans.lin.weight, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous vérifions que la contrainte sur chaque colonne de la matrice de transition et bien vérifiée :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.301975Z",
     "iopub.status.busy": "2022-06-03T06:45:03.301468Z",
     "iopub.status.idle": "2022-06-03T06:45:03.304397Z",
     "shell.execute_reply": "2022-06-03T06:45:03.304764Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1585, 0.1758, 0.1918, 0.1538, 0.1644, 0.1707, 0.1391, 0.1451, 0.1596,\n",
       "        0.1781, 0.1750, 0.1880], grad_fn=<SumBackward1>)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.softmax(trans.lin.weight, axis=1).sum(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exprimons maintenant pour chacun des bureaux de vote les probabilités de préférence qui sont exprimées localement :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.308064Z",
     "iopub.status.busy": "2022-06-03T06:45:03.307512Z",
     "iopub.status.idle": "2022-06-03T06:45:03.309784Z",
     "shell.execute_reply": "2022-06-03T06:45:03.310126Z"
    }
   },
   "outputs": [],
   "source": [
    "sum_1, sum_2 = n_1.sum(axis=1), n_2.sum(axis=1)\n",
    "p_1 = n_1/sum_1[:, None]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cette probabilité va pouvoir être multiplié par la matrice de transition de probabilité et nous vérifions dans les lignes suivantes la compatibilité entre les différentes dimensions des données représentées :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.314118Z",
     "iopub.status.busy": "2022-06-03T06:45:03.313518Z",
     "iopub.status.idle": "2022-06-03T06:45:03.316490Z",
     "shell.execute_reply": "2022-06-03T06:45:03.316839Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([13911, 12]),\n",
       " tensor([1.0000, 1.0000, 1.0000,  ..., 1.0000, 1.0000, 1.0000]))"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_1.shape, p_1.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.320029Z",
     "iopub.status.busy": "2022-06-03T06:45:03.319558Z",
     "iopub.status.idle": "2022-06-03T06:45:03.321874Z",
     "shell.execute_reply": "2022-06-03T06:45:03.322171Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([13911, 12]), torch.Size([2, 12]))"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_1.shape, trans.lin.weight.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ces différentes vérifications nous permettent de valider l'utilisation directe du modèle pour prédire la probabilité de préférence dans ce bureau de vote au second tour à partir de celle observée au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.325335Z",
     "iopub.status.busy": "2022-06-03T06:45:03.324863Z",
     "iopub.status.idle": "2022-06-03T06:45:03.338596Z",
     "shell.execute_reply": "2022-06-03T06:45:03.338923Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.0787, 0.0875, 0.0945, 0.0762, 0.0817, 0.0876, 0.0689, 0.0725, 0.0810,\n",
       "         0.0899, 0.0864, 0.0951], grad_fn=<MeanBackward1>),\n",
       " tensor(1.0000, grad_fn=<SumBackward0>))"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_1_pred = trans(n_2/sum_2[:, None])\n",
    "p_1_pred.mean(axis=0), p_1_pred.mean(axis=0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Au cours de l'apprentissage, nous allons pouvoir comparer cette probabilité prédit avec celle qui a été effectivement observée :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.342024Z",
     "iopub.status.busy": "2022-06-03T06:45:03.341555Z",
     "iopub.status.idle": "2022-06-03T06:45:03.344670Z",
     "shell.execute_reply": "2022-06-03T06:45:03.345015Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.5502, 0.4498]), tensor(1.))"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_2 = n_2/sum_2[:, None]\n",
    "p_2.mean(axis=0), p_2.mean(axis=0).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.348721Z",
     "iopub.status.busy": "2022-06-03T06:45:03.347784Z",
     "iopub.status.idle": "2022-06-03T06:45:03.350839Z",
     "shell.execute_reply": "2022-06-03T06:45:03.351161Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([13911, 12])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.matmul(p_2, torch.softmax(trans.lin.weight, axis=0)).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons aussi vérifier graphiquement que les résultats moyen des votes au second tour peuvent être inférer à partir des données de probabilité multiplié par la taille de chacun des bureaux de vote :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.367147Z",
     "iopub.status.busy": "2022-06-03T06:45:03.364273Z",
     "iopub.status.idle": "2022-06-03T06:45:03.481455Z",
     "shell.execute_reply": "2022-06-03T06:45:03.481788Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13, 5))\n",
    "k = df_1.sum()/df_1.sum().sum()\n",
    "ax = k.plot.bar(ax=ax)\n",
    "p_1_average = (p_1*sum_1[:, None]).sum(axis=0)/sum_1.sum()\n",
    "ax.plot(p_1_average)\n",
    "ax.set_xlabel('Candidat')\n",
    "ax.set_ylabel('pourcentage');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ainsi que la concordance entre les résultats finaux obtenu est ce que nous représentons dans notre modèle :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.486959Z",
     "iopub.status.busy": "2022-06-03T06:45:03.486395Z",
     "iopub.status.idle": "2022-06-03T06:45:03.489226Z",
     "shell.execute_reply": "2022-06-03T06:45:03.489586Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(ARTHAUD           0.560931\n",
       " ROUSSEL           2.284204\n",
       " MACRON           27.846250\n",
       " LASSALLE          3.133866\n",
       " LE PEN           23.149769\n",
       " ZEMMOUR           7.073121\n",
       " MÉLENCHON        21.955401\n",
       " HIDALGO           1.754605\n",
       " JADOT             4.633798\n",
       " PÉCRESSE          4.778629\n",
       " POUTOU            0.765426\n",
       " DUPONT-AIGNAN     2.063999\n",
       " dtype: float64,\n",
       " tensor([ 0.5574,  2.2767, 28.0722,  3.1070, 22.9868,  7.0757, 21.8803,  1.7588,\n",
       "          4.6858,  4.7777,  0.7654,  2.0562]))"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k*100, p_1_average*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.493155Z",
     "iopub.status.busy": "2022-06-03T06:45:03.492664Z",
     "iopub.status.idle": "2022-06-03T06:45:03.496214Z",
     "shell.execute_reply": "2022-06-03T06:45:03.496544Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.8100)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F.binary_cross_entropy(p_1_average, p_1_average, reduction=\"sum\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modèle `torch` d'apprentissage\n",
    "\n",
    "Maintenant que nous avons défini le modèle de transition des probabilités entre les préférences au premier tour et au second tour, nous pouvons maintenant écrire un algorithme d'apprentissage qui permet d'optimiser la concordance entre la prédiction et les observations. \n",
    "\n",
    "Nous allons utiliser les distributions observées $q$ et prédites $\\hat{q}$ (celle-ci dépendant de $M$) pour calculer un coût à minimiser\n",
    "$$\n",
    "\\mathcal{L} =  KL(q, \\hat{q})\n",
    "$$\n",
    "\n",
    "où la [divergence de Kullback-Leibler](https://fr.wikipedia.org/wiki/Divergence_de_Kullback-Leibler) est calculée comme\n",
    "\n",
    "$$\n",
    "KL(P, Q) = \\sum_j P_j \\cdot \\log \\frac {P_j}{Q_j}\n",
    "$$\n",
    "\n",
    "\n",
    "Cette divergence est l'équivalent d'une distance dans les espaces de probabilité. Mathématiquement, c'est une semi-normes car elle obéit à deux propriétés fondamentales: elle est toujours positive et est égale à zéro quand elle est appliquée à distributions identiques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.509395Z",
     "iopub.status.busy": "2022-06-03T06:45:03.508863Z",
     "iopub.status.idle": "2022-06-03T06:45:03.510732Z",
     "shell.execute_reply": "2022-06-03T06:45:03.511084Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch.nn.functional as F\n",
    "\n",
    "learning_rate = 0.001\n",
    "beta1, beta2 = 0.99, 0\n",
    "# beta1, beta2 = 0.9, 0.999\n",
    "num_epochs = 2 ** 10 + 1\n",
    "batch_size = 2 ** 9\n",
    "do_optim = False\n",
    "do_optim = True\n",
    "\n",
    "def pdf_loss(p_pred, p, weight, loss_type):\n",
    "    if loss_type=='kl':\n",
    "        ind_nonzero = (p==0) + (p_pred==0)\n",
    "        p[p==0] = 1.\n",
    "        p_pred[p_pred==0] = 1.\n",
    "        p[p_pred==0] = 1.\n",
    "        kl_div = p * (p.log() - p_pred.log())\n",
    "        kl_div[ind_nonzero] = 0\n",
    "        loss_train = (kl_div * weight[:, None]).sum()\n",
    "    elif loss_type=='l1':\n",
    "        div = torch.absolute(p - p_pred)\n",
    "        loss_train = (div * weight[:, None]).sum() \n",
    "    else:\n",
    "        loss_train = F.binary_cross_entropy(p_pred, p, reduction=\"sum\", weight=weight[:, None])\n",
    "        loss_train -= F.binary_cross_entropy(p, p, reduction=\"sum\", weight=weight[:, None])\n",
    "    return loss_train\n",
    "\n",
    "def fit_data(\n",
    "    df_1,\n",
    "    df_2,\n",
    "    learning_rate=learning_rate,\n",
    "    batch_size=batch_size,\n",
    "    num_epochs=num_epochs,\n",
    "    loss_type='bce',\n",
    "    beta1=beta1,\n",
    "    beta2=beta2, \n",
    "    do_optim=do_optim, \n",
    "    split_ratio=.9, \n",
    "    seed=2022, # graine du générateur de nombre aléatoires utilisé dans le split test vs train\n",
    "    verbose=False\n",
    "):\n",
    "\n",
    "    device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "    N_1er, N_2eme = len(df_1.columns), len(df_2.columns)\n",
    "    trans = TransfertVoix(N_1er, N_2eme)\n",
    "    trans = trans.to(device)\n",
    "    trans.train()\n",
    "    \n",
    "    # apprentissage\n",
    "    if beta2==0: \n",
    "        optimizer = torch.optim.SGD(trans.parameters(), lr=learning_rate, momentum=beta1, nesterov=do_optim)\n",
    "    else:\n",
    "        optimizer = torch.optim.Adam(trans.parameters(), lr=learning_rate, betas=(beta1, beta2), amsgrad=do_optim)\n",
    "\n",
    "    if torch.cuda.is_available(): torch.cuda.empty_cache()    \n",
    "    # the data\n",
    "    X_1, X_2 = df_1.values, df_2.values\n",
    "    x_1, x_2 = torch.Tensor(X_1), torch.Tensor(X_2)\n",
    "\n",
    "    # split train and test\n",
    "    dataset = TensorDataset(x_1, x_2)\n",
    "    train_set_size = int(len(dataset) * split_ratio)\n",
    "    test_set_size = len(dataset) - train_set_size\n",
    "    train_set, test_set = random_split(dataset, [train_set_size, test_set_size], generator=torch.Generator().manual_seed(seed))\n",
    "    train_loader = DataLoader(train_set, batch_size=int(batch_size), shuffle=True)\n",
    "\n",
    "    for epoch in range(int(num_epochs)):\n",
    "        losses = []\n",
    "        for n_1, n_2 in train_loader:\n",
    "            n_1, n_2 = n_1.to(device), n_2.to(device)\n",
    "\n",
    "            sum_1, sum_2 = n_1.sum(axis=1), n_2.sum(axis=1)\n",
    "            p_1 = n_1/sum_1[:, None]\n",
    "            p_2 = n_2/sum_2[:, None]\n",
    "\n",
    "            p_1_pred = trans(p_2)\n",
    "            weight = sum_1 / train_set_size # /sum_2.sum() # donne un poids à chaque bureau de vote proportionnel à sa taille\n",
    "\n",
    "            loss_train = pdf_loss(p_1_pred, p_1, weight, loss_type=loss_type)\n",
    "\n",
    "            optimizer.zero_grad()\n",
    "            loss_train.backward()\n",
    "            optimizer.step()\n",
    "\n",
    "            losses.append(loss_train.item())\n",
    "\n",
    "        if verbose and (epoch % (num_epochs // 32) == 0):\n",
    "            print(f\"Iteration: {epoch} / {num_epochs} - Loss: {np.sum(losses):.5e}\")\n",
    "\n",
    "    loss_train = np.sum(losses) # somme des loss à la dernière époque\n",
    "    loss_train = loss_train/split_ratio # normalise par rapport à la taille du train dataset\n",
    "\n",
    "    # Test\n",
    "    with torch.no_grad():\n",
    "        n_1, n_2 = dataset[test_set.indices]\n",
    "        sum_1, sum_2 = n_1.sum(axis=1), n_2.sum(axis=1)\n",
    "        p_2 = n_2/sum_2[:, None]\n",
    "        p_1 = n_1/sum_1[:, None]\n",
    "        p_1_pred = trans(p_2)\n",
    "        weight = sum_1 / test_set_size # normalise par rapport à la taille du test dataset\n",
    "        loss_test = pdf_loss(p_1_pred, p_1, weight, loss_type=loss_type)\n",
    "\n",
    "    return trans, loss_train, loss_test, p_1.detach().numpy(), p_2.detach().numpy(), p_1_pred.detach().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.514314Z",
     "iopub.status.busy": "2022-06-03T06:45:03.513830Z",
     "iopub.status.idle": "2022-06-03T06:45:03.515977Z",
     "shell.execute_reply": "2022-06-03T06:45:03.516368Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([13911, 12]), torch.Size([13911, 12]))"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_1.shape, p_1_pred.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T06:45:03.522098Z",
     "iopub.status.busy": "2022-06-03T06:45:03.521483Z",
     "iopub.status.idle": "2022-06-03T07:00:41.126044Z",
     "shell.execute_reply": "2022-06-03T07:00:41.126417Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='bce'\n",
      "Iteration: 0 / 1025 - Loss: 2.42769e+02\n",
      "Iteration: 32 / 1025 - Loss: 4.06306e+01\n",
      "Iteration: 64 / 1025 - Loss: 4.04177e+01\n",
      "Iteration: 96 / 1025 - Loss: 4.03436e+01\n",
      "Iteration: 128 / 1025 - Loss: 4.03076e+01\n",
      "Iteration: 160 / 1025 - Loss: 4.02939e+01\n",
      "Iteration: 192 / 1025 - Loss: 4.02752e+01\n",
      "Iteration: 224 / 1025 - Loss: 4.02625e+01\n",
      "Iteration: 256 / 1025 - Loss: 4.02576e+01\n",
      "Iteration: 288 / 1025 - Loss: 4.02513e+01\n",
      "Iteration: 320 / 1025 - Loss: 4.02449e+01\n",
      "Iteration: 352 / 1025 - Loss: 4.02419e+01\n",
      "Iteration: 384 / 1025 - Loss: 4.02378e+01\n",
      "Iteration: 416 / 1025 - Loss: 4.02361e+01\n",
      "Iteration: 448 / 1025 - Loss: 4.02348e+01\n",
      "Iteration: 480 / 1025 - Loss: 4.02299e+01\n",
      "Iteration: 512 / 1025 - Loss: 4.02283e+01\n",
      "Iteration: 544 / 1025 - Loss: 4.02269e+01\n",
      "Iteration: 576 / 1025 - Loss: 4.02343e+01\n",
      "Iteration: 608 / 1025 - Loss: 4.02286e+01\n",
      "Iteration: 640 / 1025 - Loss: 4.02226e+01\n",
      "Iteration: 672 / 1025 - Loss: 4.02241e+01\n",
      "Iteration: 704 / 1025 - Loss: 4.02221e+01\n",
      "Iteration: 736 / 1025 - Loss: 4.02191e+01\n",
      "Iteration: 768 / 1025 - Loss: 4.02240e+01\n",
      "Iteration: 800 / 1025 - Loss: 4.02200e+01\n",
      "Iteration: 832 / 1025 - Loss: 4.02197e+01\n",
      "Iteration: 864 / 1025 - Loss: 4.02201e+01\n",
      "Iteration: 896 / 1025 - Loss: 4.02165e+01\n",
      "Iteration: 928 / 1025 - Loss: 4.02139e+01\n",
      "Iteration: 960 / 1025 - Loss: 4.02151e+01\n",
      "Iteration: 992 / 1025 - Loss: 4.02148e+01\n",
