2022-05-23_transfert-des-voix.ipynb

{
 "cells": [
  {
   "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,
   "metadata": {},
   "outputs": [],
   "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": {},
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "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",
    "\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,
   "metadata": {},
   "outputs": [
    {
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       "\n",
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       "  <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>Unnamed: 95</th>\n",
       "      <th>Unnamed: 96</th>\n",
       "      <th>Unnamed: 97</th>\n",
       "      <th>Unnamed: 98</th>\n",
       "      <th>Unnamed: 99</th>\n",
       "      <th>Unnamed: 100</th>\n",
       "      <th>Unnamed: 101</th>\n",
       "      <th>Unnamed: 102</th>\n",
       "      <th>Unnamed: 103</th>\n",
       "      <th>Unnamed: 104</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>24868</td>\n",
       "      <td>14101</td>\n",
       "      <td>56.70</td>\n",
       "      <td>...</td>\n",
       "      <td>47</td>\n",
       "      <td>0.19</td>\n",
       "      <td>0.44</td>\n",
       "      <td>12</td>\n",
       "      <td>M</td>\n",
       "      <td>DUPONT-AIGNAN</td>\n",
       "      <td>Nicolas</td>\n",
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       "      <td>0.76</td>\n",
       "      <td>1.77</td>\n",
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       "      <th>69678</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
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       "      <td>11ème circonscription</td>\n",
       "      <td>231</td>\n",
       "      <td>Taipei</td>\n",
       "      <td>0001</td>\n",
       "      <td>1709</td>\n",
       "      <td>942</td>\n",
       "      <td>55.12</td>\n",
       "      <td>...</td>\n",
       "      <td>10</td>\n",
       "      <td>0.59</td>\n",
       "      <td>1.32</td>\n",
       "      <td>12</td>\n",
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       "      <td>DUPONT-AIGNAN</td>\n",
       "      <td>Nicolas</td>\n",
       "      <td>10</td>\n",
       "      <td>0.59</td>\n",
       "      <td>1.32</td>\n",
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       "    <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>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>12</td>\n",
       "      <td>M</td>\n",
       "      <td>DUPONT-AIGNAN</td>\n",
       "      <td>Nicolas</td>\n",
       "      <td>1</td>\n",
       "      <td>0.85</td>\n",
       "      <td>1.96</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>713</td>\n",
       "      <td>553</td>\n",
       "      <td>77.56</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.63</td>\n",
       "      <td>12</td>\n",
       "      <td>M</td>\n",
       "      <td>DUPONT-AIGNAN</td>\n",
       "      <td>Nicolas</td>\n",
       "      <td>1</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.63</td>\n",
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       "    <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>136</td>\n",
       "      <td>78</td>\n",
       "      <td>57.35</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>12</td>\n",
       "      <td>M</td>\n",
       "      <td>DUPONT-AIGNAN</td>\n",
       "      <td>Nicolas</td>\n",
       "      <td>1</td>\n",
       "      <td>0.74</td>\n",
       "      <td>1.82</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 105 columns</p>\n",
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      ],
      "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     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]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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…"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "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)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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 :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <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",
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      ],
      "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": {},
   "outputs": [
    {
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       "\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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": [
    "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": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 19,
     "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": 20,
   "metadata": {},
   "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": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The history saving thread hit an unexpected error (OperationalError('database is locked')).History will not be written to the database.\n"
     ]
    },
    {
     "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": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.columns[:23]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "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": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.columns[23:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "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": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.iloc[0, 23:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Nom            MACRON\n",
       "Unnamed: 30    LE PEN\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 24,
     "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": 25,
   "metadata": {
    "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": 25,
     "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": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69682"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "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": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead 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": 28,