      "Iteration: 1024 / 1025 - Loss: 4.02194e+01\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='kl'\n",
      "Iteration: 0 / 1025 - Loss: 2.00754e+02\n",
      "Iteration: 32 / 1025 - Loss: 3.37362e+01\n",
      "Iteration: 64 / 1025 - Loss: 3.35264e+01\n",
      "Iteration: 96 / 1025 - Loss: 3.34536e+01\n",
      "Iteration: 128 / 1025 - Loss: 3.34221e+01\n",
      "Iteration: 160 / 1025 - Loss: 3.33982e+01\n",
      "Iteration: 192 / 1025 - Loss: 3.33834e+01\n",
      "Iteration: 224 / 1025 - Loss: 3.33750e+01\n",
      "Iteration: 256 / 1025 - Loss: 3.33664e+01\n",
      "Iteration: 288 / 1025 - Loss: 3.33636e+01\n",
      "Iteration: 320 / 1025 - Loss: 3.33547e+01\n",
      "Iteration: 352 / 1025 - Loss: 3.33527e+01\n",
      "Iteration: 384 / 1025 - Loss: 3.33508e+01\n",
      "Iteration: 416 / 1025 - Loss: 3.33477e+01\n",
      "Iteration: 448 / 1025 - Loss: 3.33419e+01\n",
      "Iteration: 480 / 1025 - Loss: 3.33412e+01\n",
      "Iteration: 512 / 1025 - Loss: 3.33419e+01\n",
      "Iteration: 544 / 1025 - Loss: 3.33389e+01\n",
      "Iteration: 576 / 1025 - Loss: 3.33345e+01\n",
      "Iteration: 608 / 1025 - Loss: 3.33372e+01\n",
      "Iteration: 640 / 1025 - Loss: 3.33314e+01\n",
      "Iteration: 672 / 1025 - Loss: 3.33311e+01\n",
      "Iteration: 704 / 1025 - Loss: 3.33296e+01\n",
      "Iteration: 736 / 1025 - Loss: 3.33291e+01\n",
      "Iteration: 768 / 1025 - Loss: 3.33303e+01\n",
      "Iteration: 800 / 1025 - Loss: 3.33293e+01\n",
      "Iteration: 832 / 1025 - Loss: 3.33282e+01\n",
      "Iteration: 864 / 1025 - Loss: 3.33268e+01\n",
      "Iteration: 896 / 1025 - Loss: 3.33257e+01\n",
      "Iteration: 928 / 1025 - Loss: 3.33284e+01\n",
      "Iteration: 960 / 1025 - Loss: 3.33247e+01\n",
      "Iteration: 992 / 1025 - Loss: 3.33254e+01\n",
      "Iteration: 1024 / 1025 - Loss: 3.33269e+01\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='l1'\n",
      "Iteration: 0 / 1025 - Loss: 3.69474e+02\n",
      "Iteration: 32 / 1025 - Loss: 1.24658e+02\n",
      "Iteration: 64 / 1025 - Loss: 1.24419e+02\n",
      "Iteration: 96 / 1025 - Loss: 1.24349e+02\n",
      "Iteration: 128 / 1025 - Loss: 1.24318e+02\n",
      "Iteration: 160 / 1025 - Loss: 1.24269e+02\n",
      "Iteration: 192 / 1025 - Loss: 1.24240e+02\n",
      "Iteration: 224 / 1025 - Loss: 1.24243e+02\n",
      "Iteration: 256 / 1025 - Loss: 1.24219e+02\n",
      "Iteration: 288 / 1025 - Loss: 1.24232e+02\n",
      "Iteration: 320 / 1025 - Loss: 1.24215e+02\n",
      "Iteration: 352 / 1025 - Loss: 1.24203e+02\n",
      "Iteration: 384 / 1025 - Loss: 1.24206e+02\n",
      "Iteration: 416 / 1025 - Loss: 1.24219e+02\n",
      "Iteration: 448 / 1025 - Loss: 1.24217e+02\n",
      "Iteration: 480 / 1025 - Loss: 1.24214e+02\n",
      "Iteration: 512 / 1025 - Loss: 1.24204e+02\n",
      "Iteration: 544 / 1025 - Loss: 1.24198e+02\n",
      "Iteration: 576 / 1025 - Loss: 1.24201e+02\n",
      "Iteration: 608 / 1025 - Loss: 1.24210e+02\n",
      "Iteration: 640 / 1025 - Loss: 1.24187e+02\n",
      "Iteration: 672 / 1025 - Loss: 1.24181e+02\n",
      "Iteration: 704 / 1025 - Loss: 1.24191e+02\n",
      "Iteration: 736 / 1025 - Loss: 1.24197e+02\n",
      "Iteration: 768 / 1025 - Loss: 1.24178e+02\n",
      "Iteration: 800 / 1025 - Loss: 1.24193e+02\n",
      "Iteration: 832 / 1025 - Loss: 1.24199e+02\n",
      "Iteration: 864 / 1025 - Loss: 1.24175e+02\n",
      "Iteration: 896 / 1025 - Loss: 1.24195e+02\n",
      "Iteration: 928 / 1025 - Loss: 1.24191e+02\n",
      "Iteration: 960 / 1025 - Loss: 1.24191e+02\n",
      "Iteration: 992 / 1025 - Loss: 1.24187e+02\n",
      "Iteration: 1024 / 1025 - Loss: 1.24195e+02\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for loss_type in ['bce', 'kl', 'l1']:\n",
    "    print(f'{loss_type=}')\n",
    "    trans, loss_train, loss_test, p_1, p_2, p_1_pred = fit_data(df_1, df_2, verbose=True, loss_type=loss_type)\n",
    "\n",
    "    fig, axs = plt.subplots(1, N_1er, figsize=(13, 3))\n",
    "    for i_col, candidat in enumerate(df_1.columns):\n",
    "        #axs[i_col].scatter(p_2[:,i_col], p_2_pred[:,i_col], alpha=.005)\n",
    "        axs[i_col].plot([0, 1], [0, 1], 'r--')\n",
    "        sns.histplot(x=p_1[:, i_col], y=p_1_pred[:, i_col], ax=axs[i_col])\n",
    "        axs[i_col].set_xlabel(candidat)\n",
    "        axs[i_col].set_xlim(0, 1)\n",
    "        axs[i_col].set_ylim(0, 1)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ces graphiques représentent en abscisse les probabilités observées et en ordonnée les probabilités prédites. L'intérieur du graphique représente au niveau de bleu l'histogramme des différentes valeurs telles qu'elles sont observés sur la base de test, c'est-à-dire sur 10 % de l'ensemble des bureeaux de vote."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut maintenant récupérer du modèle la matrice de transition qui a été inférée grâce a notre apprentissage automatique :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:00:41.130396Z",
     "iopub.status.busy": "2022-06-03T07:00:41.129493Z",
     "iopub.status.idle": "2022-06-03T07:00:41.132583Z",
     "shell.execute_reply": "2022-06-03T07:00:41.132975Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.61850872e-03, 1.55309243e-02, 4.51046795e-01, 6.59184018e-03,\n",
       "        1.12110763e-04, 5.50301075e-02, 2.88578272e-01, 2.40875185e-02,\n",
       "        8.20070580e-02, 6.26551807e-02, 5.54780057e-03, 7.19385175e-03],\n",
       "       [1.09621491e-02, 3.15805785e-02, 6.20487966e-02, 5.81059195e-02,\n",
       "        5.84429145e-01, 8.88994485e-02, 8.16443339e-02, 7.77875213e-03,\n",
       "        3.05833120e-04, 2.37906631e-02, 1.03636505e-02, 4.00908180e-02]],\n",
       "      dtype=float32)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = torch.softmax(trans.lin.weight, axis=1).detach().numpy()\n",
    "M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On vérifie dans un premier temps que la contrainte est toujours bien respectée :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:00:41.136872Z",
     "iopub.status.busy": "2022-06-03T07:00:41.136324Z",
     "iopub.status.idle": "2022-06-03T07:00:41.138513Z",
     "shell.execute_reply": "2022-06-03T07:00:41.138844Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1., 1.], dtype=float32), (2, 12))"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.sum(axis=1), M.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons nous inspirer d'[un graphique de la galerie matplotlib](https://matplotlib.org/stable/gallery/misc/table_demo.html#sphx-glr-gallery-misc-table-demo-py) pour représenter la la proportion des report de voix en fonction de chacun des choix efféctués au deuxième tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:00:41.154361Z",
     "iopub.status.busy": "2022-06-03T07:00:41.150933Z",
     "iopub.status.idle": "2022-06-03T07:00:42.560326Z",
     "shell.execute_reply": "2022-06-03T07:00:42.560752Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shape mismatch: objects cannot be broadcast to a single shape.  Mismatch is between arg 0 with shape (2,) and arg 1 with shape (12,).",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Input \u001b[0;32mIn [78]\u001b[0m, in \u001b[0;36m<cell line: 18>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     17\u001b[0m cell_text \u001b[38;5;241m=\u001b[39m []\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m row \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(n_rows):\n\u001b[0;32m---> 19\u001b[0m     \u001b[43max\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbar\u001b[49m\u001b[43m(\u001b[49m\u001b[43mindex\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mM\u001b[49m\u001b[43m[\u001b[49m\u001b[43mrow\u001b[49m\u001b[43m]\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m100\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mbar_width\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mbottom\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43my_offset\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcolor\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcolors\u001b[49m\u001b[43m[\u001b[49m\u001b[43mrow\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     20\u001b[0m     y_offset \u001b[38;5;241m=\u001b[39m y_offset \u001b[38;5;241m+\u001b[39m M[row]\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m100\u001b[39m\n\u001b[1;32m     21\u001b[0m     cell_text\u001b[38;5;241m.\u001b[39mappend([\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mx\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m100\u001b[39m\u001b[38;5;132;01m:\u001b[39;00m\u001b[38;5;124m1.1f\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m%\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;28;01mfor\u001b[39;00m x \u001b[38;5;129;01min\u001b[39;00m M[row]])\n",
      "File \u001b[0;32m/usr/local/lib/python3.9/site-packages/matplotlib/__init__.py:1412\u001b[0m, in \u001b[0;36m_preprocess_data.<locals>.inner\u001b[0;34m(ax, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1409\u001b[0m \u001b[38;5;129m@functools\u001b[39m\u001b[38;5;241m.\u001b[39mwraps(func)\n\u001b[1;32m   1410\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21minner\u001b[39m(ax, \u001b[38;5;241m*\u001b[39margs, data\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m   1411\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m data \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m-> 1412\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[43max\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;28;43mmap\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43msanitize_sequence\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1414\u001b[0m     bound \u001b[38;5;241m=\u001b[39m new_sig\u001b[38;5;241m.\u001b[39mbind(ax, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m   1415\u001b[0m     auto_label \u001b[38;5;241m=\u001b[39m (bound\u001b[38;5;241m.\u001b[39marguments\u001b[38;5;241m.\u001b[39mget(label_namer)\n\u001b[1;32m   1416\u001b[0m                   \u001b[38;5;129;01mor\u001b[39;00m bound\u001b[38;5;241m.\u001b[39mkwargs\u001b[38;5;241m.\u001b[39mget(label_namer))\n",
      "File \u001b[0;32m/usr/local/lib/python3.9/site-packages/matplotlib/axes/_axes.py:2342\u001b[0m, in \u001b[0;36mAxes.bar\u001b[0;34m(self, x, height, width, bottom, align, **kwargs)\u001b[0m\n\u001b[1;32m   2339\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m yerr \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m   2340\u001b[0m         yerr \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_convert_dx(yerr, y0, y, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mconvert_yunits)\n\u001b[0;32m-> 2342\u001b[0m x, height, width, y, linewidth, hatch \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbroadcast_arrays\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m   2343\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;66;43;03m# Make args iterable too.\u001b[39;49;00m\n\u001b[1;32m   2344\u001b[0m \u001b[43m    \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43matleast_1d\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mheight\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mwidth\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlinewidth\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mhatch\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2346\u001b[0m \u001b[38;5;66;03m# Now that units have been converted, set the tick locations.\u001b[39;00m\n\u001b[1;32m   2347\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m orientation \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mvertical\u001b[39m\u001b[38;5;124m'\u001b[39m:\n",
      "File \u001b[0;32m<__array_function__ internals>:180\u001b[0m, in \u001b[0;36mbroadcast_arrays\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
      "File \u001b[0;32m/usr/local/lib/python3.9/site-packages/numpy/lib/stride_tricks.py:539\u001b[0m, in \u001b[0;36mbroadcast_arrays\u001b[0;34m(subok, *args)\u001b[0m\n\u001b[1;32m    532\u001b[0m \u001b[38;5;66;03m# nditer is not used here to avoid the limit of 32 arrays.\u001b[39;00m\n\u001b[1;32m    533\u001b[0m \u001b[38;5;66;03m# Otherwise, something like the following one-liner would suffice:\u001b[39;00m\n\u001b[1;32m    534\u001b[0m \u001b[38;5;66;03m# return np.nditer(args, flags=['multi_index', 'zerosize_ok'],\u001b[39;00m\n\u001b[1;32m    535\u001b[0m \u001b[38;5;66;03m#                  order='C').itviews\u001b[39;00m\n\u001b[1;32m    537\u001b[0m args \u001b[38;5;241m=\u001b[39m [np\u001b[38;5;241m.\u001b[39marray(_m, copy\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m, subok\u001b[38;5;241m=\u001b[39msubok) \u001b[38;5;28;01mfor\u001b[39;00m _m \u001b[38;5;129;01min\u001b[39;00m args]\n\u001b[0;32m--> 539\u001b[0m shape \u001b[38;5;241m=\u001b[39m \u001b[43m_broadcast_shape\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    541\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mall\u001b[39m(array\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m==\u001b[39m shape \u001b[38;5;28;01mfor\u001b[39;00m array \u001b[38;5;129;01min\u001b[39;00m args):\n\u001b[1;32m    542\u001b[0m     \u001b[38;5;66;03m# Common case where nothing needs to be broadcasted.\u001b[39;00m\n\u001b[1;32m    543\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m args\n",
      "File \u001b[0;32m/usr/local/lib/python3.9/site-packages/numpy/lib/stride_tricks.py:421\u001b[0m, in \u001b[0;36m_broadcast_shape\u001b[0;34m(*args)\u001b[0m\n\u001b[1;32m    416\u001b[0m \u001b[38;5;124;03m\"\"\"Returns the shape of the arrays that would result from broadcasting the\u001b[39;00m\n\u001b[1;32m    417\u001b[0m \u001b[38;5;124;03msupplied arrays against each other.\u001b[39;00m\n\u001b[1;32m    418\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    419\u001b[0m \u001b[38;5;66;03m# use the old-iterator because np.nditer does not handle size 0 arrays\u001b[39;00m\n\u001b[1;32m    420\u001b[0m \u001b[38;5;66;03m# consistently\u001b[39;00m\n\u001b[0;32m--> 421\u001b[0m b \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbroadcast\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[38;5;241;43m32\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    422\u001b[0m \u001b[38;5;66;03m# unfortunately, it cannot handle 32 or more arguments directly\u001b[39;00m\n\u001b[1;32m    423\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m pos \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m32\u001b[39m, \u001b[38;5;28mlen\u001b[39m(args), \u001b[38;5;241m31\u001b[39m):\n\u001b[1;32m    424\u001b[0m     \u001b[38;5;66;03m# ironically, np.broadcast does not properly handle np.broadcast\u001b[39;00m\n\u001b[1;32m    425\u001b[0m     \u001b[38;5;66;03m# objects (it treats them as scalars)\u001b[39;00m\n\u001b[1;32m    426\u001b[0m     \u001b[38;5;66;03m# use broadcasting to avoid allocating the full array\u001b[39;00m\n",
      "\u001b[0;31mValueError\u001b[0m: shape mismatch: objects cannot be broadcast to a single shape.  Mismatch is between arg 0 with shape (2,) and arg 1 with shape (12,)."
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 936x936 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13, 13))\n",
    "\n",
    "columns = df_2.columns\n",
    "rows = df_1.columns\n",
    "\n",
    "# Get some shades for the colors\n",
    "colors = plt.cm.tab20c(np.linspace(0, 1, len(rows)))\n",
    "n_rows = len(rows)\n",
    "\n",
    "index = np.arange(len(columns)) + 0.3\n",
    "bar_width = 0.4\n",
    "\n",
    "# Initialize the vertical-offset for the stacked bar chart.\n",
    "y_offset = np.zeros(len(columns))\n",
    "\n",
    "# Plot bars and create text labels for the table\n",
    "cell_text = []\n",
    "for row in range(n_rows):\n",
    "    ax.bar(index, M[row]*100, bar_width, bottom=y_offset, color=colors[row])\n",
    "    y_offset = y_offset + M[row]*100\n",
    "    cell_text.append([f'{x*100:1.1f}%' for x in M[row]])\n",
    "ax.set_ylim(0, 100)\n",
    "\n",
    "# Add a table at the bottom of the axes\n",
    "the_table = ax.table(cellText=cell_text,\n",
    "                      rowLabels=rows,\n",
    "                      rowColours=colors,\n",
    "                      colLabels=columns,\n",
    "                      loc='bottom')\n",
    "\n",
    "# Adjust layout to make room for the table:\n",
    "plt.subplots_adjust(left=0.2, bottom=0.2)\n",
    "\n",
    "plt.ylabel(\"Pourcentage de report des voix\")\n",
    "plt.yticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.xticks([])\n",
    "plt.title(\"Report des voix par résultat du 2nd tour\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C'est des données. Ces données correspondent aux intuitions qu'on peut se faire quand au report des votes. Notamment on remarque que la plupart des individus qui s'abstiennent au second tour se sont abstenus au premier (avec une petite proportion de Mélenchon qui se sont abstenus). Remarque aussi que la majorité des électeurs de Le Pen au premier tour en voter pour la même personne au deuxième tour. Environ un quart des électeurs de Le Pen au second tour s'était abstenu au premier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:00:42.564941Z",
     "iopub.status.busy": "2022-06-03T07:00:42.564459Z",
     "iopub.status.idle": "2022-06-03T07:00:42.566658Z",
     "shell.execute_reply": "2022-06-03T07:00:42.567048Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.2,  1.6, 45.1,  0.7,  0. ,  5.5, 28.9,  2.4,  8.2,  6.3,  0.6,\n",
       "         0.7],\n",
       "       [ 1.1,  3.2,  6.2,  5.8, 58.4,  8.9,  8.2,  0.8,  0. ,  2.4,  1. ,\n",
       "         4. ]], dtype=float32)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(precision=1)\n",
    "np.set_printoptions(suppress=True)\n",
    "M*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On observe aussi quelques points intéressants dans les votes nuls qui proviennent majoritairement de voteur \"nul\" au premier tour (40 %) et ensuite par des électeurs ayant voté pour des candidats marginaux au premier tour (Arnaud, Lassalle, Hidalgo). On observe à peu près la même structure pour les voteurs \"blanc\" avec cette particularité que les individus ayant voté pour Jadot au premier tour ont relativement plus exprimé de votes \"blanc\" (~12 %) par rapport à ce qu'on observe pour les votes \"nul\". On rappelle qu'en France, un vote nul est un bulletin qui n'a pas été validé car il est par exemple raturé alors qu'un vote blanc est exprimé par un bulletin de vote totalement blanc (et qu'il faut préparer en avance). On peut donc expliquer ce dernier par rapport aux particularités du vote écologiques liés aux candidat Jadot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Muni de cette matrice de transition on peut maintenant opérer une transformation de telle sorte à ce que nous allons regarder la distribution des report de voix pour chacun des choix qui sont faits au premier tour."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:00:42.571038Z",
     "iopub.status.busy": "2022-06-03T07:00:42.570566Z",
     "iopub.status.idle": "2022-06-03T07:00:42.572718Z",
     "shell.execute_reply": "2022-06-03T07:00:42.573049Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.2,  1.1],\n",
       "       [ 1.6,  3.2],\n",
       "       [45.1,  6.2],\n",
       "       [ 0.7,  5.8],\n",
       "       [ 0. , 58.4],\n",
       "       [ 5.5,  8.9],\n",
       "       [28.9,  8.2],\n",
       "       [ 2.4,  0.8],\n",
       "       [ 8.2,  0. ],\n",
       "       [ 6.3,  2.4],\n",
       "       [ 0.6,  1. ],\n",
       "       [ 0.7,  4. ]], dtype=float32)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MT = M.T\n",
    "MT /= MT.sum(axis=0)\n",
    "MT*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:00:42.639558Z",
     "iopub.status.busy": "2022-06-03T07:00:42.632175Z",
     "iopub.status.idle": "2022-06-03T07:00:42.736470Z",
     "shell.execute_reply": "2022-06-03T07:00:42.736911Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shape mismatch: objects cannot be broadcast to a single shape.  Mismatch is between arg 0 with shape (12,) and arg 1 with shape (2,).",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Input \u001b[0;32mIn [81]\u001b[0m, in \u001b[0;36m<cell line: 18>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     17\u001b[0m cell_text \u001b[38;5;241m=\u001b[39m []\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m row \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(n_rows):\n\u001b[0;32m---> 19\u001b[0m     \u001b[43max\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbar\u001b[49m\u001b[43m(\u001b[49m\u001b[43mindex\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mMT\u001b[49m\u001b[43m[\u001b[49m\u001b[43mrow\u001b[49m\u001b[43m]\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m100\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mbar_width\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mbottom\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43my_offset\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcolor\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcolors\u001b[49m\u001b[43m[\u001b[49m\u001b[43mrow\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlinewidth\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m     20\u001b[0m     y_offset \u001b[38;5;241m=\u001b[39m y_offset \u001b[38;5;241m+\u001b[39m MT[row]\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m100\u001b[39m\n\u001b[1;32m     21\u001b[0m     cell_text\u001b[38;5;241m.\u001b[39mappend([\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mx\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m100\u001b[39m\u001b[38;5;132;01m:\u001b[39;00m\u001b[38;5;124m1.1f\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m%\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;28;01mfor\u001b[39;00m x \u001b[38;5;129;01min\u001b[39;00m MT[row]])\n",
      "File \u001b[0;32m/usr/local/lib/python3.9/site-packages/matplotlib/__init__.py:1412\u001b[0m, in \u001b[0;36m_preprocess_data.<locals>.inner\u001b[0;34m(ax, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1409\u001b[0m \u001b[38;5;129m@functools\u001b[39m\u001b[38;5;241m.\u001b[39mwraps(func)\n\u001b[1;32m   1410\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21minner\u001b[39m(ax, \u001b[38;5;241m*\u001b[39margs, data\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m   1411\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m data \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m-> 1412\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[43max\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;28;43mmap\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43msanitize_sequence\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1414\u001b[0m     bound \u001b[38;5;241m=\u001b[39m new_sig\u001b[38;5;241m.\u001b[39mbind(ax, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m   1415\u001b[0m     auto_label \u001b[38;5;241m=\u001b[39m (bound\u001b[38;5;241m.\u001b[39marguments\u001b[38;5;241m.\u001b[39mget(label_namer)\n\u001b[1;32m   1416\u001b[0m                   \u001b[38;5;129;01mor\u001b[39;00m bound\u001b[38;5;241m.\u001b[39mkwargs\u001b[38;5;241m.\u001b[39mget(label_namer))\n",
      "File \u001b[0;32m/usr/local/lib/python3.9/site-packages/matplotlib/axes/_axes.py:2342\u001b[0m, in \u001b[0;36mAxes.bar\u001b[0;34m(self, x, height, width, bottom, align, **kwargs)\u001b[0m\n\u001b[1;32m   2339\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m yerr \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m   2340\u001b[0m         yerr \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_convert_dx(yerr, y0, y, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mconvert_yunits)\n\u001b[0;32m-> 2342\u001b[0m x, height, width, y, linewidth, hatch \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbroadcast_arrays\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m   2343\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;66;43;03m# Make args iterable too.\u001b[39;49;00m\n\u001b[1;32m   2344\u001b[0m \u001b[43m    \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43matleast_1d\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mheight\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mwidth\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlinewidth\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mhatch\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2346\u001b[0m \u001b[38;5;66;03m# Now that units have been converted, set the tick locations.\u001b[39;00m\n\u001b[1;32m   2347\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m orientation \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mvertical\u001b[39m\u001b[38;5;124m'\u001b[39m:\n",
      "File \u001b[0;32m<__array_function__ internals>:180\u001b[0m, in \u001b[0;36mbroadcast_arrays\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
      "File \u001b[0;32m/usr/local/lib/python3.9/site-packages/numpy/lib/stride_tricks.py:539\u001b[0m, in \u001b[0;36mbroadcast_arrays\u001b[0;34m(subok, *args)\u001b[0m\n\u001b[1;32m    532\u001b[0m \u001b[38;5;66;03m# nditer is not used here to avoid the limit of 32 arrays.\u001b[39;00m\n\u001b[1;32m    533\u001b[0m \u001b[38;5;66;03m# Otherwise, something like the following one-liner would suffice:\u001b[39;00m\n\u001b[1;32m    534\u001b[0m \u001b[38;5;66;03m# return np.nditer(args, flags=['multi_index', 'zerosize_ok'],\u001b[39;00m\n\u001b[1;32m    535\u001b[0m \u001b[38;5;66;03m#                  order='C').itviews\u001b[39;00m\n\u001b[1;32m    537\u001b[0m args \u001b[38;5;241m=\u001b[39m [np\u001b[38;5;241m.\u001b[39marray(_m, copy\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m, subok\u001b[38;5;241m=\u001b[39msubok) \u001b[38;5;28;01mfor\u001b[39;00m _m \u001b[38;5;129;01min\u001b[39;00m args]\n\u001b[0;32m--> 539\u001b[0m shape \u001b[38;5;241m=\u001b[39m \u001b[43m_broadcast_shape\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    541\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mall\u001b[39m(array\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m==\u001b[39m shape \u001b[38;5;28;01mfor\u001b[39;00m array \u001b[38;5;129;01min\u001b[39;00m args):\n\u001b[1;32m    542\u001b[0m     \u001b[38;5;66;03m# Common case where nothing needs to be broadcasted.\u001b[39;00m\n\u001b[1;32m    543\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m args\n",
      "File \u001b[0;32m/usr/local/lib/python3.9/site-packages/numpy/lib/stride_tricks.py:421\u001b[0m, in \u001b[0;36m_broadcast_shape\u001b[0;34m(*args)\u001b[0m\n\u001b[1;32m    416\u001b[0m \u001b[38;5;124;03m\"\"\"Returns the shape of the arrays that would result from broadcasting the\u001b[39;00m\n\u001b[1;32m    417\u001b[0m \u001b[38;5;124;03msupplied arrays against each other.\u001b[39;00m\n\u001b[1;32m    418\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    419\u001b[0m \u001b[38;5;66;03m# use the old-iterator because np.nditer does not handle size 0 arrays\u001b[39;00m\n\u001b[1;32m    420\u001b[0m \u001b[38;5;66;03m# consistently\u001b[39;00m\n\u001b[0;32m--> 421\u001b[0m b \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbroadcast\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[38;5;241;43m32\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    422\u001b[0m \u001b[38;5;66;03m# unfortunately, it cannot handle 32 or more arguments directly\u001b[39;00m\n\u001b[1;32m    423\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m pos \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m32\u001b[39m, \u001b[38;5;28mlen\u001b[39m(args), \u001b[38;5;241m31\u001b[39m):\n\u001b[1;32m    424\u001b[0m     \u001b[38;5;66;03m# ironically, np.broadcast does not properly handle np.broadcast\u001b[39;00m\n\u001b[1;32m    425\u001b[0m     \u001b[38;5;66;03m# objects (it treats them as scalars)\u001b[39;00m\n\u001b[1;32m    426\u001b[0m     \u001b[38;5;66;03m# use broadcasting to avoid allocating the full array\u001b[39;00m\n",
      "\u001b[0;31mValueError\u001b[0m: shape mismatch: objects cannot be broadcast to a single shape.  Mismatch is between arg 0 with shape (12,) and arg 1 with shape (2,)."