     "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": 29,
   "metadata": {},
   "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": "markdown",
   "metadata": {},
   "source": [
    "### 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": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 11)"
      ]
     },
     "execution_count": 30,
     "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": 31,
   "metadata": {},
   "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": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 2)"
      ]
     },
     "execution_count": 32,
     "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": 33,
   "metadata": {},
   "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": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0)"
      ]
     },
     "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": [
    "### 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": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_12 = pd.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_12['1_MÉLENCHON'] = df_1['MÉLENCHON'].copy()\n",
    "df_12['MACRON'] = df_2['MACRON'].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 69670 entries, 0 to 69681\n",
      "Data columns (total 2 columns):\n",
      " #   Column       Non-Null Count  Dtype\n",
      "---  ------       --------------  -----\n",
      " 0   1_MÉLENCHON  69670 non-null  int64\n",
      " 1   MACRON       69670 non-null  int64\n",
      "dtypes: int64(2)\n",
      "memory usage: 1.6 MB\n"
     ]
    }
   ],
   "source": [
    "df_12.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "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": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ieof79256mv+TtRHdnOA8BuAaEblKRHLQk5gvpTcSkUkAbwXwB10cCxEREQ2RrkVUSqlARD4C4KsAfABfUEo9KSIfMu/fazb9+wD+m1JqqVtj6TduJHTs6HTd62Ek5vWpjta1WkvMYrd94FRp1X7t4qL0642er3U87md3ErMxUiIiIqurnYyVUg8BeCj12r2p58cBHO/mOIiIiGi4sJMxERFRD6pUKgiCYLuH0be4FlULnVbvuNGR76mmcc4Dp0pxdVI1FNx169SaPtONatJVRvb9Rsc4cbIEAA0/Lz2+9D45X8XfLb19M/bzmzUqdGO2NDuGY0enncdTdWOwx7Hj6YdoiutfEdFanZ1ZwLPPPovrrrtuu4fSl3gFh4iIqAdJhtcgNoITHCIioh4U1qqMqDZAlGrWe683HTlyRD3++OObdrx20YEbhbiRSaNt7HatPsc9XrP91loxlI6CmlUdud/VNhB0m/vZ79WuIqrZedgKNuJq99mbHQm1Ot5WxU+MuYj6UqOmtx0ZmdylHvvm13HjjTdu5ngGUcNzzCs4REREPcjPF5BhTLVunOAQERHRwOEEh4iIqAeFtSpOnz7N+3DWaeivfaXLj4HmJcjufR/ufS/N7glpdM+E+7xRV2J3m/T+xx8p4e7bVt8L43ury71DJQ23s59jH6dLzdNjbMR+V7es3F2c0y7W6R7bPc/utuly9pyvVr3ujjM9tmaLcjYroV+vVvtv1X0xvP+GaLh4nodPfPkJHDp0iKXi68ArOERERD0oUyhi/LIr2m9IDXGCQ0RE1IOCagUzZ37AiGqdhj6ialTy3W4xyXYlw82eu4+rYX001rijsNR9Vt6vP4afmp4mUZSCb147cbIE33yUG6Wly8SbRUJu52Q7btsR+djRqfgz0/tXQ0mNdXUslT5XjTot2890S9ObxWluDGa/A2MdIupbUYiwPLfdo+hbvIJDRETUgzKFIvZc+waWiq8TJzhEREQ9yEZUrKRan6HvZLwWrSqNGnX3bdURuFGFFKBjqHRFkuVGQm5UUw2lblFMd7v0sez4bHTlRlbutmvVaFHRZlFUqy7M7lgbjafRd21GV501fr9VF+lOukqzqzARdWjdnYxHd+5VN9/5Uagowm/+/E+wkqo5djImIiLqF5lCEftf+yOspFonTnCIiIh6UFCt4JUf/A0rqdaJdy614DaoO3Z0qmF00ajJn/ueG3Gkn7sxiW3g98CpUl2040ZRbmM9/ViPzTbHs5GObvRnNkyNL46upD7e8T0VV3a51Uw2bnKjstBJjuy29VGTrKqiatZQMX3+GkVrjc67+12bxVTFrKo7nnucVpVyjRo9rqeKbi0R1mY1JCSiARKFCBdnWEm1TpzgEBER9SAbUc2fe46VVOvAiIqIiKgHuREVK6nWjlVUbTSKlJpV+KSlYxnfU1io6jllMaNQCfXrxWz9sWxM4a7NZF+3kUuokDTwM4/LgX7Bl2SfvJ+8Xswkr9vYqdn3SMcxjSIUt/KqWeSTVg1l1bgbxVFuHJdu7ueOOx31pb9DszW+Gm3TKh5qFEs1+t1oFzF1+lmdHIuI+sKGq6gAsJKqtYbnmNe8iIiIepCNqABg/txz2zuYPsQJDhERUQ+yERUAlGdexunTkzh8+DDvx+kQI6o2mlXhWLYSqFFzvkZN/2z8UK4lV9Tuvm0KJ06azxHE0VXG3CEVRMlzN96x8ZX9fHvMUAny5r1KKHXRlGW3t/FYs6gnvWZWENVHao0qi2y0ZseT/n6W25Aw/Z3Sx7bnNFS6cquTxopA459fp838mmlVubUWjKKIhsKmRFQAY6oWGFERERH1CzeiAhhTrRUnOERERD3IjagAHVMFwWu3cUT9hRFVC82iDKD5+kXNqn0AHUvZ2MmtHrLrK6X3sRVHtrGeuwZTs+OmBZGOrPRnKuR9/XolRPzYHi8dAwE6bnJjqWoo8XvpKiq7npYbe6XPif2OdgzptaIaxTbu/jZWS6/Rld7OnsdmzRmbVX+lf+adRGHumledNgTcDt0eDyM3ooY2LaIqz17A8Y+9DzfeeOOmDGyAMKIiIiLqF40iKt5g3DmeKSIioh7EiGpjOMFpoVUTOcut8AGwas0mmwJVQx0j2Xjn+CMlFJ1YyTYAHM9F8WuVUDCei+JjzFY8TDjxj1uB5AtwfkUfY08hwrypYJrIKlRMxuVGUqEShErVRVEVUzE1novq1qwKgLqKKBtFuY9PnKyPadx1t9xIyF17ylZW1Tf1Wx3vuJVc9jvYYzxwqtQ21kofz+VWRDX6WTdqhGjPvd3PjdnarXfVbjzd1O3PYzRFtMnMWlQW16RaG05wiIiIehAjqo3hmSIiIupBjSIqNvvr3NBXUa0lKnCjELeBHIC66iYbqeR8hdmKjo2m81HDtamA+qZ/AOoqrRqtOWXNO/uNOs38ggiYq+mDTGaj+PG+Yhh/VjGrxzlvorG8r+I1rEIl8eNGkZBtROhGXult3EqsdPRjz89dt041Pf8PPjq7ajugPuJytwXqI5ITJ0t1+9l909xmg+nKqk5/NzrZrl2MttXxTq9VeBENsE2rogLY7K8JVlERERH1i3REBbDZ31o06Z5CRERE1L94BYeIiKgHpe/BAXgfzlrwHpwG9yI068jaauFN9z33Ppd02bhdONPeAwMk5eCW3T/jAeeXPezIR6v2CaL6e3UAoBwkHYvdzsYV53MmzOfYcdgux3lnkUt3wU99XA8/97YJAMlCmmnpbsruNulFPW1ped6vvwemEqJhp2e7n5XuoNxMert2nYzTC6Ku5X6ZTo/dyHoW/2zVMZn31xD1lE29BwfgfTgN8B4cIiKiftHoHhyA9+F0ihMcIiKiHtQoogKAcGEGwE1bP6A+wwlOA80u76fLk4H6LryAjiiKTboNA0kktFAVFE1pdzFTH1fZuCjnK+wrJtHVxWUf0yauWooExWxkjuUhUEDGuUhnI6JyTTBX1W/sGYniaCrv2wU3V8dNoQIqUdIJOe9HcWzii9QtlmlLxW3cZM+JG80Vs0mkd+JkKT4/5ZrUnR/7unsugfqo6sFHZ3UZu7Nds+jQ7SQNNI+c3EioWefqdl2tW3VRTr9vt7GvrSde6rRjMhH1sVQnY0AvuPnxO9+Kw4cPb9Og+kdXJzgicjuAT0H/nfm8UuqTDbZ5G4BfA5AFcFEp9dZujomIiKgfNCsTP3ToEG8w7kDXzpCI+AA+C+DHAJwB8JiIfEkp9ZSzzRSAzwG4XSn1gojs6dZ4iIiI+gmrqDama1VUInIUwL9SSv0d8/yfAoBS6hPONj8HYL9S6v/s9LibXUW1Wdp1zLUVQjY6qoYSVz+51UM5X9VFM+nqpBnTGXksoxCo+s+zFVJLgdR1NrZVVIFKOh4vBYKJrMLLZdPxOKfq4iq7TzGjcOzoVLwwZs5XdYtfut/Hxl933za1ahFLdzFRO163gso+b/Q5tqOz+9h+brrqKd1tutlimY2qntLvpfdx2U7J9vu1qpBqdoxm1VrbURHFyiuirmEVVfdteRXVAQAvOs/PALgltc21ALIi8nUA4wA+pZT6rfSBROQDAD4AAAcPHuzKYImIiLab+/euMLmLVVQb0M0JTqMZVfp/pzMAbgbwowBGAJwSkT9TSj1Tt5NS9wG4D9BXcLowViIiom3n/r0b3X1ANaqiKs+8jCB47VYPre90c4JzBsAVzvPLAZxtsM1FpdQSgCUR+QaA1wN4Bltkowsq2ijGbbrmsvFHHrIqkrHvVWoeMp4bD+l/Fz37PGnGV/BV/HjcqZSyVVGW21CwEq6ea66Y1yZz+hi+KCyZRoEZSaqrfE/hxMlSvCjnhNOQsOIs1rlrJISd09pKpyRuQl0jQ/u9T5ws1TUVdM9NGCURnu+puBrKRkjNfxbJ68eOTjWMr3S81LhJnnuMVlVTNp5qpFks1cnvWvr9rYqNGE8R9aAGVVQAEJbntmEw/aebE5zHAFwjIlcBeAnAHQDuTG3zBwA+IyIZADnoCOv/18UxERER9YVWjf54g3F7XTtDSqlARD4C4KvQZeJfUEo9KSIfMu/fq5R6WkS+AuCvAUTQpeRPdGtMRERE/aJZoz9bSQWA1VQtDP1aVBvVrFKnEbdyyvdUXFnkixNPORVYK6Gg4CtMmAZ4sxUPxYyOemzDQEBXVu0pOPmUY67mIWs2LWYilAP9mXlfYa4q8TpXlyoeRs3n5D2Fl8o6FDpQDFHMqroqqEbjdtfdCtXqyqc4dnO2sxGSrZa669apunWq7HlNnze3Yiu93lf6Z+Ee262ccps22misUYTYaXTTbP0otyqs0ftrsRnrWXWyzhURbapNr6ICgOKOvShfegX3ffjHWU3