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(25, 8))\n",
    "\n",
    "columns = df_1.columns\n",
    "rows = df_2.columns\n",
    "\n",
    "# named colors: https://matplotlib.org/stable/gallery/color/named_colors.html\n",
    "colors = ['darkviolet', 'steelblue', 'brown' ]\n",
    "n_rows = len(rows)\n",
    "\n",
    "index = np.arange(len(columns)) + 0.3\n",
    "bar_width = 0.4\n",
    "\n",
    "# Initialize the vertical-offset for the stacked bar chart.\n",
    "y_offset = np.zeros(len(columns))\n",
    "\n",
    "# Plot bars and create text labels for the table\n",
    "cell_text = []\n",
    "for row in range(n_rows):\n",
    "    ax.bar(index, MT[row]*100, bar_width, bottom=y_offset, color=colors[row], linewidth=1)\n",
    "    y_offset = y_offset + MT[row]*100\n",
    "    cell_text.append([f'{x*100:1.1f}%' for x in MT[row]])\n",
    "ax.set_ylim(0, 100)\n",
    "\n",
    "# Add a table at the bottom of the axes\n",
    "the_table = ax.table(cellText=cell_text,\n",
    "                      rowLabels=rows,\n",
    "                      rowColours=colors,\n",
    "                      colLabels=columns,\n",
    "                      loc='bottom')\n",
    "\n",
    "# Adjust layout to make room for the table:\n",
    "plt.subplots_adjust(left=0.2, bottom=0.2)\n",
    "\n",
    "plt.ylabel(\"Pourcentage de report des voix\")\n",
    "plt.yticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.xticks([])\n",
    "plt.title(\"Report des voix par résultat du 1er tour\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut aussi se restreindre aux votes exprimés :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:00:42.741126Z",
     "iopub.status.busy": "2022-06-03T07:00:42.740537Z",
     "iopub.status.idle": "2022-06-03T07:00:42.742749Z",
     "shell.execute_reply": "2022-06-03T07:00:42.743094Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.2],\n",
       "       [ 6.3],\n",
       "       [ 5.9],\n",
       "       [59.1],\n",
       "       [ 9. ],\n",
       "       [ 8.3],\n",
       "       [ 0.8],\n",
       "       [ 0. ],\n",
       "       [ 2.4],\n",
       "       [ 1. ],\n",
       "       [ 4.1]], dtype=float32)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MT = M[1:, 1:].T\n",
    "MT /= MT.sum(axis=0)\n",
    "MT*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:00:42.752470Z",
     "iopub.status.busy": "2022-06-03T07:00:42.751236Z",
     "iopub.status.idle": "2022-06-03T07:00:42.894271Z",
     "shell.execute_reply": "2022-06-03T07:00:42.894614Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(16, 5))\n",
    "\n",
    "columns = df_1.columns[1:]\n",
    "rows = df_2.columns[1:]\n",
    "\n",
    "# named colors: https://matplotlib.org/stable/gallery/color/named_colors.html\n",
    "colors = ['steelblue', 'brown' ]\n",
    "n_rows = len(rows)\n",
    "\n",
    "index = np.arange(len(columns)) + 0.3\n",
    "bar_width = 0.4\n",
    "\n",
    "# Initialize the vertical-offset for the stacked bar chart.\n",
    "y_offset = np.zeros(len(columns))\n",
    "\n",
    "# Plot bars and create text labels for the table\n",
    "cell_text = []\n",
    "for row in range(n_rows):\n",
    "    ax.bar(index, MT[row]*100, bar_width, bottom=y_offset, color=colors[row], linewidth=1)\n",
    "    y_offset = y_offset + MT[row]*100\n",
    "    cell_text.append([f'{x*100:1.1f}%' for x in MT[row]])\n",
    "ax.set_ylim(0, 100)\n",
    "# Add a table at the bottom of the axes\n",
    "the_table = ax.table(cellText=cell_text, colLoc='center', \n",
    "                      rowLabels=rows, rowLoc='center',\n",
    "                      rowColours=colors,\n",
    "                      colLabels=columns,\n",
    "                      loc='bottom')\n",
    "the_table.auto_set_font_size(False)\n",
    "the_table.set_fontsize(10)\n",
    "# Adjust layout to make room for the table:\n",
    "plt.subplots_adjust(left=0.2, bottom=0.2)\n",
    "\n",
    "plt.ylabel(\"Pourcentage de report des voix\")\n",
    "plt.yticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.xticks([])\n",
    "plt.title(\"Report des voix exprimées connaissant le choix exprimé au 1er tour\")\n",
    "plt.savefig('2022-05-23_transfert-des-voix.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ce tableau donne le pourcentage de chances d'exprimer une voix pour un candidat ou pour l'autre en fonction du choix qu'on a exprimé au premier tour. \n",
    "\n",
    "Ce tableau montre des tendances claires, par exemple que si on a voté Macron, Jadot ou Pécresse au premier tour, alors on va certainement voter Macron au deuxième tour. Ses électeurs se montre particulièrement consensuel et suivent le « pacte républicain » mise en place pour faire un barrage au Front National. Il montre aussi que si on a voté Le Pen ou Dupont-Aignan au premier tour alors on va voter Le Pen au deuxième, un clair vote de suivi. (On pourra aussi remarquer les ~ 3 % des voix pour Macron au premier tour qui ont voté Le Pen au deuxième tour, soit tout de même environ 320k individus…)\n",
    "\n",
    "Connaissant les couleurs politiques d'autres candidats du premier tour, on peut être surpris que les électeurs de Arthaud, Roussel ou Hidalgo ont majoritairement choisi Le Pen au deuxième tour, signifiant alors un rejet du candidat Macron. Les électeurs de Zemmour sont aussi partagés, signifiant un rejet des deux alternatives. **Ce résultat est à prendre avec des pincettes car ces derniers candidats ont obtenu moins de votes et donc que le processus d'inférence est forcément moins précis car il y a moins de données disponibles.** Pour se rendre compte de la variabilité des résultats qu'on obtient là, je conseille au lecteur (*à l'électeur*) de relancer ces notebook en utilisant différents « graines » pour le générateur de nombre aléatoire qui permet de séparer les données (le paramètre `seed`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:00:42.898696Z",
     "iopub.status.busy": "2022-06-03T07:00:42.898155Z",
     "iopub.status.idle": "2022-06-03T07:00:42.910824Z",
     "shell.execute_reply": "2022-06-03T07:00:42.911199Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "index 2 is out of bounds for axis 1 with size 1",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "Input \u001b[0;32mIn [84]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\"\"\u001b[39m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;124mTotal des voix au 1er tour= \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mx_1\u001b[38;5;241m.\u001b[39msum()\u001b[38;5;132;01m:\u001b[39;00m\u001b[38;5;124m.0f\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m, dont Macron = \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mx_1[:, \u001b[38;5;241m5\u001b[39m]\u001b[38;5;241m.\u001b[39msum()\u001b[38;5;132;01m:\u001b[39;00m\u001b[38;5;124m.0f\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m (soit une pourcentage de \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mx_1[:, \u001b[38;5;241m5\u001b[39m]\u001b[38;5;241m.\u001b[39msum()\u001b[38;5;241m/\u001b[39mx_1\u001b[38;5;241m.\u001b[39msum()\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m100\u001b[39m\u001b[38;5;132;01m:\u001b[39;00m\u001b[38;5;124m.2f\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m%), \u001b[39m\n\u001b[0;32m----> 3\u001b[0m \u001b[38;5;124m-> nombre de reports de Macron du 1er vers Le Pen au 2eme = \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mx_1[:, \u001b[38;5;241m5\u001b[39m]\u001b[38;5;241m.\u001b[39msum()\u001b[38;5;241m*\u001b[39mMT[\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m2\u001b[39m]\u001b[38;5;132;01m:\u001b[39;00m\u001b[38;5;124m.0f\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m personnes.\u001b[39m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124m\"\"\"\u001b[39m)\n",
      "\u001b[0;31mIndexError\u001b[0m: index 2 is out of bounds for axis 1 with size 1"
     ]
    }
   ],
   "source": [
    "print(f\"\"\"\n",
    "Total des voix au 1er tour= {x_1.sum():.0f}, dont Macron = {x_1[:, 5].sum():.0f} (soit une pourcentage de {x_1[:, 5].sum()/x_1.sum()*100:.2f}%), \n",
    "-> nombre de reports de Macron du 1er vers Le Pen au 2eme = {x_1[:, 5].sum()*MT[1, 2]:.0f} personnes.\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Influence des parametres\n",
    "\n",
    "Finalement, on valide nos résultats en testant différentes paramétrisation de l'apprentissage et en donnant la valeur du loss calculé sur la base de test :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:00:42.916430Z",
     "iopub.status.busy": "2022-06-03T07:00:42.915439Z",
     "iopub.status.idle": "2022-06-03T07:05:53.774012Z",
     "shell.execute_reply": "2022-06-03T07:05:53.774360Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAIN: Loss avec do_optim=True = 137.99 / Loss avec alternative choice do_optim=False = 44.69 \n",
      "TEST: Loss avec do_optim=True = 123.11 / Loss avec alternative choice do_optim=False = 39.45 \n"
     ]
    }
   ],
   "source": [
    "trans, loss_train_alt, loss_test_alt, p_1, p_2, p_2_pred = fit_data(df_1, df_2, verbose=False, do_optim=not do_optim)\n",
    "print(f'TRAIN: Loss avec {do_optim=} = {loss_train:.2f} / Loss avec alternative choice do_optim={not do_optim} = {loss_train_alt:.2f} ')\n",
    "print(f'TEST: Loss avec {do_optim=} = {loss_test:.2f} / Loss avec alternative choice do_optim={not do_optim} = {loss_test_alt:.2f} ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:05:53.777920Z",
     "iopub.status.busy": "2022-06-03T07:05:53.777334Z",
     "iopub.status.idle": "2022-06-03T07:05:53.779687Z",
     "shell.execute_reply": "2022-06-03T07:05:53.780010Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "do_optim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:05:53.785798Z",
     "iopub.status.busy": "2022-06-03T07:05:53.785211Z",
     "iopub.status.idle": "2022-06-03T07:42:11.257358Z",
     "shell.execute_reply": "2022-06-03T07:42:11.257706Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour learning_rate= 1.00e-04, loss_train=4.48e+01 / loss_test=3.95e+01; le temps de calcul est 308.750 s\n",
      "Pour learning_rate= 2.15e-04, loss_train=4.47e+01 / loss_test=3.95e+01; le temps de calcul est 309.241 s\n",
      "Pour learning_rate= 4.64e-04, loss_train=4.47e+01 / loss_test=3.95e+01; le temps de calcul est 310.825 s\n",
      "Pour learning_rate= 1.00e-03, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 309.735 s\n",
      "Pour learning_rate= 2.15e-03, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 316.872 s\n",
      "Pour learning_rate= 4.64e-03, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 312.782 s\n",
      "Pour learning_rate= 1.00e-02, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 308.833 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import time\n",
    "N_scan = 7\n",
    "results_train, results_test = [], []\n",
    "\n",
    "learning_rates = learning_rate * np.logspace(-1, 1, 7, base=10)\n",
    "for learning_rate_ in learning_rates:\n",
    "    tic = time.time()\n",
    "    trans, loss_train, loss_test, p_1, p_2, p_2_pred = fit_data(df_1, df_2, learning_rate=learning_rate_, verbose=False)\n",
    "    print(f'Pour learning_rate= {learning_rate_:.2e}, {loss_train=:.2e} / {loss_test=:.2e}; le temps de calcul est {time.time()-tic:.3f} s')\n",
    "    results_train.append(loss_train)\n",
    "    results_test.append(loss_test)\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (13, 8))\n",
    "# ax.plot(learning_rates, results_train, '--')\n",
    "ax.plot(learning_rates, results_test)\n",
    "ax.set_xlabel = 'learning rate'\n",
    "ax.set_ylabel = 'Loss'\n",
    "ax.set_yscale('log');\n",
    "ax.set_xscale('log');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T07:42:11.264848Z",
     "iopub.status.busy": "2022-06-03T07:42:11.264045Z",
     "iopub.status.idle": "2022-06-03T08:21:51.861864Z",
     "shell.execute_reply": "2022-06-03T08:21:51.862238Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  64  256  576 1024 1600 2304]\n",
      "Pour batch_size= 64, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 520.688 s\n",
      "Pour batch_size= 256, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 350.158 s\n",
      "Pour batch_size= 576, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 334.385 s\n",
      "Pour batch_size= 1024, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 335.520 s\n",
      "Pour batch_size= 1600, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 399.317 s\n",
      "Pour batch_size= 2304, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 440.242 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results_train, results_test = [], []\n",
    "batch_sizes = (batch_size * np.arange(1, N_scan) ** 2) // 8\n",
    "print(batch_sizes)\n",
    "for batch_size_ in batch_sizes:\n",
    "    tic = time.time()\n",
    "    trans, loss_train, loss_test, p_1, p_2, p_2_pred = fit_data(df_1, df_2, batch_size=batch_size_, verbose=False)\n",
    "    print(f'Pour batch_size= {batch_size_}, {loss_train=:.2e} / {loss_test=:.2e}; le temps de calcul est {time.time()-tic:.3f} s')\n",
    "    results_train.append(loss_train)\n",
    "    results_test.append(loss_test)\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (13, 8))\n",
    "# ax.plot(batch_sizes, results_train, '--')\n",
    "ax.plot(batch_sizes, results_test)\n",
    "ax.set_xlabel = 'batch size'\n",
    "ax.set_ylabel = 'Loss'\n",
    "ax.set_yscale('log');\n",
    "ax.set_xscale('log');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T08:21:51.866362Z",
     "iopub.status.busy": "2022-06-03T08:21:51.865730Z",
     "iopub.status.idle": "2022-06-03T08:21:51.867723Z",
     "shell.execute_reply": "2022-06-03T08:21:51.868077Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.  1.  1.  1.  1.  1.  0.9]\n"
     ]
    }
   ],
   "source": [
    "beta1s = 1 - (1 - beta1) * np.logspace(-1, 1, 7, base=10)\n",
    "print(beta1s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T08:21:51.873676Z",
     "iopub.status.busy": "2022-06-03T08:21:51.872910Z",
     "iopub.status.idle": "2022-06-03T08:58:20.808583Z",
     "shell.execute_reply": "2022-06-03T08:58:20.808919Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.  1.  1.  1.  1.  1.  0.9]\n",
      "Pour beta1= 9.99e-01, loss_train=4.96e+01 / loss_test=4.37e+01; le temps de calcul est 310.031 s\n",
      "Pour beta1= 9.98e-01, loss_train=4.49e+01 / loss_test=3.96e+01; le temps de calcul est 320.982 s\n",
      "Pour beta1= 9.95e-01, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 312.062 s\n",
      "Pour beta1= 9.90e-01, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 313.891 s\n",
      "Pour beta1= 9.78e-01, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 313.424 s\n",
      "Pour beta1= 9.54e-01, loss_train=4.47e+01 / loss_test=3.95e+01; le temps de calcul est 308.998 s\n",
      "Pour beta1= 9.00e-01, loss_train=4.48e+01 / loss_test=3.95e+01; le temps de calcul est 309.403 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results_train, results_test = [], []\n",
    "beta1s = 1 - (1 - beta1) * np.logspace(-1, 1, 7, base=10)\n",
    "print(beta1s)\n",
    "for beta1_ in beta1s:\n",
    "    tic = time.time()\n",
    "    trans, loss_train, loss_test, p_1, p_2, p_2_pred = fit_data(df_1, df_2, beta1=beta1_, verbose=False)\n",
    "    print(f'Pour beta1= {beta1_:.2e}, {loss_train=:.2e} / {loss_test=:.2e}; le temps de calcul est {time.time()-tic:.3f} s')\n",
    "    results_train.append(loss_train)\n",
    "    results_test.append(loss_test)\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (13, 8))\n",
    "#ax.plot(beta1s, results_train, '--')\n",
    "ax.plot(beta1s, results_test)\n",
    "ax.set_xlabel = 'beta1'\n",
    "ax.set_ylabel = 'Loss';\n",
    "ax.set_yscale('log');\n",
    "#ax.set_xscale('log');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T08:58:20.814769Z",
     "iopub.status.busy": "2022-06-03T08:58:20.814176Z",
     "iopub.status.idle": "2022-06-03T09:35:01.331274Z",
     "shell.execute_reply": "2022-06-03T09:35:01.331634Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour beta2= 9.95e-01, loss_train=4.49e+01 / loss_test=3.96e+01; le temps de calcul est 314.849 s\n",
      "Pour beta2= 9.89e-01, loss_train=4.49e+01 / loss_test=3.96e+01; le temps de calcul est 312.830 s\n",
      "Pour beta2= 9.77e-01, loss_train=4.49e+01 / loss_test=3.97e+01; le temps de calcul est 312.748 s\n",