FtaiIiIj6R7OIyvJ8v+l7xAkOERFRT2oWUVmspmpt6Cc4bkO6VppFAMeOTq9q8uc2uHOb9t11a9LIrlz1kkol0fGT3c6uN1UNBUuBoBzYpntRHGHlPYW5WtL076WyjyvHkpjKVk6NZRQWzf6XKknHQN8DRrMqjrr2FSPM10wVlQfsKiRR2MvlJObyaxJXRLlRURhJHEkFEZDLKsCJjuyaVWEkddVesxUvjuAeOFWqa2oYj9W5+GjPZ3rdKnvu3Go2txILQN177s/Mdz6zWeVVq7WkWlVbpaOpTiKiZmtjtRpPs+fp31tGU0R9pEkVlcVqqtaGfoJDRETUi9pFVKymao1nhoiIqAd1ElFxXarmWEXVoWYRlVsRZLlVOW7EkF5/ysZD7hpRbvVRukFfoBDHOfM1qauuWgmBPSM6L5qpJJHSYiCYNJHSnBOLTWZ13GXH/3Nvm4jH/XLZi49VCQW+JFFWJZS42d/5ZS+uwgpVfXTVbM0q+75VFz+p1c8BXQFlx2bX7bLbuetStTo2gFVrTqXZn3GryKnZvuljuM/tPulYq9kYOvkcIuobXamisrguFQBWUREREfWPdhEVwHWpWuEEh4iIqAe1i6gAVlK1MvQRVadrUbXaP4wkjj/ee8t0XbM4q1EDuiBZnqmueiiuTFKCvN94LSlfkmZ8uwoRVkLBHlP59OKSH681tSsfoWY+2q2oWqwJDhTDuPFfMRPVVWXZJn6VSDCaUXh+UX/WNZNBPIZyTerGbddneuBUKa78smx85Z6fdLyUPnduoz9XECVVVG6TP3tMIInW3Gor+3N2mzO6P/sTJ0t143E/2117qtHPvJmtaqy30d9jIuqarkZU5dkLOP6x9+HGG29c78cMAkZURERE/aLTiIo3GDfGs0JERNSDOo2oWEnVGM/GOtkoxW/UmM5L4hPb1C4PHWnYSKUSSlzRNF/1sGtEb1gNndgnUphxmvONZRQCk6DMVT1M5/STlVAwV022m8xFyJimfRcrHi4zx56pJFVUB4ohQiVYMeNbCZOKqLyPuOnfSijICHBoXG84W/GQMRcDAwVkzHcNomTdJWD1mlVlczwd2ejHNg6y5+T4IyXcfdtUfH7tPnffVr+OVM6JnSph0kSwEibRlS+r15Zq1JyxruGfyKoqqnQ0ZaUr5JrpJDZayzpSraq/OtGPa1ExfqOh1abRHwDk8zl84stP4NChQ8NeSbUKJzhEREQ9qJOICmAlVTMNrj8QERER9TdewSEiIupBndyDA/A+nGZ4Jlpo1Xk23bk4vcij5ZYpV0OJ7+n41J/Mx/fD/NzbJvC5r88D0Pfv2K7GdmHNrHPPy4RzPLvdM/MZZATJfTi5CMvxYpsR8uY+mVLVw2jGdB6OPBR84GJF38ByeTGMy8QXyxIv3PlS2ceeQhCXX+c9FY/rg2+ZxPFHSvp1v/7eo2oojUvDnfJqd4FOe4z7H9aLxxUzyb016XNarkn8nj1nAFD04NzjhFXcn5Fb/m3vS0mX8gNIla3Xv5cuUbfbN1q8tdW9L+0Wzlzv6xvdtlf045iJNkUH9+AAvA+nGU5wiIiIelCn9+AAvA+nEU5wiIiIelCnERXAmKqRoe9k7GpXjtosZmjUuRhAXVm4LSu2+/7GN+YwbcqyLy4neUveT7oNAzqeciMd62LFQ8FPysQncxFeMce5cizAxRWdp4w4nXkLPjBbNdGVibps/FVTyWPfU/H+WQ/IiIpLyCtRssjni0s+9heTEnQ7nowAxUz975X7HWyX4/Q2oUq6OLsLaqb3971kIc+cn5zj9Pl2fy7Hjk458ZeqO64bXaW5x05rFEs2iqfsNuuNWtzFW9PHdMdBRD2pq52MXUO88CY7GRMREfWLtURUAGOqNE5wiIiIetBaIiogiakAMKoCJzh10cFaLvXXdcB1qmvcY6QrasJI4pgk76k4mvI9FVc6ZTzE3YoBHfecW9YfECrBWCZy3tMbjmV0x2NbIbVUkziCqoQSb+d7CrsK+vEfvpLHD00EmDSVTos1wa5Csn+o9BW/vfkQi4HEC3uOZVUcUa2EgiUTNxV8FXc4Hs9FcRdiACgHHibM58xXvTiaO3Z0Cr/xjbm4GswXYMZUcu0rhnEM5Ut9VOQuvunGdm4X4hMnS/Al6cgMJNFUsxgpjKRlDOQuEgrUd7NuFU25Y2tWldcqbrLHblahRUQDqsMqKiufz+HTj15C+Y+exn0f/vFhjKrqDP0Eh4iIqBetNaKyPN9vv9EQ4ASHiIioB601orLChRkAN23+gPrM0E9wGjVrs9JVNTY+0FFBEiWcOFmKF4509zt2dDpegDKIdMRkK6R25hWKJlLKeLpZHwAcGgviaqiDowEqkcSN9fKeQsFMzJfD5PHFiocrR0P85WwWAHD1aBAv0jmVjTBqIqW5arLY5tt3VAEgrnxarCULdo5lFEazodlH4HuIF/b0PRXHPrvyURwvNVIOkuzOVke51Ui6SWASc33wLZNx7LNQ9XDPmyfj8+3uV3GaCLqx0oOPzsbRmG2wOGp+w0+cLNUtnGm5sY/9DLdqqVlzx2T8wN3O4p3piMn+fqUjKTdOe+8t002jK1f68xstxtno9W5iJRdRF60xogKA8uwFfPzOt+Lw4cNdGlT/GPoJDhERUS9aT0Q1f+45HDp0aOhvMAY4wSEiIupJ64moWEmVGPpGf60igVZVL83c//BcHJ9UQ4mjqwUTD9k4JiNJtZT72I3MbHWVG/XUzHYvln1cMx4AAF5Z9jGWiVCqJRHTiqk0msxFyRpVAF4x0dXOXITA+azLi2HcBDBUEu9/5VgQPwZ0M8AVs87TaDap/gqVxN9hNKO/p622KgcCX5IqMdvArxzofWxVVTWUuvfc8+jy65/GKiHq1qg6dnQqjpGK2fomgG50aOOsdLM+N6JMR5mNGgnafRo1Dmz0u9Pu/UZVU4yEiPrOljX6s4o79qJ86ZVhqqRioz8iIqJ+sd4qKoCVVAAnOERERD1pvVVUANemAjjBaRkdpCtdWj22EcY9b06iC19Wxys20qlEEu+z4qwDBSCudJqpeFgMBGOmUmkyFwFmn+lshMcv6aqp68cDlGpevF2p6mHOWc/KjaX2F8L483flQyyb8Z0p+5gykdCIRDg4qh9fqnhxFRaAurjKrcqqhMk4fdFN/2bN507no7g5nhsvFTMKoaqPf+w6VeO5CAsmWitmVF0E5J5TX5LGe3lfx1SAjp0eOFWK46d0A8ZKmHxOq7in1TpVbnzkNv1rtH+rY7vHT1dttYuxiGiAraOKysrnc/jEl5/AoUOHhiWmWmXoJzhERES9aCMRFcC1qTjBISIi6kEbiaiA+ooqYPiqqoa+iirdAK6TNYLcxnPuGklWs8jFjVbmq15cEbUzH2HeqXQ6t6If5z2F2Vry+hXFEKFpmFeqeXEV1PMrHp6pCF5j1pmayihkzHgmnEZ8l6oe9o/oDOe8iY/s+/OBxI/HMhH+el7HX6+bqCFQgpr53BFfxbHW3pEorpxyq718T2GpJnG0lXFiqfFcVB9dOefq/IqHnaaiypf6NZhs9GSrpNzzHzq/wjYCCxWQ81XTn48bL7kxkFv5lv49aNZYz9UqRkrHTY1+txr9/nUSTXW6HRFtuS2vonIVd+yF5/tYvHB2kKuqWEVFRETULzYaUQ07TnCIiIh60EYjKtcwrk819BOcdNO4ZmsE1e3jqabVNem1kcbNGk6zFQ+jGYWzZZ2x7MxHcJaviquRAgUcKNp1oDzkBNiV189nKh5eMOtU3TAe4KkF/fjVoyGmMh52miqoby1k8GpzjPlAsMfEPjWlK6wAICfAZSauAoBL1QwAOwbBm6ZrAHRcdqAY4qKJzSZzCpNoXFVlY6DRjG4AaOOk2YoXN/MLI4nXr7q47CPvq7gJ4J5CUm0VKsTN+NJ040D9uJhVcWWZy10bzH6uO86k6qk+unLjSreRn+81b8znHttdlyyMJD5+o9+lTiIlxk5EQ2wDVVSuYV2faugnOERERL1osyKqYV2fari+LRERUZ/YrIgqXU3lGuTKqq5+KxG5HcCnAPgAPq+U+mTq/bcB+AMAPzAv/a5S6uPdHFNaOWh+g3u6WspGT++9ZRr3PzwHAChmpC7mcJuzuRU5oxmFIEJcJbQYSNxsbq4KnDXR01IITGaTCqi5QJDxdDz06HwGb5nS0dFKKJgxYz+odHXTyyZGOhcAZy7pz7lhNIPv2lgsozBp4qHvLPkYzUR4alH/CuzOKry4rPe/ZizEojn2C8s+gkhQdqKoUCXrXNkGhXNVL660yhdDhEpQMXnTdD6Kq6CApBKqmNE7zJlKsZ1ehMAc41LFw54R/STnq7p1s+waVfbnkoyrPppyIyK3gu3YLdN18VP8uvn52mjsrluTn2W5JqsquNL7Ac2r8NpxY9F0fNYuptqMCqphqMLiOl7UdzYposrnc/j0o5fgPT5X9/qAV1Z1b4IjIj6AzwL4MQBnADwmIl9SSj2V2vRhpdTf7dY4iIiI+hGrqDbGa7/Jur0JwLNKqdNKqSqALwJ4dxc/j4iIiAhAdyOqAwBedJ6fAXBLg+2OishfATgL4KNKqSe7OCYiIqK+sJll4lahUICYxH7xwlkMcul4Nyc4jW5uSbdN/ksAVyqlFkXkXQB+H8A1qw4k8gEAHwCAgwcPbuog73nz6huv3BLwRnn9A6dKuOfNU3XPXfZ+D18QLxip7xsRVAK9zVhGxffgnK94OFgM4v3PruibPVZCwZXFEN9b1M9/ZDLAhYofb1cw92j80WwG/8vuGvbk9evlSDA1mtzT89pRU3YeCL6zpF+f8BXGsgo3T9bi45XMvTC1KLnP5lAxRKCAq0xJ+YtlH9NZfQ+Mu0Do/mKIGdOhuBLfF6P/XQ4QdzwezajkHpZQEKpkkc5KKHHJ+I58VFfCf/dtUwD0/THJGdAaLcTpS305//FHkoU33X0eOFWq2/+9t0zHpeKt7ktx33OP0alWx+7kWO7+m3FPyTDclzIM35H6n/v3Llec2JR7cKzy7AX84p1vxaFDh8wrNw106Xg3JzhnAFzhPL8c+ipNTCk17zx+SEQ+JyK7lFIXU9vdB+A+QC/V0L0hExERbR/3793kgUNqM+/BseXig3pTcVo3JziPAbhGRK4C8BKAOwDc6W4gInsBvKKUUiLyJuh7gjZvukpERNSnNjuialYuPqil4l37RkqpQEQ+AuCr0GXiX1BKPSkiHzLv3wvgPQB+VkQCAMsA7lBbvPpno6jAlgnn/Obday1bSu6WK9tSZ99POhQvVD0EKll4cqbiIWPimOsnAsxV9RulmhcveumLwtllPy4bXwkFT5tS7l0ZhZw51o+MRXjwvI99Wf1ewVN40my321ls8xsXy9g/NhY/f+RSFgdMp+WaQlxCPl/zcKGmD35lIcKufBjHaXvyUdy9+EzZi7ss1ypeHFEdKIYYzah4AdGaSsrjgwhxyXfGA/Ki6hYkteexEiIpLQ8l/pnoc5uU35cDiSPCSijImNvm7c/E/vyKWdSxrx876paMS9177v6NFsC0+7mtAdz9092L6yM0WbV9o/2b6TRuGYbyb6KBtUll4lajcvFBLhXv6pRNKfUQgIdSr93rPP4MgM90cwxERET9iGXiGzN416SIiIgGQDeqqNLKMy8jCF7b1c/YLkM/wamG9TGEfizx82Ydb5NYwUQOpjLowUdnkfdt9VDSrbiYiRAoiauJMqKwGOg8ZTSbtPnNewpL5vWMp6ugXmXinW+UsrhkNq0oQd6kHC/VBDcVI3yrrLe7Ki+Yq+rqqKUoi1HTCfnm6VEsRXoAu7MKGS/pEHzteIAXTcfj/SMhXqrqX41d+RCjWYVXbDSWj+KOxVeOhXGkNFuVOIYCgOcX/WTR0JoXn4fFQDBpqrDiBTMz9QuS2u9uI65dI2Ec7WQ8YMlZbNNWXQF64U27XTXU25RN1OZWUAH1EY/bmThdiWW/XzrqaVR9lfbgo7Px/raiq9kin2vVLjp132MHX6I+tckRVSNhea79Rn1q6Cc4REREvWgrIqr5c88N5A3GACc4REREPWmrIqp0ZdWgVFX1/zfYINvUrdlr6YUVgdVN3i4u+3G1VN5XcRVV3ld18ctELsL5ZRtLKfie