      "Pour beta2= 9.50e-01, loss_train=4.50e+01 / loss_test=3.97e+01; le temps de calcul est 313.169 s\n",
      "Pour beta2= 8.92e-01, loss_train=4.49e+01 / loss_test=3.97e+01; le temps de calcul est 312.876 s\n",
      "Pour beta2= 7.68e-01, loss_train=4.49e+01 / loss_test=3.97e+01; le temps de calcul est 313.768 s\n",
      "Pour beta2= 5.00e-01, loss_train=4.50e+01 / loss_test=3.97e+01; le temps de calcul est 320.022 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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R44ySbE0rzlJGKn9dA8BQqjl4RH9+f49u+fjEE/YFVpQX6aGV1Xpl815VlBcNYYWJg3/hAGAImZnKcjNUlpuhxTNGSYqElF0NLR/ZJ+WVzXv15Ns10cdIEwrCkVGU4mOjKeEgf4UDwGB5dPVOmaTr5514Ba1543KVk5GiF6rqCSSniX/NAMBjZqbinHQV56Trk9OP/WO2u7ElFlAqaxv15tb9euqd2uhjpHF5odhISnlJZHWw7HRWeQGAM9XW0aVH39qpT0wpVElO+gmvDfh9unTqSC2vqldbRxcLmJwGAgkADFMjs9I0MitNF089Nnd57+FWVdY1qLImMuVrbfVB/eHdutj5MXkZx/ZJiYaVnIxUL8oHgLj14oZ67Wtq1ZJ5Y07p+oryIj2+tkZvbN2nj08uHOTqEg+BBADiSEFmUBdNLtRFPf7BO9DcFutJqaxt0Hs1h/TH93bFzpeOSI9t5BgJK1nKCwe9KB8A4sKylTtUOiJdiyYVnNL1F0zMVzgY0AtV9QSS00AgAYA4lxtK1aJJBR/5h7PhSHssoHQvRby8qj52vjg7TdNLjo2ilJdkqzAzzYvyAWBY2bKnSW9+uF//s2Ky/D47pcekpfh10ZRCvVi1Wz+8yp3y4xBBIAGABJSdkaILJubrgon5sWONLe2qqm1UVV1DbOf5lzbulnOR84WZwdhGjt27zo/MCsqMf1gBJI9lq6qV4jddN6esX4+rmF6kZ96t05rtBzRvfN4gVZeYCCQAkCSy0lK0YEKeFkw49g9lU2uHNu6KbOTYPe3r5ff3qCsaUvLDqbGelPKSyLSv4uw0QgqAhHS0rVNPrq1RRfko5fdzauvHJxcoGPDp+cp6Akk/EUgAIImFgwGdNzZX543NjR070tahjbsOf2QZ4hUf7FNnNKXkhlI1vTgrNopSXpytstx0QgqAuPfMe3VqbOnQDSdZ6rcvoWBAiyYV6IWqen3v09P4O7EfCCQAgI/ISA1o9pgRmj1mROxYS3unNtUfjvSjREPKfSs+VHtnJKRkp6dEelGKj035GpObIR/zqAHEkWUrq3VWYVhzx+We/OI+VEwv0p827NZ7NQ06pyxnYItLYAQSAMBJpaX4NbMsRzN7/APb2tGpzfVNkX6UaAP9A69vV1tnlyQpMxjQtOhGjjNKI/ukjM8PEVIADEvraxr0bk2D/s8ZjG5cMnWkAj7T85X1BJJ+IJAAAE5LMODXjNJI2OjW3tmlzbsPq6q2MRZUHlpZrdaOSEgJpfo1LTrdq3sp4gkFYVakAeC5ZauqlZ7i19WzS0/7ObIzIr16yyt36X9VTGba1ilKykBiZuMl/b2kbOfcNV7XAwCJIsXv0/TiyGjIdedFVqjp6OzSlr1NqqxtjPWlPLp6p462b5ckpaX4NG1UZCSleyniiYVhpfjZ7RjA0Ghsadfv19XpM+cUKyst5Yyeq6K8SH//VKU2727S5KLMAaowsZ00kJhZmqRXJQWj1z/hnPteH9fdJukmSSbpV865O6LHcyTdJ6lckpP0Nefcm9Fz/03S16PH10v6qnOupb8vwsx+LekKSXucc+W9zlVIulOSX9J9zrl/dc59KOlGM3uiv/cCAPRPwO/TlKIsTSnK0jXR3zx2djlt2xeZ7rW+plGVdQ168u1a/ebNaklSMODTlFFZKo9O+SovydakkZlKDRBSAAy8p96u1dH2Tt0w/9R2Zj+RS6eN1P9+ulLPV+4ikJyiUxkhaZX0Cedck5mlSHrNzJ53zq3svsDMyhUJI3MltUlabmbPOue2KBIGljvnrjGzVEkZ0ceUSPq2pGnOuaNm9pikz0t6sMfzFko66pw73OPYxOjz9vSgpJ9J+o+eB83ML+keSZdKqpH0lpn9wTm34RReNwBgkPh9pomFmZpYmKnPzooc6+py2r6/ObaR4/qaBv3h3TotW7VDkpTq92lyUWZsI8fy4mxNLspUWorfw1cCIN4557R0ZbXO6TUF9XQVZqZpzpgRWl5Zr9svmTQAFSa+kwYS55yT1BT9NiX65XpdNlXSKufcEUkys1ckXW1m/y5pkaSvRJ+rTZHA0vP+6WbWrkhQqev1vBdKutnMLnfOtZrZTZKulrS4V42vmtnYPsqfK2lLdEREZvaopCslEUgAYJjx+UzjC8IaXxDWlTNLJEV+UNhx4Eh0I8fIlK/n1tfrkdU7JUkBn2nSyEhI6Z7yNW1UFiEFwClbve2APtjTpB9/7uwBe86K8lH6wbMbtH1fs8bmhwbseRPVKfWQREca1kqaKOke59yqXpdUSvonM8uTdFTS5ZLWSBonaa+kB8zsnOhz3Oaca3bO1ZrZv0naEX3Mi865F3s+qXPucTMbJ+m3Zva4pK8pMtpxqkok7ezxfY2kedE6/0nSLDP7rnPuX/p4zZ+W9OmJEyf243YAgIFkZhqTF9KYvJCuOLtYUiSk1Bw8GtvIcX1to17auEePramRFB19KQhH90mJjKZMK85SRmpStk0COIllq3YoKy2gT59TPGDPedn0kfrBsxv0QlW9vnnhhAF73kR1Sn87O+c6Jc2M9oM8ZWblzrnKHuc3mtmPJL0oqVnSOkmd0ec/V9KtzrlVZnanpO9I+gczG6HIaMU4SYckPW5mNzjnlva694+jIxv3SprgnGvSGXLO7Zd080mueUbSM3PmzLnpTO8HABg4Zqay3AyV5WZo8YxRkiIhZVdDy0c2c3xl8149+XZN9DHShIJwZBSl+NhoSjhISAGS2b6mVj1fuUs3zB+j9NSBG1ktHZGhGSXZer6SQHIq+vU3sXPukJm9LKlCkVGRnuful3S/JJnZPysyGlEjqabHiMoTigQSSbpE0jbn3N7oY34n6XxJHwkkZrZQkYb4pyR9T9K3+lFyraSyHt+XRo8BABKImak4J13FOen65PSi2PHdjS2xgFJZ26g3t+7XU+/URh8jjcsLRTdyjIykTC/OVnb6ma2wAyB+PLZmp9o7nZacxs7sJ1NRXqSfvPC+djUc1ajs9AF//kRyKqtsFUhqj4aRdEWmTP2oj+sKnXN7zGy0In0e86OP2Wlmk51z70u6WMf6N3ZImm9mGYpM2bpYkWlePZ9zlqRfKrKC1jZJy8zsh865/32Kr+8tSWdFp33VKtI0/4VTfCwAIM6NzErTyKw0XTx1ZOzY3sOtkY0cayJTvtZWH9Qf3j3WwjgmL+PYPinRsJKTkepF+QAGUVeX08Ordmj++FxNLBz41bC6A8mLVbv15fPHDvjzJ5JTGSEZJek30T4Sn6THnHPPSpKZPSfp6865OklPRnsz2iXd4pw7FH38rYoEiVRJH0r6qiRFp3A9IeltSR2S3lEkfPSUIek659zW6P2+pGiDfE9m9oikj0vKN7MaSd9zzt3vnOsws29JekGRZX9/7ZyrOoXXDABIUAWZQV00uVAXTS6MHTvQ3BbrSamsbdB7NYf0x/d2xc6XjkiPbeQYCStZygsHvSgfwAB55YO9qjl4VN9ZPGVQnn9CQVhnFYb1fOUuAslJWGQRLRzPnDlz3Jo1a05+IQAgoTQcaY8FlO6liLfta46dL85Oi23k2D3lqzAzzcOKAfTH13/zltbtbNAb3/nEoO1x9NMX39fPXt6it/7+En6JIcnM1jrn5vQ+TjcfAAB9yM5I0QUT83XBxPzYscaWdlXVNqqqrrsvpUEvbdyt7t/tFWYGYxs5lkfDysisoMzMo1cBoC+1h47qz5v26K8/PmFQN1y9rLxId/15i17auFt/dd7A96kkCgIJAACnKCstRQsm5GnBhLzYsabWDm3cFdnIsXva18vv71FXNKTkh1NjPSnlJZFpX8XZaYQUwEOPrt4hJ+n6uYMbEqaNylJZbrqWV9YTSE6AQAIAwBkIBwM6b2yuzhubGzt2pK1DG3cd/sgyxCs+2KfOaErJDaVqenFWbBSlvDhbZbnphBRgCLR3dunRt3bqosmFKh2RMaj3MjNVTC/Sg29sV2NLu7LSWMWvLwQSAAAGWEZqQLPHjNDsMSNix1raO7Wp/nCkHyUaUu5b8aHaOyMhJTs9JdKLUnxsyteY3Az5fIQUYCD9acNu7T3cqhvmD82IRUX5KP1qxTa9vGmPrpxZMiT3jDcEEgAAhkBail8zy3I0sywndqy1o1Ob65si/SjRBvoHXt+uts4uSVJmMKBp0Y0cZ5RG9kkZnx8ipABnYOnKapXkpOvCSYUnv3gAzCrLUWFmUMsr6wkkx0EgAQDAI8GAXzNKI2GjW3tnlzbvPqyq2sZYUHloZbVaOyIhJZTq17TodK/upYgnFITlJ6QAJ7V1b5Pe2Lpf/+OyyUP2/xmfz3TZ9CI9sbZGR9s6B3RH+ERBIAEAYBhJ8fs0vTgyGnLdeWWSpI7OLm3Z26TK2sZYX8qjq3fqaPt2SVJaik/TRkVGUrqXIp5YGFaKf/BWDwLi0cOrdijFb7puTtmQ3ndxeZEeWlmtVzbvVUV50ZDeOx4QSAAAGOYCfp+mFGVpSlGWrpldKknq7HLati8y3Wt9TaMq6xr05Nu1+s2b1ZKkYMCnKaOyNKNHX8qkkZmDusQpMJy1tHfqibU1umx6kQoyh3ZPkLnjcpWTkaIXquoJJH0gkAAAEIf8PtPEwkxNLMzUZ2dFjnV1OW3f3xzbI6WytlG/X1enpSt3SJJS/T5NLsqMNs1HRlQmjcxUWgpTSJD4nnm3Tg1H27Vk3pghv3fA79OlU0dqeVW92jq6+MVALwQSAAAShM9nGl8Q1viCcKx5tqvLaefBI9GQEpny9dz6XXpkdSSkBHymSSMzNXdcrm6/5CzlZKR6+RKAQbNs1Q5NLAxr/vjck188CCrKi/T42hq9sXWfPj55aBrq4wWBBACABObzmcbkhTQmL6Qrzi6WJDnnVHPwaGwjx/W1jVq6slrLK+v10+vO0fk9dqcHEkFlbYPW7Tyk7316mmf7/VwwMV/hYEAvVNUTSHphvAgAgCRjZirLzdDiGaP0Py6bov/42lw99TcXKCPo15L7V+lfntuo1o5Or8sEBsyyVdVKS/Hp6nNLPashLcWvi6YU6sWq3bFNUhFBIAEAAJpRmq1nb/2YvjB3tP791Q/12Xve0JY9h70uCzhjjS3t+v26On3mnGJlp3u7U3rF9CLtb27TW9sPeFrHcEMgAQAAkiI7zP/TZ2fovi/NUX1jiz5112t66M3tco7f5iJ+Pf1OrY60deqG+UPfzN7bxycXKBjwaXllvdelDCsEEgAA8BGXTBup5bcv1PzxefqH31fpxt+s0d7DrV6XBfSbc05LV1ZrRkm2zi7N8bochYIBLZpUoBeq6gn6PRBIAADAXyjMTNODXz1P//iZ6Xptyz5V3PGq/rxpt9dlAf2ypvqgNu9u0g3zR3tdSkzF9CLtamjRuzUNXpcybBBIAABAn8xMXz5/rJ699WMqyAzqaw+u0T88XamjbTS8Iz4sXVmtzLSAPn1OsdelxFwydaQCPmPaVg8EEgAAcEKTRmbq99+6QDctHKeHVlbrirtXqLKW3+5ieNvf1Krn19frc+eWKiN1+Ox0kZ2RogUT8rS8chfTtqIIJAAA4KSCAb/+/lPTtPTGeWpq7dBnf/66fvHKVnWxfCmGqcfX1qits0tL5g2f6VrdKsqLtH3/EW3e3eR1KcMCgQQAAJyyj52Vr+W3LdIlU0fqX5/fpCX3rVLdoaNelwV8RFeX08OrdmjeuFydNTLT63L+wqXTRspMer5yl9elDAsEEgAA0C8jQqn6+ZJz9ePPna13aw6p4o5X9ex7dV6XBcS8+sFe7ThwREuGwVK/fSnMTNN5Y3LpI4kikAAAgH4zM113Xpme+/ZCjS8I61sPv6P//ti7OtzS7nVpgJat2qH8cKoqphd5XcpxXVZepE31h7V9X7PXpXiOQAIAAE7b2PyQHr95gb598Vl66p0aXX7XCq2tZhdqeKfu0FH958bdum5OmVIDw/dH3cumj5QkLa9ilGT4vksAACAupPh9+ttLJ+mxby6Qc9K1v3hT/+9Pm9XR2eV1aUhCj67eISfp+rnDr5m9p9IRGTq7NJtpWyKQAACAATJnbK6ev22hrppVojv/8wNd++9vqno/01EwdNo7u/ToWzv18UkFKsvN8Lqck7psepHW7TykXQ3JvTAEgQQAAAyYzLQU/fS6mbr7+lnauqdJl9+5Qo+v2cl+CxgSL23YrT2HW3XDMG1m762iPNLj8kKSj5IQSAAAwID79DnFWn77Is0ozdb/eOI93fLw2zp0pM3rspDglq6qVklOuj4+udDrUk7JhIKwzioMJ30fCYEEAAAMiuKcdC37+nx9Z/EU/WnDblXcsUJvbNnndVlIUB/ubdLrW/br+rll8vvM63JO2eLyIq3edkD7m1q9LsUzBBIAADBo/D7TzRdO0FN/c4Eygn594b5V+qc/blBrR6fXpSHBPLxqhwK+yHLU8eSy8iJ1Oemljbu9LsUzBBIAADDoykuy9cdbF+qG+aP1qxXbdNU9b+iD3Ye9LgsJoqW9U4+vrdFl04tUmJnmdTn9Mm1Ulspy0/V8EveREEgAAMCQSE/164dXzdB9X5qjPY0tuuLu1/SbN7bT8I4z9sf3dqnhaLuWzB/eS/32xcy0uHyUXt+yT41JurEogQQAAAypS6aN1PLbF2nBhDx97w9V+tqDb2nv4eSdP48zt3RVtcYXhLRgfJ7XpZyWy6YXqb3T6eVNe7wuxRMEEgAAMOQKMoN64Cvn6ftXTtcbW/er4o5X9Z9JPIcep6+qrkHv7DikJfPGyCx+mtl7mlWWo8LMoJ5fn5zTtggkAADAE2amLy0Yq2dv/ZgKs9J042/W6H8/vV5H22h4x6lbtmqH0lJ8uubcUq9LOW0+n+my6UX6r817kvLzTyABAACeOmtkpp6+5Xx9Y9F4LV25Q1fcvUKVtQ1el4U4cLilXU+/U6tPn12s7IwUr8s5I4vLi9TS3qVXNu/1upQhRyABAACeCwb8+rvLp2rZ1+epubVTn/356/rFK1vV2UXDO47v6XdqdaStU0viZGf2E5k7Llc5GSl6IQk3SSSQAACAYeOCiflafvtCXTJ1pP71+U1act9K1R066nVZGIacc1q2aofKS7J0Tmm21+WcsYDfp0unjtRLG3erraPL63KGFIEEAAAMKzkZqfr5knP142vO1vqaBlXc8aqeebfO67IwzKytPqhN9Yd1Qxw3s/e2eEaRDrd06I2t+7wuZUgRSAAAwLBjZrpuTpmeu22hxheEdesj7+hvH1unw0m6TwP+0tKV1coMBvSZmcVelzJgzp+Qr3AwkHTTtggkAABg2BqTF9LjNy/Qty8+S0+/U6vL71qhtdUHvC4LHjvQ3Kbn1tfr6nNLlJEa8LqcAZOW4tdFUwr1YtXupOqfIpAAAIBhLcXv099eOkmP37xAknTtL97UT/+0WR2dyTXPHsc8vman2jq7EqKZvbeK6UXa39ymt7YnT/AmkAAAgLgwe0yunvv2Ql01q0R3/ecHuuYXb2r7vmavy8IQ6+pyenj1Ds0dm6tJIzO9LmfAfXxygYIBn5ZXJs+0LQIJAACIG5lpKfrpdTP1sy/M0od7m3T5XSv02Jqdci55prcku9e27FP1/iNaMn+016UMilAwoEWTCvRCVb26kmTaFoEEAADEnSvOLtby2xfp7NJs/c8n3tPfLHtbB5vbvC4LQ2DpymrlhVJVUV7kdSmDpmJ6kXY1tOi9JNkglEACAADiUnFOuh7++nx9d/EUvbRxtyrufFWvb0mu5VKTza6Go3pp425dO6dMwYDf63IGzSVTRyrgs6SZtkUgAQAAccvnM33zwgl66m8uUDgY0JL7Vumf/rhBrR2dXpeGQfDo6p1ykpbMS8zpWt2yM1K0YEKellfuSorpiAQSAAAQ98pLsvXsrQv1xflj9KsV23TVPW9o8+7DXpeFAdTe2aVH39qhCycVqCw3w+tyBl1FeZG27z+i95Pgc0wgAQAACSE91a8fXFWu+788R3saW/Tpu1/Tb97YnhS/YU4G/7lxt3Y3tmrJvMRb6rcvl04bKTPphcrdXpcy6AgkAAAgoVw8daSW375I50/I0/f+UKWvPviW9hxu8bosnKFlq3aoODtNn5hS6HUpQ6IwM00lOenavj/xl7YmkAAAgIRTkBnUr79ynr5/5XS9uXW/Ft+xQi9tSPzfNCeqbfuateKDfbp+7mj5feZ1OUMmHAyoqbXD6zIGHYEEAAAkJDPTlxaM1bO3fkwjs9L09f9Yo79/ar2OttHwHm8eXlWtgM/0V+eVeV3KkAoHA2omkAAAAMS3s0Zm6qlbztc3Fo3Xw6t36FN3r9D6muTY3yERtLR36vG1Nfrk9JEqzErzupwhFSKQAAAAJIZgwK+/u3yqlt04T0daO/XZn7+ue/9rqzqTZCfsePbc+l06dKRdNyRJM3tPTNkCAABIMOdPzNfy2xfqsulF+tHyTfrCr1aq9tBRr8vCCSxdWa3x+SEtmJDndSlDLhT0q7k18acYEkgAAEBSyclI1c++MEv/du05qqxtUMUdr+qZd+u8Lgt92FDXqLd3HNIX5o2WWfI0s3djyhYAAECCMjNdM7tUz922UBMLw7r1kXf0t79dp8Mt7V6Xhh6WrapWMODTNbNLvS7FE+FgQM1tHQm/lw6BBAAAJK0xeSE9/s0Fuv2Ss/T0ulotvnOF1mw/4HVZkNTU2qGn36nVFWcXKycj1etyPBEKBtTlpKPtiT1ti0ACAACSWsDv0+2XTNLjN58vn5mu+/c39dMX31d7Z5fXpSW1p9+pVXNbp26YP9rrUjwTCgYkKeEb2wkkAAAAkmaPGaHnbluoq88t1V1/3qJrfvGmtu9L/F2yhyPnnJaurNb04izNLMvxuhzPhIN+SUr4xnYCCQAAQFQ4GNC/XXuO7vnCudq+r1mX37VCv31rR8LP4R9u3t5xUJvqD2vJvDFJ2czeLZQaHSFpYYQEAAAgqXzq7FFafvtCnVOao//15Hr99dK3dbC5zeuyksaylTsUDgZ05cxir0vxVJgpWwAAAMlrVHa6ln19nr67eIr+c9NuVdz5ql77YJ/XZSW8g81tenb9Ll19bkmshyJZdb/+RF/6l0ACAABwHD6f6ZsXTtBTf3OBMtNSdMP9q/TDZzeotSOx5/R76fG1O9XW0aUlSbgze2/htGggaSOQAAAAJLXykmw9862P6Yvzx+i+17bpyp+9rs27D3tdVsLp6nJ6eNUOnTd2hCYXZXpdjueYsgUAAICY9FS/fnBVuX79lTna19SqK+5+TQ++vo2G9wH0+tZ92r7/iG6Yz+iIxJQtAAAA9OETU0bq+dsW6YIJefo/z2zQVx54S3sOt3hdVkJYurJauaFUVZQXeV3KsJCREln2t4llfwEAANBTQWZQv/7KefrBldO18sP9qrhjhf60YbfXZcW1+oYWvbRxj66dU6pgwO91OcOCz2cKpfoZIQEAAMBfMjN9ccFY/fHbH1NRVppu+o81+run1utIgjcgD5ZH39qhzi6nJXOZrtVTKBggkAAAAOD4JhZm6qlbztc3F43XI6t36Iq7XtP6mgavy4orHZ1denT1Ti2aVKDReRlelzOshIMBmtoBAABwYsGAX9+9fKqWfX2ejrR16rM/f10//68t6uyi4f1U/OemPapvbNEN80Z7XcqwwwgJAAAATtn5E/K1/PaFumx6kX68/H1d/6uVqj101Ouyhr2lK6s1KjtNn5hS6HUpw04o6FczTe0AAAA4VTkZqfrZF2bp3649R1W1Daq441X9fl2t12UNW9v3NWvFB/v0+fNGK+DnR9PewsGADjNCAgAAgP4wM10zu1TP3bZQZxWGdduj6/TffrtOjS3tXpc27Dyyeof8PtPn55Z5XcqwxJQtAAAAnLYxeSE99s0Fuv2Ss/SHd+u0+I4Vemv7Aa/LGjZa2jv12Jqd+uS0kRqZleZ1OcMSgQQAAABnJOD36fZLJumxby6Q32f6q39/U//3xffV3tnldWmee75ylw4eadeSeSz1ezyZrLIFAACAgTB7zAg9d9tCXX1uqe7+8xZd84s3tW1fs9dleWrZyh0alx/S+RPyvC5l2AoFA2rt6FJHAgdYAgkAAMAQCQcD+rdrz9HPl5yr7fua9am7Vui3b+2Qc8m3PPCm+katqT6oJfNGy+czr8sZtkLBgCQl9EpbBBIAAIAhdvmMUVp++0LNLMvR/3pyvW5eulYHm9u8LmtILV1ZrdSAT587t9TrUoa1cNAvSWpqS9xpWwQSAAAAD4zKTtfSG+fp7y6foj9v2qPL7nhVKz7Y63VZQ6KptUNPvV2rK84epRGhVK/LGdaOjZAQSAAAADDAfD7TNxZN0NO3XKCs9BR98f7V+sGzG9TSnrjTcyTp9+tq1dzWqRvm08x+Mt2BJJEb2wkkAAAAHptenK1nvvUxfWnBGN3/2jZddc/rer/+sNdlDQrnnJau3KGpo7I0qyzH63KGvTAjJInJzMab2f1m9oTXtQAAAEhSeqpf37+yXA985Tzta2rVp3/2mn792jZ1dSVWw/s7Ow9p465G3TB/tMxoZj+ZUCqBRGaWZmarzexdM6sys388znW3mVll9JrbexzPMbMnzGyTmW00swWncq4/zOzXZrbHzCr7OFdhZu+b2RYz+44kOec+dM7deDr3AgAAGEwXTSnU8tsX6WMT8/X9ZzfoKw++pT2NLV6XNWCWrqxWOBjQlTNLvC4lLoRjU7YSdxrfqYyQtEr6hHPuHEkzJVWY2fyeF5hZuaSbJM2VdI6kK8xsYvT0nZKWO+emRM9t7PHQE52TmRWaWWavYxP1lx6UVNH7oJn5Jd0jabGkaZKuN7Npp/CaAQAAPJMfDur+L8/RD64q1+pt+1Vx5wq9WFXvdVln7GBzm559b5eumlUc+0EbJxbqXmWrpd3jSgbPSQOJi2iKfpsS/eo9djhV0irn3BHnXIekVyRdbWbZkhZJuj/6XG3OuUOSdKJzPVwo6WkzC0Yfc5Oku/uo8VVJB/oof66kLdERkTZJj0q68mSvGQAAwGtmpi/OH6Nnb/2YRmWn6RsPrdV3f7deR+J4+dcn365RW0cXzez9EFtlqy25R0hkZn4zWydpj6Q/OedW9bqkUtJCM8szswxJl0sqkzRO0l5JD5jZO2Z2n5mFoo850TlJknPucUkvSPqtmS2R9DVJ1/bj9ZVI2tnj+xpJJdE6fyFplpl99ziv+dNm9suGhoZ+3A4AAGBgTSzM1FN/c4G+eeF4PfrWDl1x12t6r+aQ12X1W1eX07JVOzRnzAhNKcryupy4EQz4FPAZq2w55zqdczMllUqaG52i1fP8Rkk/kvSipOWS1knqlBSQdK6ke51zsyQ1S/pO9GEnOtfzuX8sqUXSvZI+02O05rQ55/Y75252zk1wzv3Lca55xjn3jezs7DO9HQAAwBlJDfj03cVTtezr83S0vVNX//wN3fPyFnXGUcP7G1v3a9u+Zi2ZP9rrUuKKmSmcFkjupvaeolOqXlYf/RrOufudc7Odc4skHZS0WZERiZoeIypPKBJCdJJzMWa2UFK5pKckfa8/9UqqVWSkpltp9BgAAEDcOX9CvpbftkiXlRfpJy+8r+t/tVI1B494XdYpWbaqWiMyUrS4fJTXpcSdUGoguUdIzKzAzHKif06XdKmkTX1cVxj972hJV0t62DlXL2mnmU2OXnaxpA2SdKJzPZ5zlqRfKtL38VVJeWb2w368vrcknWVm48wsVdLnJf2hH48HAAAYVrIzUvSz62fp/157jjbUNWrxnSv0+3XD+/etuxtb9OKG3bpuTpnSUvxelxN3wkFGSEZJetnM3lPkB/w/OeeelSQze87MiqPXPWlmGyQ9I+mWHg3qt0paFn38TEn/3OO5T3ROkjIkXeec2+qc65L0JUnVvQs0s0ckvSlpspnVmNmNkhRtsP+WIn0oGyU95pyrOoXXDAAAMGyZmT43u1TP37ZQk0Zm6rZH1+n2R99R4zBdienR1TvV2eV0/Vyma52OUNCv5gRe9teci5+5h16YM2eOW7NmjddlAAAA9Kmjs0v3vLxVd/35AxVlpen//dVMzR2X63VZMR2dXVr445c1sTCsh26c53U5cemL96/S4ZYOPX3LBV6XckbMbK1zbk7v40m5UzsAAECiCPh9uu2Ss/T4zQsU8Js+/8s39ZMXNqm9s8vr0iRJf960R7saWljq9wwwZQsAAADD3rmjR+iP316oz51bqnte3qpr7n1D2/Y1e12Wlq7aoaKsNF08pdDrUuJWiEACAACAeBAOBvSTa8/RvUvO1fb9R3T5nSv0yOod8mqK/o79R/Tq5r36/NwyBfz82Hm6wsEkX2ULAAAA8WXxjFFafvtCzRqdo+/+br2++dBaHWhuG/I6lq2ult9n+vx5NLOfiVDQr+a2Ts+C5WAjkAAAACSgUdnpWnrjPP395VP1X+/vVcUdr+rVzXuH7P6tHZ16fE2NLplaqKLstCG7byIKBQPq7HJqaR8efUEDjUACAACQoHw+002LxuupW85XVnqKvvTr1fr+MxvU0j74S8gur6zXgeY2mtkHQDgYkKSEnbZFIAEAAEhw04uz9eytH9OXF4zRr1/fpqvueV2b6hsH9Z5LV1ZrbF6GLpiQP6j3SQah1EggSdTGdgIJAABAEkhL8esfryzXA185T/uaWvWZn72uX7+2TV1dA9+XsKm+UW9tP6gvzBstn88G/PmTTTiNERIAAAAkiIumFGr57Yu0cGK+vv/sBn35gdXa09gyoPd4eNUOpQZ8unZ22YA+b7LqnrLFCAkAAAASQn44qPu+PEc/vKpcb20/oMvueFUvVNUPyHM3t3bod2/X6ooZozQilDogz5nsQt2BpI1AAgAAgARhZrph/hg9e+tClYxI1zcfWqvv/u49HTnDH3p/v65OTa0dWjKfpX4HSjjolyQ1tQ7+YgReIJAAAAAksYmFYf3ury/QzRdO0KNv7dSn7npN7+48dFrP5ZzTslXVmlKUqXNHjxjYQpNYiClbAAAASGSpAZ++s3iKHv76fLW0d+pz976he17eos5+Nryv23lIVXWNumH+GJnRzD5QCCQAAABICgsm5Gn5bYtUUV6kn7zwvq7/5UrVHDxyyo9funKHQql+XTWrZBCrTD7dy/6yyhYAAAASXnZGiu6+fpZ+et052rCrUYvvWKHfr6s96eMOHWnTs+/V6apZJbFVoTAw/D5TeoqfERIAAAAkBzPT1eeW6vnbFmpSUaZue3Sdbnv0HTUcbT/uY55YW6PWji4tmcfO7IMhFAzQ1A4AAIDkUpabod9+Y77+9tJJeva9Xbr8zhVave3AX1znnNPDq3bo3NE5mlac5UGliS8c9DNlCwAAAMkn4Pfp2xefpSduXqCA3/T5X76pn7ywSe2dXbFr3ty6Xx/ua9YN8xkdGSyhYIApWwAAAEhes0aP0B+/vVDXzC7VPS9v1efufUMf7m2SJC1dVa2cjBRdPmOUx1UmrsiULQIJAAAAklg4GNCPrzlH9y45V9X7j+hTd72mX7yyVS9W7da1s0uVluL3usSElZnAIyQsgQAAAIB+WTxjlGaNHqH//vg6/evzmyRJX6CZfVAl8pQtAgkAAAD6rSg7TQ99bZ4eWlmtptYOjcsPeV1SQkvkVbYIJAAAADgtPp/py+eP9bqMpBAOsg8JAAAAAI+EggEdbe9UZ5fzupQBRyABAAAAhrlwMDKxqbkt8UZJCCQAAADAMBfqDiQJOG2LQAIAAAAMcwQSAAAAAJ4JByN7vCTiSlsEEgAAAGCYC6VGRkiaWhghAQAAADDEuqdsNTFlCwAAAMBQC9NDAgAAAMAr4TSW/QUAAADgkTBTtgAAAAB4JRjwye8zpmwBAAAAGHpmplCqX80s+wsAAADAC+FggClbAAAAALwRCgaYsgUAAADAGyFGSAAAAAB4JcwICQAAAACvhIJ+RkgAAAAAeCPSQ8IqWwAAAAA8wCpbAAAAADzTvcqWc87rUgYUgQQAAACIA+FgQB1dTq0dXV6XMqAIJAAAAEAcCAcDkpRwK20RSAAAAIA4EIoFksRqbCeQAAAAAHEgHPRLUsI1thNIAAAAgDgQGyFpI5AAAAAAGGLdgYQREgAAAABDjqZ2AAAAAJ4JEUgAAAAAeCWcGgkkh1sIJAAAAACGWCi6yhbL/gIAAAAYcgG/T8GAj1W2AAAAAHgjMy3AKlsAAAAAvBEKBmhqBwAAAOCNUCqBBAAAAIBHwkGmbAEAAADwSCjoZ5UtAAAAAN6ghwQAAACAZ5iyBQAAAMAzjJAAAAAA8EwoGFBzW6e6upzXpQwYAgkAAAAQJ8JBvyQl1G7tBBIAAAAgToSCAUlKqJW2CCQAAABAnAhHA0kiNbYTSAAAAIA4EY6NkBBIAAAAAAyxEIEEAAAAgFeYsgUAAADAM7ERElbZAgAAADDUQtFlf5tYZQsAAADAUKOpHQAAAIBn0lP88hmBBAAAAIAHzEyh1ABN7QAAAAC8EQoGGCEBAAAA4I1Q0M8ICQAAAABvhIMBVtkCAAAA4A2mbAEAAADwTJhAAgAAAMArkSlbBBIAAAAAHmDKFgAAAADPRAIJTe1xzczGm9n9ZvaE17UAAAAA/REO+tXW2aW2ji6vSxkQJw0kZpZmZqvN7F0zqzKzfzzOdbeZWWX0mtt7HM8xsyfMbJOZbTSzBb0e5zezd8zs2dN9EWb2azPbY2aVfZyrMLP3zWyLmX1HkpxzHzrnbjzd+wEAAABeCQUDkpQw07ZOZYSkVdInnHPnSJopqcLM5ve8wMzKJd0kaa6kcyRdYWYTo6fvlLTcOTclem5jr+e/rY9j3c9baGaZvY5N7OPSByVV9PF4v6R7JC2WNE3S9WY27bivFAAAABjmugNJojS2nzSQuIim6Lcp0S/X67KpklY554445zokvSLpajPLlrRI0v3R52pzzh3qfpCZlUr6lKT7jnP7CyU9bWbB6PU3Sbq7jxpflXSgj8fPlbQlOiLSJulRSVee7DUDAAAAw1W4e4SkLUkCiRSbVrVO0h5Jf3LOrep1SaWkhWaWZ2YZki6XVCZpnKS9kh6ITsu6z8xCPR53h6T/KanPCXDOucclvSDpt2a2RNLXJF17qi9OUomknT2+r5FUEq3zF5Jmmdl3j/OaP21mv2xoaOjH7QAAAIDBlYxTtuSc63TOzZRUKmludIpWz/MbJf1I0ouSlktaJ6lTUkDSuZLudc7NktQs6TuSZGZXSNrjnFt7knv/WFKLpHslfabHaM1pc87td87d7Jyb4Jz7l+Nc84xz7hvZ2dlnejsAAABgwISDfknS4ZYkCiTdotOtXlYf/RrOufudc7Odc4skHZS0WZERiZoeIypPKBJQJOkCSZ8xs+2KTKX6hJkt7f28ZrZQUrmkpyR9rz/1SqpVZKSmW2n0GAAAABCXjo2QJMbSv6eyylaBmeVE/5wu6VJJm/q4rjD639GSrpb0sHOuXtJOM5scvexiSRskyTn3XedcqXNurKTPS/qzc+6GXs85S9IvFen7+KqkPDP7YT9e31uSzjKzcWaWGr3PH/rxeAAAAGBYCaUm35StUZJeNrP3FPkB/0/OuWclycyeM7Pi6HVPmtkGSc9IuqVH8/qtkpZFHz9T0j/3o74MSdc557Y657okfUlSde+LzOwRSW9KmmxmNWZ2oyRFG+y/pUgfykZJjznnqvpxfwAAAGBYyUxLrFW2Aie7wDn3nqRZxzl3eY8/LzzONeskzTnJPf5L0n/1cfz1Xt+3S/pVH9ddf4Lnfk7Scye6PwAAABAvkrKpHQAAAMDwkOL3KTXgU1MyLfsLAAAAYPgIBwOMkAAAAADwRijoT55VtgAAAAAML6HUQMI0tRNIAAAAgDjDlC0AAAAAngkRSAAAAAB4JRxkyhYAAAAAj4SCfgIJAAAAAG9EpmyxyhYAAAAAD4SDATW3dcg553UpZ4xAAgAAAMSZcDAg56QjbfE/SkIgAQAAAOJMKBiQpIRYaYtAAgAAAMSZcDSQJEJjO4EEAAAAiDPHRkiYsgUAAABgiIWCfkmMkAAAAADwQJgeEgAAAABeiU3ZaiOQAAAAABhiNLUDAAAA8Ez3CElTC4EEAAAAwBDLSIk0tdNDAgAAAGDI+XymUKpfTSz7CwAAAMALoWCAERIAAAAA3ginBdTEKlsAAAAAvBBmhAQAAACAV0KpBBIAAAAAHgkFAzS1AwAAAPBGOOhnhAQAAACAN1hlCwAAAIBnwsGAmggkAAAAALwQCgbU2tGl9s4ur0s5IwQSAAAAIA6FggFJivtpWwQSAAAAIA6Fg35JivtpWwQSAAAAIA4dGyGJ76V/CSQAAABAHOoOJIyQAAAAABhymfSQAAAAAPAKTe0AAAAAPBNmyhYAAAAArzBCAgAAAMAzoeiyv81trLIFAAAAYIgFA36l+I0pWwAAAAC8EQoGmLIFAAAAwBuh1AAjJAAAAAC8EQ4G1NRCIAEAAADggVDQr+Y2AgkAAAAAD4SCATW1ssoWAAAAAA+EaWoHAAAA4BUCCQAAAADPRKZsEUgAAAAAeKB7hMQ553Upp41AAgAAAMSpUDCgLie1tHd5XcppI5AAAAAAcSoc9EtSXE/bIpAAAAAAcSoUDEhSXDe2E0gAAACAONUdSBghAQAAADDkwoyQAAAAAPAKIyQAAAAAPENTOwAAAADPHGtq7/S4ktNHIAEAAADiFKtsAQAAAPBMKJUeEgAAAAAe8ftMGal+RkgAAAAAeCMUDKi5jUACAAAAwAPhYEBNNLUDAAAA8EIoyJQtAAAAAB4JpQZoagcAAADgjXAwwAgJAAAAAG+ECCQAAAAAvBIKMmULAAAAgEfCQT+BBAAAAIA3QsGAWtq71NHZ5XUpp4VAAgAAAMSxcDAgSWpui8+9SAgkAAAAQByLBZI4nbZFIAEAAADiWIhAAgAAAMAr3SMk8drYTiABAAAA4tixERJ6SAAAAAAMsVDQL4kREgAAAAAeoKkdAAAAgGdiU7baCCQAAAAAhhhN7QAAAAA8Ewz45PeZmloIJAAAAACGmJkplOqnhwQAAACAN8LBgJpY9jd+mNl4M7vfzJ7wuhYAAADgTIWCgcQdITGzNDNbbWbvmlmVmf3jca67zcwqo9fc3uN4jpk9YWabzGyjmS2IHi8zs5fNbEP0Mbed7osws1+b2R4zq+zjXIWZvW9mW8zsO5LknPvQOXfj6d4PAAAAGE7CaYGEXmWrVdInnHPnSJopqcLM5ve8wMzKJd0kaa6kcyRdYWYTo6fvlLTcOTclem5j9HiHpP/unJsmab6kW8xsWq/nLTSzzF7HJuovPSipovdBM/NLukfSYknTJF3f+x4AAABAvItM2UrQQOIimqLfpkS/XK/Lpkpa5Zw74pzrkPSKpKvNLFvSIkn3R5+rzTl3KPrnXc65t6N/PqxIUCnp9bwXSnrazIKSZGY3Sbq7jxpflXSgj/LnStoSHRFpk/SopCtP9poBAACAeBJKTeApW1JkpMHM1knaI+lPzrlVvS6plLTQzPLMLEPS5ZLKJI2TtFfSA2b2jpndZ2ahPp5/rKRZkj7yvM65xyW9IOm3ZrZE0tckXduP11ciaWeP72sklUTr/IWkWWb23eO85k+b2S8bGhr6cTsAAABg6EV6SBK4qd051+mcmympVNLc6BStnuc3SvqRpBclLZe0TlKnpICkcyXd65ybJalZ0nd6PtbMwpKelHS7c66xj3v/WFKLpHslfabHaM1pc87td87d7Jyb4Jz7l+Nc84xz7hvZ2dlnejsAAABgUIWD/sSdstVTdLrVy+qjX8M5d79zbrZzbpGkg5I2KzIiUdNjROUJRQKKJMnMUhQJI8ucc7/r655mtlBSuaSnJH2vP/VKqlVkpKZbafQYAAAAkDC6V9lyrndnxfB3KqtsFZhZTvTP6ZIulbSpj+sKo/8dLelqSQ875+ol7TSzydHLLpa0IXqdKdJbstE599Pj3HuWpF8q0vfxVUl5ZvbDfry+tySdZWbjzCxV0ucl/aEfjwcAAACGvVAwoI4up9aOLq9L6bdTGSEZJellM3tPkR/w/+Sce1aSzOw5MyuOXvekmW2Q9IykW7qb1yXdKmlZ9PEzJf1z9PgFkr4o6RNmti76dXmve2dIus45t9U51yXpS5KqexdoZo9IelPSZDOrMbMbJSnaYP8tRfpQNkp6zDlXdQqvGQAAAIgb4WBAkuJy2lbgZBc4595TpOG8r3OX9/jzwuNcs07SnD6OvybJTnLv13t93y7pV31cd/0JnuM5Sc+d6D4AAABAPAtFA0lza4fyw0GPq+mfpNypHQAAAEgk4aBfUnyOkBBIAAAAgDh3bIQk/pb+JZAAAAAAcS7cY8pWvCGQAAAAAHEunpvaCSQAAABAnAsxQgIAAADAKyFGSAAAAAB4JZQaWWWLpnYAAAAAQy7g9yktxafmNkZIAAAAAHggHAwwZQsAAACAN0LBAE3tAAAAALwRSg2oqYVAAgAAAMADI0Ip2tfc5nUZ/UYgAQAAABLA6NyQduxv9rqMfiOQAAAAAAlgXH6GDh5pV8ORdq9L6RcCCQAAAJAAxuSFJEnb4myUhEACAAAAJIBx+ZFAUk0gAQAAADDURudmyEzato9AAgAAAGCIpaX4NSorTdX7j3hdSr8QSAAAAIAEMTY/xAgJAAAAAG+MyQvRQwIAAADAG/G49C+BBAAAAEgQY+Nw6V8CCQAAAJAgxsbh0r8EEgAAACBBxOPSvwQSAAAAIEHE49K/BBIAAAAggcTb0r8EEgAAACCBjM2Pr6V/CSQAAABAAhmbF19L/xJIAAAAgAQSb0v/EkgAAACABBJvS/8SSAAAAIAEEm9L/xJIAAAAgASSluJXcXZ63Cz9SyABAAAAEsyYvAxGSAAAAAB4Y2x+SNvpIQEAAADghbF5GTp0pF2HjrR5XcpJEUgAAACABNO99O/2OOgjIZAAAAAACWZcHC39SyABAAAAEkxZHC39SyABAAAAEkw8Lf1LIAEAAAASULws/UsgAQAAABJQvCz9SyABAAAAEtC4vFBcLP1LIAEAAAAS0Ji8DEnDf+lfAgkAAACQgOJl6V8CCQAAAJCA4mXpXwIJAAAAkIDiZelfAgkAAACQoMbmD/+lfwkkAAAAQIIakzf8l/4lkAAAAAAJKh6W/iWQAAAAAAkqHpb+JZAAAAAACWpcfkh+n2l3Y4vXpRxXwOsCAAAAAAyOCQVhbfpBhVL8w3ccgkACAAAAJCifz+STeV3GCQ3fqAQAAAAg4RFIAAAAAHiGQAIAAADAMwQSAAAAAJ4hkAAAAADwDIEEAAAAgGcIJAAAAAA8QyABAAAA4BkCCQAAAADPEEgAAAAAeIZAAgAAAMAzBBIAAAAAniGQAAAAAPAMgQQAAACAZwgkAAAAADxDIAEAAADgGQIJAAAAAM+Yc87rGoY1M9srqdrjMrIlNXhcA3A6+OxiIPF5Sm68//GN92/4yZe0b4jvOcY5V9D7IIEkDpjZL51z3/C6DqC/+OxiIPF5Sm68//GN92/4MbM1zrk5XtchMWUrXjzjdQHAaeKzi4HE5ym58f7HN94/HBcjJAAAAECSYYQEAAAAgJd+6XUB3RghAQAAAOAZRkgAAAAAeIZAkiTMbLyZ3W9mT3hdC3Cq+NxiIPF5Sm68//GP9zBxEUgGiZltN7P1ZrbOzNacwfP82sz2mFllH+cqzOx9M9tiZt850fM45z50zt14unUgOZhZjpk9YWabzGyjmS04zefhc5vkzGxy9O+/7q9GM7v9NJ+Lz1McMrP/ZmZVZlZpZo+YWdppPg/vv0fM7Lbo+1d1uv//jT4P7yFOiEAyuC5yzs3sawUDMys0s8xexyb28RwPSqro4/F+SfdIWixpmqTrzWyamc0ws2d7fRUOyKtBMrhT0nLn3BRJ50ja2PMkn1ucKufc+9G//2ZKmi3piKSnel7D5ylxmVmJpG9LmuOcK5fkl/T5Xtfw/g9jZlYu6SZJcxX59+CK3u8P72FiMbOQmf3GzH5lZkuG8t4EEu9cKOlpMwtKkpndJOnu3hc5516VdKCPx8+VtCX624I2SY9KutI5t945d0Wvrz2D+DqQIMwsW9IiSfdLknOuzTl3qNdlfG5xOi6WtNU5V93rOJ+nxBaQlG5mAUkZkup6nef9H96mSlrlnDvinOuQ9Iqkq3tdw3s4zB1vdOo4I1NXS3rCOXeTpM8MZZ0EksHjJL1oZmvN7C92JnXOPS7pBUm/jabQr0m6th/PXyJpZ4/va6LH+mRmeWb2C0mzzOy7/bgPksc4SXslPWBm75jZfWYW6nkBn1ucps9LeqT3QT5Pics5Vyvp3yTtkLRLUoNz7sVe1/D+D2+VkhZG/3fLkHS5pLKeF/AexoUH1Wt06ngjU5JKdez96BzCGhUYypslmY8552qjQ4x/MrNN0d8QxDjnfmxmj0q6V9IE51zTYBXjnNsv6ebBen4khICkcyXd6pxbZWZ3SvqOpH/oeRGfW/SHmaUq8pu2Pn944POUmMxshKQrFflFxyFJj5vZDc65pT2v4/0fvpxzG83sR5JelNQsaZ36+CGV93B4c869amZjex2OjUxJUvT9u1KRQFiqyHs9pIMWjJAMkuhvhxQdYnxKkTf/I8xsoaTy6Pnv9fMWtfrobypKo8eA01UjqcY5tyr6/ROKBJSP4HOLflos6W3n3O6+TvJ5SliXSNrmnNvrnGuX9DtJ5/e+iPd/eHPO3e+cm+2cWyTpoKTNva/hPYxLxxuZ+p2kz5nZvZKeGcqCCCSDINoUlNn9Z0mfVGTos+c1sxTZIfNKSV+VlGdmP+zHbd6SdJaZjYv+BvLzkv4wEPUjOTnn6iXtNLPJ0UMXS9rQ8xo+tzgN16uP6VoSn6cEt0PSfDPLMDNT5O+T3otk8P4Pc92N5GY2WpH+god7nec9TCDOuWbn3Fedc3/tnFs2lPcmkAyOkZJeM7N3Ja2W9Efn3PJe12RIus45t9U51yXpS5J6N3zKzB6R9KakyWZWY2Y3SlK0wexbiszd3CjpMedc1aC9IiSLWyUtM7P3JM2U9M+9zvO5xSmL/kLmUkV+69YXPk8JKjrS+oSktyWtV+TnjV/2uoz3f/h70sw2KPLb8lv6WOiE9zA+DbuRKXPOeXl/AAAAAIMk2kPybHQJbkVXvtusyMhlrSIjVV/wMgwyQgIAAAAkoL5Gp4bjyBQjJAAAAAA8wwgJAAAAAM8QSAAAAAB4hkACAAAAwDMEEgAAAACeIZAAAAAA8AyBBAAAAIBnCCQAAAAAPEMgAQAAAOAZAgkAAAAAz/x/ByoyRDG9DPcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 936x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results_train, results_test = [], []\n",
    "beta2s = 1 - (1 - .95) * np.logspace(-1, 1, 7, base=10)\n",
    "for beta2_ in beta2s:\n",
    "    tic = time.time()\n",
    "    trans, loss_train, loss_test, p_1, p_2, p_2_pred = fit_data(df_1, df_2, beta2=beta2_, verbose=False)\n",
    "    print(f'Pour beta2= {beta2_:.2e}, {loss_train=:.2e} / {loss_test=:.2e}; le temps de calcul est {time.time()-tic:.3f} s')\n",
    "    results_train.append(loss_train)\n",
    "    results_test.append(loss_test)\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (13, 8))\n",
    "# ax.plot(beta2s, results_train, '--')\n",
    "ax.plot(beta2s, results_test)\n",
    "ax.set_xlabel = 'beta2 with Adam instead of SGD'\n",
    "ax.set_ylabel = 'Loss'\n",
    "ax.set_yscale('log');\n",
    "ax.set_xscale('log');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T09:35:01.337638Z",
     "iopub.status.busy": "2022-06-03T09:35:01.336736Z",
     "iopub.status.idle": "2022-06-03T10:35:01.199517Z",
     "shell.execute_reply": "2022-06-03T10:35:01.199946Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 129  513 1153 2049 3201 4609]\n",
      "Pour num_epochs=129, loss_train=4.48e+01 / loss_test=3.95e+01; le temps de calcul est 39.438 s\n",
      "Pour num_epochs=513, loss_train=4.47e+01 / loss_test=3.95e+01; le temps de calcul est 156.765 s\n",
      "Pour num_epochs=1153, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 349.070 s\n",
      "Pour num_epochs=2049, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 621.422 s\n",
      "Pour num_epochs=3201, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 1000.203 s\n",
      "Pour num_epochs=4609, loss_train=4.47e+01 / loss_test=3.94e+01; le temps de calcul est 1432.706 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results_train, results_test = [], []\n",
    "num_epochss = ((num_epochs-1) * np.arange(1, N_scan) ** 2) // 8 + 1\n",
    "print(num_epochss)\n",
    "for num_epochs_ in num_epochss:\n",
    "    tic = time.time()\n",
    "    trans, loss_train, loss_test, p_1, p_2, p_2_pred = fit_data(df_1, df_2, num_epochs=num_epochs_, verbose=False)\n",
    "    print(f'Pour num_epochs={num_epochs_}, {loss_train=:.2e} / {loss_test=:.2e}; le temps de calcul est {time.time()-tic:.3f} s')\n",
    "    results_train.append(loss_train)\n",
    "    results_test.append(loss_test)\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (13, 8))\n",
    "#ax.plot(num_epochss, results_train, '--')\n",
    "ax.plot(num_epochss, results_test)\n",
    "ax.set_xlabel = 'batch size'\n",
    "ax.set_ylabel = 'Loss'\n",
    "ax.set_yscale('log');\n",
    "ax.set_xscale('log');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "include_colab_link": true,
   "name": "Welcome To Colaboratory",
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
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