3nCpJvBN9U8YCEbNIpRPLWawO6vixn83j4WYMxVHJ+dCvH5M//j+YnYJM0vA66ZG9X5LASZzumzo4twsHn9ZX+J8/auujiuvvl328IZihIz5fifO5fDOad1s8HuLPq43zQEvVny8UBYsmWhsMhfBFGuZSil9wKwHLNZsBZRgVyHCJVNV5XuII6rJbIQXlvS4bYRlz1FGgLMmJttTCLFiPrNcS6qjgkh/rq2wcmMpRFLXHDBUycKeYSQwa3/igVOl+HHOT/a3lVluoz83Pmq0IGb6eTmQuHlko0ioWRO/Rr9n7memj5c+dqtqqWbfgRVWRD1uCyKqdGXVIFVVDf0Eh4iIqBeximpjOMEhIiLqQVsRUaXZyGoQYirZ4r56G3bkyBH1+OOPb9rx7n94btV6VI1iAdvQD9CX/O1jG5/YWKqYVThj1o4KlGAyp9/Im+3tOk1hJDi3kizmXjYxyVxNcM2Yzl8em8tgJRLcNK6joz+8KDhgMpeCp7DHVAZ942IZr5saxUUTXx3MRfi2icKUilCrVQEAURjgukkdY10IdKXVkfFkZafvmUjpyFiIoo3cPGXWi9Lfw1Z+6e8HzJhKp6zo6itAx1groaDgJw0KbXw1llXxGlY21ksqy+p+DHF05XsqXtPL7rNkvusH3zKJ3/iGvrQ6kU2iq7yPugaM7rpUbryUfj1d3eSuWZXmbttu/bJ277ncBoJ2P/czOrGRyilGV0Sbau1lksbozr3q5js/uplj6YiKIvzmz/9EP8VUDc9xf0/PiIiIBtR2RVTz557b8s/sBk5wiIiIetB2RFTA6sqqfo2rhj6iSl+Odytnjh2dWhUXpLexMYh9//gjJYQquVrmNqK7VPFQMIlQMZNUGb1QzsRVSgAwarYpmRjm5VpyvBmThS3Pz0AyOQDAyOgkyrPnILmR+Hm1ugIA2DtSwIWqPrhSEfbkdXXVhWoIzxOM+Unk9LemdBT2SsWLP/vmyRpKNQ9jJi5aDATzNbPOVT4Z9FLgYcrGcb5CmPT8w9kVH/sLetsdTjPAcuDpNbBM479QJY0RbRQF6AjLRny2aipdLQXoxoDT+Sh+zRfUxYru9jnn+LaK6q5bpxo257PcJn2NXgeaV0ml15sC1raeVCfb91tDP0ZhNCT6LqICgOKOvfB8v1+qqhhRERER9QtWUW0MJzhEREQ9aLsiKle4MAPgpm0dw3oN/QQnbhJnNFtvKM1GH7a65/gjJQDA+RUfe0wcUw68uNFcoHRUc4WzPpONq75d9nDruH79spEQv/2y/rHcNq4/41vzFQBALlfAVWYBqh9M7MRNRb3/qYtzuOGyy/DMYiUeXy5XAAC8ND+H1++Y0N9VeRg1486Jj3MBsGQSo9EkqcJl+Qjna3pwX53JYV9W4QZTyZX3FHaYKGo6p+JmfKFyq4+A5VDiRn6jzjpQczUvrqLyPQVEgrKpzFoMBPvNPnfdmsSDLy758euzJtazMdK0E3kVM1Fd1VM5EIznVkewlVDqIirb2E83AJT4+fFHSjhxUo9Bb5+sUQYkkZCT8tVFUW61XXqfRo36rHRk2mmM41aDNfu97SWMp4ja2IJGf62UZy/g43e+FYcPH962MWzE0E9wiIiIetF2R1Tz557DoUOH+vIGY4ATHCIiop603RFVv69TNfRVVI0u59tYwo1JWjWAq4SIK6eKzjpJAOI1lJ5f9DHiJ+tK7S+EcdO8lVDw30p6/31ZDwsmdbl1PMR3lvz4OQBcYyKZxxdCVC+dBQDs3nslliLElVPBUgnwTP5Vq8Af26HHks0jqJm4K1/AqwuCp5aC+Nh2bSsAOGia9r2w7GN/PsIFs+bUbifymQsEO01ctTMf4Yk5vf9NUwHyvooronxPYSVM1qmyzQ9XQkFW6s/thImz5muSVESlzrfb+A9IKq5yftLYL1T6s8ZzyclzY6J0FZx97ErHl+4aVe76U8eOTtVFWY2OfezoVEdxU7tGga5mMRejH6Ke0pdVVJatpgJ6ep0qVlERERH1i+2OqPodJzhEREQ9aLsjqjQ3suqHqGroI6pGjf5cjd5zq2MAHWXYqpyLyz5q5q2CE1fYxn4XK378nl2r6fmyj/Ommd9KJDhnUiNb2TRfSxr1VcvzAADxM/B83bQvCmvIFcZQWSqZAS3DG53S75XnAWUa8E3vg+fpz1m+8CLuvH4/fu+iHo+Ih2vzejxTGYURM7Y/nfexN6PXvgKAa0Yi7DIN/ko1D4H5fpeNhPF6U9M5Vdeo7/klHztN3LSnEMWN+YIIcQWVPUcVpzrKjYjOm7W1RrMKGalvoGgr1cpB/VXKQCWRl9vcb6HqxdHVQtWLj5XxVjcHdKvl7D7pNa1sU0FgdaO/ZtVR6W2arWXVSWTVaSTVL9VVRAOmryOqtOKOvShfeqXXoipGVERERP2iVyMqe09Or/Pab0JERETUX1pewRGR97d6Xyn1W5s7HCIiIgJ67x4cq1/uxWl5D46I/PtGLwP4ewAOKKW2/Ftt9j049z88h3venNT5p++HcBdptPcv2JJgQC/wmPdV3T0htmS8Eialzi8umTI7c5/IfM3DBXPPSlaAUXN/yJ8veXVdhS+cPwOYRTS9bB75gm5fvFJegFrQHS5FRSjsPYTl0nkAgD8ygbCypA9QKScl47kR7J7aqccRRqhWVqDM/Tk/vKOIF0zp9a6MwpRZXHPEV5jIKLxo7oHZV3Bq1gGUzX0yL1c8XG26DU+ZxTOXw+SeHPu9xzLJ/Tm+KNPtWT8PFJAxp3uuKtgzUv9Zli/J/TbFjHvek21subbbSbjRYpm27Dw+hrOPW55+4mQpvoenGibdjoH635n08ZrdH3P8kRLuvm1q1f4u+7p7r81a77vhgpZE226g7sGxeuxenLXfg6OU+vl4bxEB8FMAfgnAnwH4/27m6IiIiCjRq/fgWL1+L07bKzAikgFwN4D/HcCjAN6jlPpul8dFREQ01Ho1orLSnY57La5qF1F9GMAvAPgagE8qpZ7fqoE1081OxjZecCMqW6rsLs5YDSUuCw6VLne2sRQAnDNxTtZDvPDmC0sZFHyF82axyOVQ8OdL+vEbnCjmXM3DD+bm4ueF4jhqtSoAwPP8uEwctQq8Zb1dNL4LuVeeRXX3VckXM7GUlxtBVF3Wr4mHWy/T3+2FqoeZIMItY/qtP1/ysLK8CEB3PM5kdAn6WydCLJuOwwBQU0DJxEOvHg0xbx4HkeBasyCnjaPsd39mPovLTXxVzESYq9kFM4Ed+aQ0fDSjsGT2XQkFY5kkurKm8xHKNYlLw2crHooZff4qkSBv4qG8r9+bcDoZB+ZhMbu6wzCgS8Hd8vacr+pK1e3vgBtbAvVl4i63JLtR3ORyuyKnI6n1lIlvtKsxuyITbZqBjKgs2+l4m7scr6tM/N8DOA/gNgD/VadU8cGUUup1mzY8IiIiivV6RNXr2k1wrmrzPhEREXVBr0dUrl6MqzrqZCwiVwF4DQAF4Gml1OluD6yZzY6oPvf1efzc2yYavud2oS3XJI6h7nnzJO5/WMdDcQWQU/Bz3iyoOZmL4sjkUsXDcih4alH/wK8uhnHF0DfnMviRSR3v/OeXVuJIKTc6hWrpFUB0pOMtz0GZ6CmzPI/ajsv160uzUJ4P31ROKT+LMKerrbygEr8e7LkaKtCLbeYndmN3zsdL8/p7qOoyLt+1FwDw8lIZ+0b1/rdMBJhxFrbcXwjxvSW7qGYNc+a9VyoeLjMVY77oTsilWrKfrazakY/ieOnlsoeCc4+aGyctBYJRE1FVQomrpcqBfjxvKtAygoZdifXPJjm27ymUzT55P6m4cjsX20or+146orJyvqqLbtIdgm3cVAl1HGaPDXQW/XTS/XijWF1FtGUGOqJybWNctfaISkQmAHwewBEA3zYHeb2I/AWAe5RS85s8SCIiIgIjqo1qd/3o0wCeAnCHMg1TTLn4PwfwGQAtGwESERHR+vRTROXqlUaA7T71R5RSd7svKJ1pfVxEvte1UW2hXSNh3XP30r27iGbeB3xPRyEPnCrFVTO26mfJxB/7ihEmTWSyEgouruiYZsRXqESCV4/qz7tUTRr95QT4rmkE6PkZRJHeprpU0vFUbSUeX2ZZXzSr7bgcCHWspSb3InP++4gyOQBAOLoDIzt03LS8MIsorAEAZOECMiauqmbyODNfAcyCnbnxnThz6QIAwM+P4pI5LU8v+Rj1gF3mOz21mME+E0W9suyjauKcK4thXCGWEwEQxQtsVkLBjnxS6WSb9NkKKluVtBRIHNtlnAuOeV/FsVHeVyg729mfk33PqoQCQKFivkceSeWV7ymEYVJF9ak/0ef0wUdnUQmT7RaqXl0jQbfazv2376m66KnRgpa2aaRvUjs31nIjKd1ccHrV651wF4PtdFHN9VRLscKKaItEIcLFme0exZrl8zl8+tFLKP/R09vaCLDdBGfd2SERERGtX79HVNvdCLDdBOebIvIvAPyycu5GFpF/Dt3NmIiIiLqgXyMqqzzzMoLgtdv2+e0mOD8P4H4Az4rIt6GrqG4C8C0AP9PdoW2NVU3bIkmiB0ned9cXApLqmIyJQGzFz2wlqRzKCnChomewSyEwmVX4+pw+3m3jwI/s0NHRn8xk431yuQKCFf1c/AxyYztQXdEN+KLlBYyefwYAoDwfwdQ+AIA3+xKU5yOcPhAfZ/mV5/QDzwfyuiIquziDzLVHAQDluQuQTB5+Xq9z5fs+Lt+xGwAwE0QIAj22Kyc8FH2Fby2YyqnxAPOmOirnK3zHRGuHQ8HVozoyWw4FWQ9xhdWBYohy4MXn8ZyJ7Xbm9dpUE/mkespGSpVI4JuX7b4A4nW/Mp7dXnC2rMdwxWiYRFK+0lGU2TdUKo4VZyte/PM6/kgJ+4rJGlNu5dW4U9VVrkldJHXiZKmuuZ/9PXHXmHrgVMlZM0vqfofSv0+W2+gPWB1TNVonLR1HdRpPucdbC3cMjKmIuqhPIyorLM+136iL2q1FNQ/gfxGRqwHcAB1Z/ZJS6vtbMTgiIqJh1e8R1fy557a1F05Hn2wmNPGkRkReDeCjSql/2K2BERERDbNBiKi2s5qqXR+c1wH4FQD7Afw+9NINnwNwC4Bf7fbgtkKYSgp8r36dohMnS/oNp/oHAALT9G8iq6t6bIO5ixUPY2ZtpFLNw4RpcDeR1XHMjSP6lO/Ihfjcs7qh3/XTWXx3xQ5E4dCOnQCA0zMXUC3PQ0U6+pHaCoKCbkooUYjchR/oXTwfiEL4sy/poWYL8EzlVWHuZZR3Xw0AqO69FlFVv+6XXkY4tQ8q0uOLIhVXTol4sPeGPb8iGPWAH5rQY5gPBEVTrbQrH+KwOSdXjwZx074d+RAvlX1cZirUAuU0RFTAlaNJ5VolFFPxpLex607lvSSGmshFmHeaDV6qeJjM6Q19UU61FuJ9fKmvggpV8rPOe0lcFaCeGx2l40u36smX5HiVmtTFUvZ35q5b69eVOnGyhLtuTY5hpWOe9PNGVUvuulbN9rPjcRsZpvdfT8TUrIpqM9a/YuRF5OjziGq7q6naTad+E8CvAzgF4HYAfwngPwL4KaXUSqsdiYiIaP36PaKytquaqt0EJ6+UOm4ef1dEPgrgY0qpsMU+MRG5HcCnAPgAPq+U+mST7X4IuirrJ5VSv9PRyImIiAZYv0dUVnqdKqvbsVXLtahE5G8AHEPSD+c/ALjTPldK/WWLfX0AzwD4MQBnADwG4JhS6qkG2/13ACsAvtBugrPZa1G5l8Xt40aX2tPrUtlqm0qomwC61VM2jlkMBFlz5p6cz+Dq0QBPm2qkczUPC6ZIZ9wDfjCrj+9l88hk8wCA4MyTCKcPxNHT6PnvYmX6SgBAdWwXcvOv6O2KU1CeH1dYVcb3IihOAQAkrCEqjOsPCqoQ3ZAaEtbg1VYQjO4AAIzsvgIri+aOd89Doaj3uXFE8JelZbx2UldbTWVU/J2WQuD68cB8Vw8F871XQsFlIyFeWdYnaVc+woqtNsuqeH2ucuBhMZD4fIXOel478lFcPVXMRHH0FERAqJK1qWYrHqZNRDVfS9avstvaaje3csoXONVNKn5cCQUTuShu7lgNJY6UbAUVUL+OlZVUbwHnTZXYnoLzhQw3LnJ/z5r9zrnv6UaBq/97bVZN5R7HalYBxXiIqGuGZi2qVuw6VdYmr1e19rWoAJwD8O+aPFcA/laLfd8E4Fm7MKeIfBHAu6GXfnD9PID/AuCH2oyFiIhoaAxKRLVd2pWJv20Dxz4A4EXn+Rnom5NjInIAwN+Hnig1neCIyAcAfAAADh48uIEhERER9S73711ubHIgIqpGbGzVzZiqXRXVXdAx1m+nXv+HAJaUUv+x1e4NXktfX/816L46oV7DszGl1H0A7gN0RNVqzGtl1zECksv39t/uekHVUOJIohIlsUol0mseFU3lVKgEc1W94WhWxWtUlQLB0wsZlE2c8PxiGa+e0LHPs+UA8EwjvEw2buyXPXA98NLTyJZ1xFAd2xOPNbt0CaGJnvLz5+AFVUhQ1WPIj6J4QVf1l3dfrdezAiCj0/AvPqe32XMIwVIJMqq/3/LMWRR3Xa6/00oZN+negPjzuQr2jRYxbyKYq4thvA5UMRScXdGXHOdqglFz9bHoK3xvIYM9ebsml46wAGA5VFgyj0czEXYVovh4vihzPvV5jKMrJaiYcqfpfIRyDXUN/WzENJ2PsGCqrcZzESqhh6rZ7oNvmYyrm8qB4J436zz4N74xF0dcRVMpF/+cQ4n3yfmqrqrKjad8TyGPpCHkvqL+0PfeMl0XbdnXAKxq5tdJPJRuAuh+fqv9G73XrnKrE52Om/EXUefcv3ejO/eqfq6iaiWfz+ETX34Chw4d6lp1Vbtp0/8O4C0NXv9PAP4EuqKqmTMArnCeXw7gbGqbIwC+aCY3uwC8S0QCpdTvtxkXERHRQBv0iGr+3HNdPX67CY6vlFpIv6iUmheRbKMdHI8BuEZErgLwEoA7oG9Qdo9zlX0sIscB/CEnN0RERINTRdVMs+oqa6PxVbs9syIyqpRacl8UkXEAuVY7KqUCEfkIgK9Cl4l/QSn1pIh8yLx/77pH3WXpNYcsW8GS95KIZDSjMF/14jhlripxw7ulmuAv5px1pjxg0jT+q06M4JnFCgAgWEo+ozZ/IW7S5y9egA9AmYipNroT+flz8bbegt5OeVlUR3ci3KHvTxqZ+UHcEDC7cAHZZR1rrEwfhF/VP8po9izUxB6oqm42iGweK8s6GlNRiD+fM5GZr8d/k6mWenrJxx5TmXRyLsStk2YdqJEI8yYqqipgOptUEJVqHsomCrxmPMRIzTb9E2REV5tpghlTjXbtRIDAHKLiREPVUOqeZyRZM0rHiPrYC1Uvfgzon6ltKOiLiqOe0YzEsVYxozCei+piyyD+GlIXSwG6agvQTRxtlHn/w3NxhVe68mopcCOv+ni0WTM/YHXDQfuePb79bPd5q0aC7ue12qbR9o3G106z7RhdEbXR543+2rGNAL3HV69ZtRlVVu0mOPcD+B0R+Vml1HMAICKvAvBZ815LSqmHADyUeq3hxEYpdXf74RIREQ2HQY+ouq1dFdWviMgigD8VkTHom4SXAHxSKfXrWzFAIiIiorVqG26ZKy73mgmO2HtyROSHlFKPdXuAREREw2jQ78FxFQoFuMXUixfOArhpQ8fs+O4dpdSiiNwgIndAdzeeg66C6muVsP7+hhMnS/UlwLaE2ekgW4kEE+Y+FN3JWMX3XcxVJS4ZXwx8FM1+148HOLviIzD3U1wIBJ5nbtapVeCN6wU2ozCAmtoLAJD5cwizBeSWdAZbK05DIn3zj/J8BHldJp6pLCC3NIOoYu4HFx+jLz+hj5cbRWjuxwnHdyHaqQvbvIvPAwAu36U/68zsDLI5Xbb+lknBkrnH6NTFBVzAWHwPzUokmDTf7/VjmfjxpWqysOhYRiEjCr7pPjyZi+LuxacXM/HimDuyISqRxB2Qw0hwoLh6FZDRjIp/TvNVD76n4q7EQaQ7S1uhWQTV3ksT30PjIb4nJ1SChWrSydi9VyeMJO5k7PKl/l4Xt2vwg4/OxvfW5FNLrtiuxzlf1f1eraWLsPu7527XbDyuZsdtVK7eSjfulUmPYbMX7yTqewN+D45Vnr2AX7zzrTh06JDz6k04fPjwho7bdoIjIldCT2iOQS++fCWAI/aeHCIiItp8w3IPzvy557rSD6ddo7+TACYBfBHAe5RS3xORH3ByQ0RE1F3DElG55eKb2dm43WKbfwAdgn0JwH9USp0UkdNKqUNNd+qybi62abnltm7JuI1CQiVxafPOfIT5arLQ5pPzGVxmIhhfVByZWN9Z1BnGs+UAkYmbgpUlwCnXzlw6o18fmURu/hUoU6o9cukHCHOjAABREZSnX48yOVRHd2Ls3NN6fPlRLO94lR7DygKqE5cBALygUhdxRbkikC/GY8uP6YU3fd/H8pIu23vrnnEshYKsiXFyHuLFNvePhPiref2LeMNYEH/XQAHzNQ/XmtLylVB3dQaAuaqH/SaGOlv2MZZRmDBl3pVQ4ihqJURcbj+Ri3B+WZ/jgg/UVFJuf/dtU027DVfCZLHNck3ixTvdSLESom4hz2JW1ZVvu2zcFSpBoBDHbnk/iZHczz92tH5sC1Uv/lz3PQDxop7A6t8/99huFGX3v+vWqbqYar3l14yEiLqCi212oLhjL8qXXllvafjaF9tUSr1bRCYB/AMA/5eIHAYwJSJvUkr9+VpHQERERJ0ZlojKclcb3wydVFHNAfgCgC+IyGUAfhLAr4nIFUqpK1rvTUREROsxLBGVtdlR1Zr2Vkq9AuDTAD5tbj7uewtOvGS5l/ptJZAbcayEwGROxwYzFQ9Z0bEJALxxuoZzJk4Z8RVeKOsZ6dPLHvZlkzhwTz6Ls6aTsTd/HmpSVzN5sy8hyhYAAH5lEfn5lxGZWGpl8nKI0vFObmkG+XNP6rEdfBNySzNYntadjLMr8yjMvgAAqEzsw+Tzupp/eedVCHM6kvJqK4hGJpEZ0ZVY2WwOtZperPPqEQ+jpvLqyWXBq3LJuCczCt8z32//SBJXjfgqju3KoeBgMcBF05U4UIDv6XxnfzHEWXNO8r7CSggUTfSzGAjGMk7sIzZGkvjnsGskrPtZnDhZwpL5XLcibjwXAaHEkZG7eGfeV3Hsk1FJh+JcVkdc9vlsxYsr4vK+fl9LLbzpxJdAEnk9cKoUx1q+SF21ln4teezGUm7VFFBfbeTGSO7+bvfiVhFTuvtxs89hTEXUA4akisqynY3Lf/T0hrsYA+1vMv5Sm/1/YkOfTkRERA0NW0RlbVZU1e4KzlEALwJ4AMCj2MDNUkRERNS5YYuoLBtVdXuxzb0Afgy6B86dAL4M4AGl1JPr/sQeY6tarPoFEutjBxtxTOcVzq/oHGIsozBTSRbbDJSOaywbXVUUsCsX4bEz+vj50SlEK3pxS5neDxXqiiN/ZQFhXkdSfmUJYWEC+ZnTep+ohpXdr9b7hFUE06+KPyc3dxbzV/6QHtOLjyEc05VTS5ddh7mrflhvlM0DlbJ+uHQJ3vIcoqKOolZqFahAR1RP1yo4MKFz0FflFLKiMGnimaoC3r6zBgD4VimD/bZizNMN/QBgV17HTYH57ofGApxf0TPy+aqHmoltxjJAIZtUmoVREku9VPZxaFzHcS+XBXtG9E6zFQ8Z0VEVoKPDjPkxBQpxA0ZAN2SsmM9ymwX6klQ7BZFu7gQAeYhp3Gie+8nYfC9ZhNOX+gqtaijxY1cYJa9fXPbNmPTzBx+dxbGjrWMgW0HVrBlfutngWmOl9D6soiLqMUMWUVn5fA6f+PITG+6N066KKgTwFQBfEZE89ETn6yLycaXUv1/3pxIREVFLwxpRAbr530Z10sk4D+DHoSc3r4K+yfh3N/zJRERE1NSwRlTA5sRU7W4y/n8B3AjgjwD8X0qpJ9b1KT3sxaXkZiZ9id5tFJc8dqOs+ZrE6ynZyMVWVc1VPZRMZdZoJkLJVPhck4/wp/M+ihN6zakwDCEmorLxFAB4YRWF87rRnxIfXm0ZSwfeAAAozD6PwsVnAQAruw6jMr5Hj23mB/CCFahMHgBQm7wcC5frfbygEjcKVOY5ANRGdyC36wpUF/TlT39kAnJeR2EHr7kJ58yQLoUCQPDOgn4hI8AZUwV142SAJ+b0r1BV+XjexHbXjES4bCRZU+qlso+9I0kzP/cxgLj6ajKn6tZyqphD7BmJ4mokGzXZ6rdKKHWVTvOmmmk0A0zno7rqJht/zdckbtIH6ChL/xt1r7uNGt97y3Qc4dhjuo0fbUVT6CRVbpXTz71NR4Fu3GQb9aWroeL9PbWquZ/d3z2O3ma6LmJy32+0flX69UbPiWibDWlEBWxOTNVuWvQ+AEsArgXwjyRZ6lMAKKXUxLo+lYiIiFoa5ogK2HhM1e4enNVNYoiIiKjrhjmiAuob/wFrb/63OSta9TEbNVluk7V73jwVP37w0VmMOw3vZivJukZ7RxSeN1HXVDZCxhxjKfBQNI9LoWBvBvjBnF7jaWR0EhLqaqRMuYRgRF8M88IavNoKACAsTABeBvn5l/Xz/ATCvN4uP/s8Rp757wAAteMqAMD001/Vn3vgDZj+7v8AACxe/sZ4zMrzgQPXAwCyfhbVlcU4JsPIBNQ+XaF1LknMUK2uIKws41Ffxxf7siqunPrBYiaurloOBW8wa0+NZRUKvoqbANYU4vNzoBjGkdSeQoTzK168HZDEUkDSMA9A3NjP91RdpZQbI2WcBnyVUK//ZI+R8xVs/DjnVF6N5yJUKvrJRFY3ALQVT8VMFMdouqIpGc/dt005MVDS6C/j2c/SEVbR7HPiZAm+oK5x5N23TTnHTqqrXOmGfPb7+Z5qGjF1WlHlrl/lfnanURUbAhJ12RBHVEDS+M97fA6LF86uufnf0E9wiIiIetGwR1QbxQkOERFRDxr2iAoACoUCRIDFC2cB3LSmfYd+guNWR9nL7bbZX7rpX9IoTsXVNpcqHgIlOFDU2cory34cez10IYfDBf14pSY4FwCFol77qTx3ATcc0pfann7++8iU9Wcpz0d512EAQJQtoDD3ErzaMgAgP3cGlZ36PakuYe6mO/TjKMTouSfi+MqvLmFp32sBAIXZF1A11VaVyf3IvfDXAIDagRuglkqAWfcqly8gipJzcW1eP84W8pgJCiiY77s/H2HUVC1dqPp162vZc3B+xdfND80+I76Kz0neU3E8VA4EBV9hqWarqTxkTKXT3pEI86ZSqqbqo8RKmFQ+uVVPOWeNqXHTdHDGRIkFP/mZjWVU3ISwGgpGnd+Bcs1dswrI+/o4oQLK1SSWPP5ICXk/icNs9ZcbcRbrojT9bxsx2XjKcqOnNDc6arSGlLtNo32aabbmVafWsj2bCBKtw5BHVOXZC/jFO9+KQ4cOAbgJhw8fXtP+Qz/BISIi6kXDHlHNn3uuq2XiREREtA2GPaJKV1FZnVZTDf0Ex1ZDWelmf+779pJ+oARz1eT1WqSb2QG6Ed7/uJgDAFw/EuGbi3q7vRlTkTSjm/ghW8DTz31PP1ycwcjsCwCAhQOvw9T3/lgfd3wfsgsvoza+T+8ThSic070Wy5e/EWNn/wqArq5a3nU4rrZS4kGUjotUJocwp9e28oIKapddAwAoPvMNlA8dRWFM//JUKyvI5QvxWJ8u62hmIutjrlrDZE43CzwQCkbNb80VI1G8/lS57OPbs/p7787rz7bVTTvyYfz4UsWL15War3qYzkdxPDORC+MYsOisHbWnEKFsKq/yvkIlqm/UZ+OmstPAb6HqYa4q2GGirWJWxT/LMBJMmHEHURIvhUo/rphufb5XXx1loytfAN9Pmvq5zQmrYX3TP9ugsJhVDdd90p+DNa8Jla5g6vXop9fHR9SThjyicquorLVUUw39BIeIiKgXDXtEtVGc4BAREfWgQY+obIXUWqylmkqUWl210cuOHDmiHn/88a4c2zY+s9VTdi0gQDdcc9cislU8QFIBAwCzVcFYNlmX6pKJspZC3ezP+u78MsLleXOApLOev3QJvmn0BwAjF76Hpb03AAC82gq8sAoAyC7NIDLRU3bxPOZedQsk0tFQlCsiN/+K2WcZlakDAIDcnqtQmb+gD1yrwBvfiUxWr1+1J5/Fhare3/d97DCxy81jIS5UJW7ot78QolTT3ykjwJipqPr+UgZXFpMufTa6AoCLK15cYZXxktgmVIKZioc9hWQ/25jPl6TpX8ZL1q3K+wq+JA3wbAM9oL5JYDGrsFD16mMlE1+5MZJbAaXHlDw+v5zEaTlf1VXZufuFqr65X31zQc2uD9WoWqpZfJOOoRo9d601BlpLoz5WQRGt2xr/hCdGd+5VN9/50c0cS88oz17Ax+MKqbVpcA9Ow3PMKzhEREQ9aJAjqo1WSHWCa00RERHRwOEVHCIioh40yPfgbLQEvBNDfw/O/Q/P4Z43JyfZ7V4MJPdKlGsSd6athoIlU7Y8V9Xdd5fNPSJjWYUn5lb/cGpK8NdLEQ6YGzdOX5oBlLm/48IPUB3bBQAQFWHiuUf1Tl4G81fcBC/Q993kFi8gP/s8AGBx/+uRXzgPQHc/zizPojqmOxZ7YQ2Rr8u6/doKlq7UC25KJgdV1V2Rc+M7EQY1hOa5l83jVeNjAICFCFgM9diuygumfIWaKfOeyihMZJP7a+bN/ThFX+Fyc5/N6SUf14wHuLjixefELqiZ95Pyb9uh2HYb3lOI4vtoKlHSYTiI6hfeDJz1UTMecNaU6L9qPEDVuc9ppuLhF96uuzvb+2bsPm45ur3vxt5nc+JkKT6GvY8mjGTVfTP2dyVUSafiY0en4v1zvlq1OGb6vhl7LMu9L+bEyVLdvT/N7plpda/OZi2IyXtwiNaN9+A0UdyxF56f3AS5ngU1Dd6DQ0RE1C8G+R6crcAJDhERUQ8a5IiqkfLMywiC127a8YZ+guNLfUTnlv9WQiCPpJNtXVdbE1e45dAA8GLZx6jZf/9IiLPL+sk3F/W+zy0s6mPMvBDvUx3bBb+iXw+nD2Blx5UAgOxyCTv+8osovfZ/AgCMvPIUIPp4Yy8/gbCg45fs3BmEhSkE5nkwugMS1gAAqjAGVMr6cVBDbnI3AEBEZz67p3YCAOZrIarOqbgqr8d7IKeQ8RRerphuw9kIM6b0/cpiiLGMKf+WZKHLuZrg6bksrh3X5e8rITAX6H0uGwmxYqKiyZzCfNWL46LzKx4mTfyVkSSKqkSCinmcb7AY5ZiJstwIqBoK9hVDJxJKIsYwShbUrIRJ/GXjF7fk+65bk9Jw+/MvZlVdlJkuIXfLw205u93eRmjuNm5s5X6Hu27Vj9vFQ+nXu9HhmNEU0TYYsk7GYXmu/UZrMPQTHCIiol40bBHV/LnnNu0GY4ATHCIiop40TBFVoVDA0sXOuxR3YuirqNIVJ261TLqixlZOuVZCQRgh7u4bRIIpE1v91XwGV5vKoqeXdLT09KzuXiyeD88388uXnkYwukM/zuZROPdd/XBpBmFhAv6K3qe8+zAmnvszAIDKjsSLaNoFNW21lResIMrohTMr170VQUl3NYbnAyaaguchP7EbQa0CAHj1xAieWdSPb5vO4QVT2XQwH+GyfIRXzPP9hRDP2aqlYogR2ynYQ1wpNVsVZJ2qp1LVw2Uj+jzYOAkAFgPBnkKE+drq8zqRVfHrYSSYzidRoO+pOOrxBfFCnOO5qO719HbpuAioXxAz49V3PE5XTtlj3XWrPo6NjtxO1u5n3nXr1Kpt3N+tjVYmsbKJqC+wiqoNt6vxOsvEWUVFRETUL4YloupWV2NOcIiIiHrQIEZUjRbYXMsCmmvR1QmOiNwO4FMAfACfV0p9MvX+uwH8MoAIQADgHyulHunmmNLcxnBpDz46i5yzEKMbUa2Y/WYqHvYWIuz0dM5RCQXnTZyzLx/FjfAszzTgCytLUJmcfjE/Cn9Z3z0++vx3sXC5/kGvTF+BsXNPoTKxDwCQLc+idM3bAABT3/s6ygdeD0AvrgkVxRFVlC1A5YoAAP/cs0BxatV3y43vhFIRlGk2eCEQvGlSj6caAXtNNVNWgPlA4vgpVIIrzAKUY1kF0w8QWTfaUR525cK6SrOVOCpSCE3TwJ0mdrLb5f1ksUvfU8ibU3f3WyZx/JFSPPailzTW8z0VPy7XJD52MaOb7PlNfrw2rko3emy2gOWDj87G0RSgm/DZCqs0ewz3WPbzXG60la6ksq+1ip86XaSTiPrUgFVRlWcv4BcbLrB5Ew4fPrzpn9e1CY6I+AA+C+DHAJwB8JiIfEkp9ZSz2dcAfEkppUTkdQAeBNC9lbeIiIj6xKBFVFuxwKarm1dw3gTgWaXUaQAQkS8CeDeAeIKjlFp0th8F0F93PBMREXXJoEVUm93Ir51uTnAOAHjReX4GwC3pjUTk7wP4BIA9AH68i+NpyI0w7PpCNjo4dnQqjkbmah72FHSkcn4laU535WiIuarEa1EtBR6KprLoWwsZHDQxjF3PKZPNAwDC+QuQ3AgAQE1eBu/c9wAA1bE9GH1F/0JXxveiMr4XgYmYcvPnMHJJNwhc2X0NMqa6KhAPUbaA/Pw5fYxrb0NoqqPCsAaYz8kURuF5OnPLZLJ4VU5hPtSRWU6Av1jU4756xMOBnH5cCgQHRyJ8Y1Hv976pWvzdZ6uCMdM879xKEsXtLUTICPDCkv71OjgaxOtKnV/2UDCxX95XcQUUAMzXdIM/IFkryrLRk23M6K4R5q5TVfSTaqswkiTykqR6yvdUHAkVMxK/XgmBYjY5lu8pZ59k/2NHp5DzVcNY6f6H5zCeQ1Nu5ZMbW7mxlPvaetaVYjxFNCAGLKLa7EZ+7XRzgtPo7odVV2iUUr8H4PdE5C3Q9+P87VUHEvkAgA8AwMGDBzd5mERERL3B/XtXmNw1cBHVZjbya6ebn3QGwBXO88sBnG22sVLqGyJytYjsUkpdTL13H4D7AN0HpxuDJSIi2m7u37vR3QfUoERU3Wjk1043JziPAbhGRK4C8BKAOwDc6W4gIocBfN/cZPxGADkAW3o9zm0yd/yREu6+baquCiZvMqw9fhTHKTvzEc6aZnc2npo2kc5YNsQrZv2pVxdDvGwqqp6pCK7NK1w9op8/PTIBFenmd2phJl47qjK5D9GizjjC/CiySzNxZBXmRuFXlwAAi/teg3zpJQBAbvECli97NSrjewAAvucjMlGU8nwUJ/R6U8tLc/Hre/JZrESCfSZiWoqAv7tLP356Cfi+iZyuNrHcT+zSFVrnlr04LrLfH9AN/GwTP93oT+LmfqESlM12gRJM5PTrQaSr0Gw11WhGYcacr51OY78HTpXi9cFsUz537aeKWdsq49U31PM9hdBEXZUQuPu2qXif0Jkmx+tCpWOxVNNHG1HZqKhRoz23Istu20izuKnRulLNjkFEA25AIqqkeqo71VLNdG2Co5QKROQjAL4KXSb+BaXUkyLyIfP+vQD+AYD3i0gNwDKAn1T91lqZiIioCwalimqrq6esroZhSqmHADyUeu1e5/G/BvCvuzkGIiKiftTPVVRuQ79uNfJrZ+g7GeedtYbuvm3KxBf6p5LzVV0VjmtPQeciGU83ALSN7H6wmEHGHPPQaBhvPx/6mA8FL9d0xpIrTqBWXQYAeFN7UYsCAIAa2wm1rKujMisLkChEtagjppHZFzB31Q/r8SzPxWtR1Sb3ApksxEReteWk+j4zsQvLCzriUCrC63dMAACyovBcVbDTbHf9aBivlzXqAVea75cTfY7sWltjGYVdJmKaq3pxLJX3k3gJqG/uN5mN4Ju39hcjzFf1k4lchJ35CEVzjEoIFExctBQIJkx8Vg4k3iZnXrNxUZi63pdeR8rGT77TOtONruy2AOJ4slF0dPyREorZJK5y/92quqlR5NSpzVprimtWEfWpPo2oVjf029poyhr6CQ4REVEv6teIarsiqTROcIiIiHpQP0VUvRBJpQ39BCfv1z8/dnSqrmrFRlOhSprMBRHiuGKh6tVFNW+YrsYN7hadJnYTvsLFQPDqgn1N8JTSTf+qSyVkdun+Pr6fRXRBb1Ed24XR899DbdRUQe28CjBVUOHoDviXkj6KXm4EXm1Fj09FgKnKCgEUxnRlz/KFF7EvPwUAuFj1MO4B+021UjkUXDOSPLbNCgMT39goLyNJJpT3FfJmu5mKB5O+YVdBx1M2bgKAJVOtthJKfK5yvkIQJZVs0/kITvFUHDcVM4grpfKmvZKNptyfRRhJXRVVNZS6Natc7rpS1gOnSjh2tHF1lP0MYHXks57op5OmfZsVKW3kOFzXamMYD9KG9ElE1SuRVNrQT3CIiIh6Ub9EVL0SSaVxgkNERNSD+iGi2o4Gfp3iBAf1l5FPnCwh58RWcbQRCe4yjeJOnCzhZdPoL4yA8xUPtchmK14czSwGgpyJSK4uhrg4n8FFE1u9ND+HqyZ1dPR8kKwRVX3l+ygceiMAIHj5WVTG98RNAKtjuwBTKYXCGPxAR1LeygJUtYzqzisBAMWJnQhDvd3unB+PAfuvxHfLZndPYWdGoWyqiV6qCkadNZ0ynomNshHGsgqh+XoFX1dPAYijJvtd95qmgBNZhbyn4jWiTi9kcM2ErhKbr0ncDO/+h+dwz5sn44oot5meGxXO1yReyyot76Nu7TDL7mtfe/DR2fi1aqqhn+U29Utzx+Z7qmmjv3aRTr9FFv0yzl7F80cb0uMR1XY18OsUJzhEREQ9qNcjql6Npiyv/SZERERE/YVXcIiIiHpQL96D04vl4M1Ivy39dOTIEfX4449v2vE+9Sfz+IW3T9S9duJkCYAuY5413XlHMyouOS4HEpeMXzLvF8x9O2fKPqrmlF5RDOP7Vb675OOZiqBa1ffN7B0pYMLcq3MhEFyc0/dmZEfGUKvoG2XUwgxyu65AtfSKPmBQjcvE4fkQUxaOsZ3IjoxhMpcFoBfOvDavj/2duWXsGy0CAPZlFbJm3N9e9vBjkyEumEUwrx8P4u/wrVIGu83ioRlPL6Jpy8Hd0u/RjMLzi775PklH4nIgCBTiTsa/8PYJHH+kFO9XiaTuGLZk+4FTpfg+mNmKF3cyBpJ7aew2YbT6PppKmJRzV0NJFtFMSd9PY9nux83u6Wl1r02ze2tavb7e8vJGxyOintX4pr8OjO7cq26+86ObOZYNKc9ewMfrysGBw4cPI5PZ9mslDc/xto+KiIiIVuu1e3B6/Z6bNE5wiIiIelCvRFQ2lur1SCpt6Cc4+4ph3fMHH52NF2ashkl5chABFbMI53guQtl03y34QE3pfwDdBfj6SV3W/bvn8viRySA+9ptGI4xM6Bjp+ZUkGrlULiNX1DGZ7/uolvU+uV1XoDp3AfD1jyk7dw610R16p8IYkNeLbXrZPPbks6iYQ1ZWyrjo61jqtZMjmMro8u0XKh5+aMKWjytcNhLiO0s5AMCrnM7D148HeKGsP3N/LkLeV1g033em4uFKs4jofNXDNeb7zVY8nF/x4nMaRoKXTCn9574+D99LOiLbc+rL6g7DtoR7NKPqyrZtNBMqgQ/ULYLqloK7C2BWQ6nrWGyP8eCjszh2tHnEY+OrzV5E0z1eszLzVvt0+jlENCB6oEy8vktxb5aDNzP0ExwiIqJe1AsRVb/FUi5OcIiIiHpQL0RU4cIM+imWcg39BGehWt8KyK3OqYQSVwYFzjazFS+OWabzEc6veKiYaOXa8SCOZt4yVcNSYGKbfISc6Kok6+nZeQDA/3z5KH7/5QoAwPMKENH7RFGIzPgOBKaKKhiZgBfo7SIAqrqsH3seXirNQi3pyOMNV14Vx1KlQHCZWcFyfyHEtxf0j9x2Lf5hE6ctBR7GsklctzuvH+d9VdexeJcfxd+1poCLy358Huy5W6h6yPsK15ruxb5zf/tsxcNETo/H9xQWql5ctQYki2CeOFmK45j7H55DMZMcJIykbhFUu7+NFtPHstz4qhEbBzXqaNxpNNQqUlpPrNVpVVa794ioD21zRGWrpvoplnIN/QSHiIioF213RGXjqR4oA1+X/hw1ERHRgNuqiMpt3ufqt6qptKFv9Neo8sY2iLON34D6BRp90U3lAGCu5iErSRVVJRTUzMKU0zmFWdNIb7bmISfAnFlssxoBV4zoDR98cQlv3TMOAHhy2cOFkr4kmR+dws1jglPn5/Tn5kdwsFgAoBfLvBAkY3rNSISSef5MRXBsTxUAEChBqWqbFUa4UNGR0ktVwdt31uJxF3yFi6YK6oBTWVYOPKyEwB4z1qVAsGQqqvaMRPG5KtcEoUrGk/dV/J4b6bnnLlRSt125Jsg3WOi0UUM9txmfG824i3U+cKrUcAFOF+McIuqynm7016h5n6tHGvm1w0Z/RERE/WIrIqp+rpJqhxMcIiKiHtTtiKpQKGDpYn/HUK0M/QSnXJOm1SfHHykhY2KXnK/i5n5uRdViTTCWTSqNKqFgxEQuFysexkw1U2iiwO8s6QzmzdM1PDanT/+BiUk8a5aVGvcATO0EoBsAfqtcwMi4HtfeDOJ1rhYCwRuK+th/WgoxOe6haqKxHxlTOLtiqpuyUTzWsazCdE6P/rW+wrllD1eO6bxoKRBMm/WnnpnPYspUOq2EgstGwjhGqoSCyVzS/NCtXArM2D74lkn8xjfm4n0++JbJeJt/97X5OO4q+hEWql683d23TdVFTPc/PBfvl46X3OjJxlVuA78HH52F7xTIuVFkOrpqxR1PM2tZV4qVTkTUsS5WUSUN/Pqred9aDP0Eh4iIqBd1M6Ia5GjK4gSHiIioB3UzournBn6dGvoJTqa+z19d3OBW9MxWPDi95uJmd7biqGJikryv4jWdlkOFi6ZqKeMplEPBa806Ts+XfUyZ7fZkVVwBVfR0dAQAr54YwbPlABkzyIKnMGHG8NRSgIlJ/eTIuI9yCIw6471oKqcmMgpXjulYaq7qYSZI1oTKesn3WAkljtlumKphpqL3318M8fxicuC8p3DJvOd7gj1+5Jwrvf/9D89hIqviJoqf+/o8do3o771npP5m9/FcVFehZj1wqoRxE4U9cKoUx03uGk7A6ljKshVV7mtu3NRpVNRJlNXtuImxFtGQ6lJE1e8N/Do19BMcIiKiXtStiKrfG/h1arC/HRERUZ/arIgq3civ3xv4dWroJzi+rL70n6xtlEQUOiZJmv4tmqjnUsXDaLa+WeIrZn2mgq/qqpGmsxFmazpred1ULW6sN1vzsNNs9/2yj9cUkuO9c6eHcphUQr1kGge+c6eHjOjtch4wkY0QmJjse8teHH9N5pJ9J3MR8mYRp4KvkJGk8mlPIcKsjZ5EIWv+Y1gKBAeKYdzEr5hVKJo1q+z2gF4Tym6T9xVCBdzzZl099bmvz6OZRvFUmhspAc3Xd3LXEbP7rdVaKqLWYz3HbrbulNugkvHV1uI5py2xCRFVUi3lNvIb3Mop19BPcIiIiHrRZkRUw1At1QwnOERERD1ooxHVoDfya2foJzg2dgKSy842ogKSyptyICias1UJBTvzOvoJItStwQQAu8x7i4HEEdHKso9QCa4wVVd/Xcpi0lQtXax6uGmqZo4ncax1dtnHaCYCoKOgqgKuNPHVhargxkl9rMlcBCfFwmgmwljWrqcFPL+sB37tRA15833LgYeJfISyidpeLnsomGKpvJ80JoyrnKIknrOVVxNONOeLjqbsOcn7ulEiABQzSXw0X/XiiqowklUxYHw8T8XxVToOaNaoz/1ZtpI+nlul1Cx26LQ54FZFF81iOtoaPOe0JTYQUQ1DI792hn6CQ0RE1Is2ElENczRlcYJDRETUgzYSUZVnXkYQvHaTR9Rfhn6Ck67iefDRWeRMVBNG4sQeEsc5gQKKtsooElxc8bB3JMmI7D57ClEcX+3KRzhT9rHL7HdlMUTJNMI7VAzjxnq78iECs8/+kRDfW/Sxr6CPPVf14lhrd05hrppUMY1loni/vSMRXirrL3HZSIhA6f3Pr/jO9rrSyVZR+R5QNOtm+Z6CKbbCy+Y4e8wYyoHEUVQzd9+m15Gy2/kCVHQqhQmnqitUiNehss/vunUKgI6E7HtuHHDiZCkeWyutoqL06241UqP3gc4rsrYrumBVD9EA2kBEFZbn2m804IZ+gkNERNSLNhpRDXojv3a89psQERER9Zfhnt4RERH1qPXcg2O7Fg9Lt+JWRKnOSmt7xZEjR9Tjjz++acc7cbIU3/cB1Hcsdjvjhs5pCiJ9nwmgS6Eznn4N0Itu2kU5ixmFp+f0HDIj9V2FwwjxPTOA7nQM6MU7bRl2MRPhsUs5XDuuF8t8sezjO0v6nph37a7G98XMVjxcrHjx8cMIccl3TQGT2Sgemy0Tr0SCMJL4vptKJJg25e3lmvu9Bb6oeOHRSpgsLJoRXUYO1N/LZEu/7394Lj4P9v6lcecc2IUz7ecVs6pp+fZ6tCoH5wKWRLRFOrhrsLHRnXvVzXd+tOPt7SKatmvx4cOHhyWmaniOh+KbExER9Zu13oPD0vB6XZ3giMjtAD4FwAfweaXUJ1Pv/xSAXzJPFwH8rFLqr7o5JiIion6wlohq2LsWN9K1iEpEfADPAPgxAGcAPAbgmFLqKWebWwE8rZSaFZF3AvhXSqlbWh13syOqRh1qbXzhlomXa1IX07iPQyVxufV0Plm0ciKr4mgr5ys8t5CJF+k8NBagHOjtagpxLJX3VdyV2PfsZ+j3zi77uH6yFo/TloLvLUSoKWCxlpSJ230WA4kX5bx8LIzHNppRWAoEo5nVpdzFrIpjo7yfvA4AGQ9xmXYl1M8BHdHZxzlfIYyk7ng2wnJLvBt1HraRUbPOwenXm8VQ9lidRFH9GFexLJyob3Q9onKjqSGKpVxbHlG9CcCzSqnTACAiXwTwbgDxBEcpddLZ/s8AXN7F8RAREfWNTiMqRlONdXOCcwDAi87zMwBaXZ25B8AfNXpDRD4A4AMAcPDgwc0aHxERUU9x/97lxiY7iqjChRkwmlqtmxOcRpeMGuZhIvJ26AnObY3eV0rdB+A+QEdUmzVAoD5+AfSl/7ruxk4llY1U8pA4esp4QCVINi/Xkioqt+JoKRDsKYTI13SOU4kEK+azJ3NJLJUVoGKrqyIF3wP2mwU6d+YjzFVtN2XBlKmOKmYilAMvXmDTrXraNRLG36caJpVS1TAZZ3wubHVUmCwgWgn1sWwVVBjq49vvbrlRVs48njPftZgNm0ZT1VDi93xP1S242So6ct+z+xw7OtWyK3E6vmr0uF/045iJqD33793ozr2qXSdjG08N64KarXRzgnMGwBXO88sBnE1vJCKvA/B5AO9USq2vJzUREdGA6SSisvHUEN5301Y3z8hjAK4RkasAvATgDgB3uhuIyEEAvwvgfUqpZ7o4FiIior7SSRUV46nmujbBUUoFIvIRAF+FLhP/glLqSRH5kHn/XgD/AsBOAJ8TEQAIlFJHujWmRjKpxSqqocSN/9y4Ku8nDfAyXrJIZDXUDfNs9FNxIpxLFQ87zOt5Hzi/4sXN+eadZnqVUOLGfIuBYKfZxxeFuZoXL8Q5llHxdoCKm/RlzEKZ+WQtTdg0cKHq1S16+dyC/pFfMRq2XDTTjaEqoW7WZ9l4zpfksVtZVq4JilmFu2+biM+jja/cMdpz7UZHjSqnHnx0Nm66aN93o6hjR5PH9nW3SaO1mU0EiYi6rs1im4ynWuvqNS2l1EMAHkq9dq/z+GcA/Ew3x0BERNSP2kVUjKda41khIiLqQe0iKsZTrQ39WlRuPALo2CTn11f5AMBdt07VVfjYaMauQWWb9k3kovg1tymejadso71iJoqrlvKeiquW8r7CWdPAbzIXISNJPDRfW72WlP3MSpg0G8x7SRVVqJIxhCoZb97Xz90Gg5bb9E/vJ/EYfE/F38HGctbFZf2htnIrWVNLNVzfyx6vEbdJn9twsdm2jbRai6qT7YmINkFXGv3ZeOod73gHr+BwLSoiIqL+0SqiYjzVHs8MERFRD2oVUZVnXkYQvHaLR9RfOMFBfUXOXbdO4f6H5wDoaMVWVJ04WYqjqzBKYqzAiYnS3KgnK7pZno2CilmF0DTtC5XEVUvnl724iqoSClaUU9Ek6SgsqY5qVOVk33PXw/JF4m30c5jPSirK5mv1a1TNVpLxlSt+/F3dJn2hWn0O3DG5Ud+Jk6X4cTMPnCrFa3G5++d81fEaU0Dzhn+N9mM81RlWoBFtkRZVVGF5bosH0384wSEiIupB7SIqxlOt8ewQERH1oGYRVaFQwNLFs2AFVWtDP8Fxq3rsJXc3WrGX43N+EpP4kmx74mQJS4HANtYrZhXsDd2+p5BRtpIoqZqy3Ooou8++YhTHWtN5Vbem02Q2wq6RKBm3E+HMVrw4IrIxTvo7uE0MbUxkGw5O56P6Nbjs+VGIGwoCutrKjeost/JsoephPBfVxUp2Ta8TJ0txrNWogs1dl8rVKs5qpZM1pxi5rA3PE9EWaRBRlWcv4BfvfCsOHbqJDf7aGPoJDhERUS9qFFHZ6qnrrrtum0bVPzjBISIi6kGNIio29+vc0E9wGq19ZF9z10AC0DCaAYDRjGpYYRVGUtf0z8ZYgF6vyUZWbsM8d+2oUOn9krWpkvWwilkFu6zTe2+ZxgOnSnG1VDWUuCnhfE3wwbckkYLbrLAaJtVS771lOo6tRp2IbinQ62zZ7+x7UcPmh++9ZTquPrvnzZM4/kgprsoKI4nPqf0MK4ykrsrLfT1uDtigx99GYpJ0FRUjl3pseEjUI1IRFdeeWpuhn+AQERH1onRExeZ+a+O134SIiIiov3AaSERE1IPS9+Cwe/HacILjsPceuGXD9h6TY0enksUfVXIviS1rXqjqi2HjueR+Fff+nuOPlFDMqrpS7Iy5x6QairMIZv39PJXQlp6bUvBs80Urjzkdme3n2O3t6+6aZO49L8cfKdUt+BmPUZJxAEAeYsriNfv6A6dKuOfNU/HnFLNJWX0lTEqxfRGUA/s5+vy539fed3PsaNLxOOerVT8Ht/v0Wu8X2cr7S/qxBL2fxko00FL34LB78dpwgkNERNSDGt2Dw/tvOsczRURE1IMYUW2MKNWgBreHHTlyRD3++ONdO/4Dp0oNy8R9T8Ul2gBw923JNgDqoicbuVRDWdXh12U7GZeDZDFLN8by61MoHDualGX7Xv12vqcaxjbudwhVckz3O6aVa4K8qUH3PYWLy35cyu57qu6czFb0d3JL3W3UZM+XPVdAfZl6ORCM56J4rHqBzdYLdAZR/fHaRVT9GBER0UBZ3SK+Q6M796qb7/xo/Lw8ewHHP/Y+3HjjjZsysAHS8BzzCg4REVEPYkS1MTxTREREPSgdUbGL8doMfUR1/JHSqsjDcmONEydLDTsZ28jG7bbrLhjpbhuq+kUjbVwTqtVdfO3+L5d9TGZ1/HP3bfWVRe5ilm4FEoBV7wGpSjCzfd2CmM7n2+qodOWXezwbMdnPa9qJOHW+XOlqMMsdq6tR1LRZMVSvdfDttfEQ0bpsSkRluxi/4x3v4FWc1RhRERER9Qs3omIX47XjmSIiIupBbkTFCqq1G/oJjq0WAhpHAm6DuoaVSSaKqdRk1fHS8VTOV3XVQLaB3zHnM48/UoqPUQ0FO/NRHHnd//Bc3EzvgVOluiorN/ppFmvoSMypqEJ9NFVu8B2qodR9jvu8mFF1FVA2ygqi1HlwUyln4U2rUcSkFw9dHZ+5ERuwerHUTuOqRtv1WhzUa+Mhoi3mNPpjk7+1G/oJDhERUS9KR1SMp9aGZ4uIiKgHMaLaGE5wHO+9ZXpVVZVbQXT8kRIAoJjFqgqhjOnh16xKKIh0zGWrqNyYy43Gitkk9rn/4bm6RngnTpaSyMzDqsjMfrbbTC/dmK/ZGk7uPm4FUzWsXw8rdM5H/TlRgP0cP/W5qfvb3WaF771lOj7HbpNFdwzummDud0hLV125x0trVo01aLHQIH4noqHBiGpDOMEhIiLqQYyoNoZni4iIqAe5ERWb/K3d0Df6czW6nG8jmIy3eh0nYHUM4h7DRkyWu8aTu65UsxjFHqtZ88F0rFQXFzkaRRS2mqtRU8L0mlXp6KeaiqnscdKxnX1eDZNoLr3Wl3tO0g0Pm62t5Z6TTuMrIqJtsuFGf2zy1xYb/REREfULG1Gxyd/6eO03ISIioq1mI6qZMz/A6dOnEQTBdg+przCiwuqmb24FkdVsTScblzRabyn9mhvVuPukK6+s9PpSjd53x9OuMigddaUrxtzYyv0OlRB1MVKj+KrRd7XbufvbY9jPcb9/szWr0ufN/Z7N4rtGNmvNqn7Gc0C05TZlLSoVRfjNn/8JXHfddZs2sAHCiIqIiKhfpKuoaG04wSEiIupBrKLamKGf4DSKdmxUYmMRwKz9ZGKTRvs0ipIaVUfZGAiQuGIodNZnSsdG9vOsTuKZRpVdjaTX4co5z911qTJe8v0qNUHg7NMo/rKVUXafopfEfe45TUeBOb9+bSu7/123uhVnq39WblVWq+il0blrFus1e6/fDeJ3IhpYptGfraI6fPjwdo+orwz9BIeIiKgXsYpqY1hFRURE1IPcKipWUK3d0E8HG12yt9GIGxelG96l4yE3bnGb2ll2/7tuXR3puPFWMavi98o1QcZDvE8nY7fcSCe9NpV9P3RSNbeCKV0d5UsSI7mxlvv56Yovt3Fgs7H5nt4vML0QgyZjOHGytCrasp/tRnFu079WlWXpsa/lPSKiLWMiKq5DtT5DP8EhIiLqRW5ExXhq7boaUYnI7SLyXRF5VkQ+1uD960TklIhUROSj3RwLERERDY+uTXBExAfwWQDvBHADgGMickNqs0sA/hGAX+nWOIiIiPqRvQdn8fxL2z2UvtTNa15vAvCsUuo0AIjIFwG8G8BTdgOl1HkA50Xkx7s4jo61Kw9utPjjA6dKTcuwbUdfd/9kQczGY3jvLdNxKXkxq1YtLJkea3pslntvSqMy6gcfnQUiiY/je8kx9L1HyXZhJA0XwQSSsvecr+pKy9PnwU89dx/ffXT1fUn6XpqkfNy9JyhdKu7ed+N+10aLgjYyyGXhRNTHohALL/4NS8TXqZsR1QEALzrPz5jX1kxEPiAij4vI4xcuXNiUwREREfUa9+9dFIbYc+0bWCK+Tt2c4DT63+d1LXyllLpPKXVEKXVk9+7dGxwWERFRb3L/3nnZHBfa3IBuTgnPALjCeX45gLNd/Lx1adQNuJNIyEp3K37w0VmnLFtWdUO2ZefNFo1046B0ZFK/qKes+mw3LuokbjtxshRHR6ETV91927RzLB0j2fgp49WP1V0EM2Omy6ECfCRRlBu7uWNKL1IaRlIXN7nl7a0062Tsxmpp7ucwmiKinhSFyOdz+MSXn8ChQ4e40OYadfMKzmMArhGRq0QkB+AOAF/q4ucRERENDFsmPn7ZFe03plW6dgVHKRWIyEcAfBX6f+i/oJR6UkQ+ZN6/V0T2AngcwASASET+MYAblFLz3RoXERFRP7BVVFxoc31EqXXdFrNtjhw5oh5//PFNO16rbrfpqiMbp7hddm2VUycLOTaLuRptu9axphfYtE6cLLWMvFotNgkkHYrdqjH3c9yox43I3M7G6Q7Ddru7bp1qWg3mLrbpLqhpX29U0dbqezCGIqJt0lk5ZwOjO/eq69/5v+Ljd74V73jHO3ijcXMNzzHXoiIiIupBmUKRVVQbwAkOERFRDwqqFTb524ChnxKmF4R0I49WzfNsVVGr2MmNc9zGdfZYnTSYaxXBuNu4ze/cfRrFQFb6uO4CnenX3YjJ/RzfmSKnK8bSC3haNjJLV1E1ak6Y5jYJbPQdOn2PiKjXRdUKPvauG9jkb514BYeIiKgH+fkC46kN4ASHiIioB4W1Khv8bQCrqDqIgOx2Vrpiqlm1VKPj2qin00qgtdjImkqtKsGaVWilq8yaR16r92023vo1pxrv12zfVt+HiGibrLuKamRyl3rsm1/HjTfeuJnjGUSsoiIiIuoXfr7AeGoDOMEhIiLqQYyoNoZTw5RWa0S5FTydVkBZtiGgrVB68NHZtg0BO41Y7Jg3Esmk14Fyj+V77de2aqRVxLTWY61131YNDBldEVFfiKLtHkFf4xUcIiKiHsSIamM4wSEiIupBjKg2ZuinhulGf+66SW6lE7B6jaZm3Moi64FTJYRKmlYOuc87ib1s5NVu+1b7u9JxUno7d/vk/LSOfTr5rmv57hvFaIqI+gojqg3hFRwiIqIexIhqYzjBISIi6kGK8dSGsNFfqlkd0DhiAtB03aRWx+u0QmqjFT7b3diu1edv99iIiLbRuhv9XXPNNerpp5/mVZz22OiPiIioX+TzeU5uNoATHCIiIho4nBo6mkVV9jW30Z/LjWA2syJoLdHOdkdArT5/u8dGRETDh1dwiIiIaOBwgkNEREQDhxMcIiIiGjhDXybeygOnSnX33dgy8WNHp9a1IGan23NRSCKigbHuMvEbb7xRPfHEE5s5lkHFMnEiIiIaDpzgEBER0cAZ+jJxt1uxXcCy0UKaYSRx9+ITJ0vI+cl7D5wqNexsnD72WsdjnzOqIiIiWhtewSEiIqKBwwkOERERDZyhj6iqoeCuW6cArI6e3Aoqt3LqrlvrOxy7N3C7lVetoqVW0dNmdkPuBYzZiIhoq/EKDhEREQ0cTnCIiIho4Ax9ROXK+TpashVRxx8pIe9EVjZmSVdNhU6vRN9TDeMYG9O0a+LXyTbrtV1REeMpIiLaaryCQ0RERAOHExwiIiIaOEMfUflOT79qKPBFR1AAUMwm2dOJk6W42sqNpGz80ihWciOh9L9b6Vakw6iIiIiGBa/gEBER0cDhBIeIiIgGztBHVMeOTuHEyRIAxBGU1azqyFZbWbqqavV2jSqiulEhxUZ6RERE9XgFh4iIiAbO0F/BISIi6kWVSgV/8zd/Ez8/fPgwMhn+2e5UV8+UiNwO4FMAfACfV0p9MvW+mPffBaAM4G6l1F92c0xpN/67J/DPjl4OIIl6bBVVqCSOlFxhJHXP3aZ/9jiAjqHstscfKaGYVViorr5o9uCjsyjX9HZu5Vb68+Zrgg++ZXLVPhmvfjzp9bDs93HX1mr0Genv0chmx2FbFa/1a4zXr+Mm6kfpJq7b7dzcCv4/D34LALB44Szu+/CP47rrrtvmUfWPrk1wRMQH8FkAPwbgDIDHRORLSqmnnM3eCeAa888tAH7d/JuIiGioedksJva+aruH0be6eQ/OmwA8q5Q6rZSqAvgigHentnk3gN9S2p8BmBKRfV0cExERUV+IajXMn3sO8+eew+KFs9s9nL4jSjWPLTZ0YJH3ALhdKfUz5vn7ANyilPqIs80fAvikUuoR8/xrAH5JKfV46lgfAPABADh48ODNzz//fFfGTEREtMmk/SbOxs7fu/3799/8ta99LX6P9+A01fAcd/NMNfrA9Gyqk22glLoPwH0AcOTIke7MyIiIiLZZ+u8d77lZv25GVGcAXOE8vxxA+hpbJ9sQERERrUk3JziPAbhGRK4SkRyAOwB8KbXNlwC8X7QfBjCnlHq5i2MiIiKiIdC1iEopFYjIRwB8FbpM/AtKqSdF5EPm/XsBPARdIv4sdJn4T3drPERERDQ8unq3klLqIehJjPvavc5jBeDD3RwDERERDR8u1UBEREQDhxMcIiIiGjic4BAREdHA4QSHiIiIBg4nOERERDRwOMEhIiKigcMJDhEREQ0cTnCIiIho4HCCQ0RERAOHExwiIiIaOJzgEBER0cDhBIeIiIgGDic4RERENHA4wSEiIqKBI0qp7R7DmojIBQDPb+IhdwG4uInHGxY8b+vD87Y+PG9rx3O2Ppt93i4qpW5fz44i8pX17kt9OMHZbCLyuFLqyHaPo9/wvK0Pz9v68LytHc/Z+vC8DQ5GVERERDRwOMEhIiKigcMJDnDfdg+gT/G8rQ/P2/rwvK0dz9n68LwNiKG/B4eIiIgGD6/gEBER0cDhBIeIiIgGzlBMcETkdhH5rog8KyIfa/C+iMinzft/LSJv3I5x9poOzttPmfP11yJyUkRevx3j7DXtzpuz3Q+JSCgi79nK8fWqTs6biLxNRL4tIk+KyJ9u9Rh7UQf/nU6KyH8Vkb8y5+2nt2OcvUZEviAi50XkiSbv8+9Cv1NKDfQ/AHwA3wdwCEAOwF8BuCG1zbsA/BEAAfDDAB7d7nFv9z8dnrdbAUybx+/keevsvDnb/TGAhwC8Z7vHvd3/dPj7NgXgKQAHzfM92z3u7f6nw/P2fwD41+bxbgCXAOS2e+zb/Q+AtwB4I4AnmrzPvwt9/s8wXMF5E4BnlVKnlVJVAF8E8O7UNu8G8FtK+zMAUyKyb6sH2mPanjel1Eml1Kx5+mcALt/iMfaiTn7fAODnAfwXAOe3cnA9rJPzdieA31VKvQAASimeu87OmwIwLiICYAx6ghNs7TB7j1LqG9Dnohn+XehzwzDBOQDgRef5GfPaWrcZNms9J/dA/9/OsGt73kTkAIC/D+DeLRxXr+vk9+1aANMi8nUR+QsRef+Wja53dXLePgPgegBnAXwHwC8opaKtGV5f49+FPpfZ7gFsAWnwWro2vpNthk3H50RE3g49wbmtqyPqD52ct18D8EtKqVD/TzWhs/OWAXAzgB8FMALglIj8mVLqmW4Prod1ct7+DoBvA/hbAK4G8N9F5GGl1HyXx9bv+Hehzw3DBOcMgCuc55dD/5/MWrcZNh2dExF5HYDPA3inUmpmi8bWyzo5b0cAfNFMbnYBeJeIBEqp39+SEfamTv87vaiUWgKwJCLfAPB6AMM8wenkvP00gE8qpRSAZ0XkBwCuA/DnWzPEvsW/C31uGCKqxwBcIyJXiUgOwB0AvpTa5ksA3m/umv9hAHNKqZe3eqA9pu15E5GDAH4XwPuG/P+iXW3Pm1LqKqXUq5RSrwLwOwB+bsgnN0Bn/53+AYA3i0hGRIoAbgHw9BaPs9d0ct5egL7qBRG5DMCrAZze0lH2J/5d6HMDfwVHKRWIyEcAfBW64uALSqknReRD5v17oStZ3gXgWQBl6P/jGWodnrd/AWAngM+ZqxGBGvJVeDs8b5TSyXlTSj0tIl8B8NcAIgCfV0o1LPEdFh3+vv0ygOMi8h3o2OWXlFIXt23QPUJEHgDwNgC7ROQMgH8JIAvw78Kg4FINRERENHCGIaIiIiKiIcMJDhEREQ0cTnCIiIho4HCCQ0RERAOHExwiIiIaOJzgEBER0cDhBIdoAIiIJyJfNc0XiYiGHvvgEA0AEbkawOVKqT/d7rEQEfUCXsEh2gYi8gUROS8iLTvxishxESmLyLjz2qdERInILvM8BPBfAHxKRL4tIh8zr39dRI6kjvc2EZkz29l//rZ5T4nIrzrbflRE/pXz/P0i8oSIPCkiT4nIR50xvif1OYvO49eIyB+LyDMi8j0R+ediWl+LyN0iEpk1zez2T4jIqzo9l0REjXCCQ7Q9jgO4vcNtnwXwbkBHUQDeDuAl5/1lpdQbnH8+2eZ4D6e2/x/m9QqA/9lOnFwi8k4A/xjAO5RSrwHwRgBz7QYuIiPQa/p8Uil1LfTimLcC+DlnszMA/lm7YxERrQUnOETbQCn1DQCXOtz8AQA/aR6/DcA3AQRdGFYA4D4A/6TBe/8UwEeVUmcBQCm1opT6zQ6OeSeAbyql/pvZrwzgIwA+5mzzhwBeIyKv3sjgiYhcnOAQ9b7vAdgtItMAjgH4Yur9kVTk9JOrD1Hnzantr3be+yyAnxKRydQ+NwL4ixbH/LfuMZ3XX5PeTyn1fQBjIjJhXooA/BsA/0ebcRMRdWzgVxMnGhC/C+AOALcA+GDqvWWl1BvWcKyHlVJ/t9EbSql5EfktAP8IwPIajvmLSqnfsU+ce3AEQLNKBvf1/wjgn4nIVWv4TCKipngFh6g/fBHALwP470qpqMuf9WsA7gEw6rz2JICb13GsJwGkb3Q+BGBRKbVgX1NKBQB+FcAvreMziIhW4QSHqA8opV6AvhH3c1vwWZcAPAg9ybE+AeDfiMheABCRvIj8ow4O9x8A3OZUao0A+DR0JJV2HMDfBrB7/aMnItI4wSHaBiLyAIBTAF4tImdE5J52+yilfsPcv5KWvgfHraL6sjn+GRH5z+a19D0472lwzF8FEFdTKaUegr4/53+IyJPQ99W0jbiVUsvQFWD/p4h8F8B3ADwG4DMNtq1CT372tDsuEVE7bPRHREREA4dXcIiIiGjgsIqKqAeIyGcB/Ejq5U8ppf6f7RgPEVG/Y0RFREREA4cRFREREQ0cTnCIiIho4HCCQ0RERAOHExwiIiIaOP9/sIT39Nonv50AAAAASUVORK5CYII=\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": [
    "## fit model de 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": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nuls</th>\n",
       "      <th>Blancs</th>\n",
       "      <th>Abstentions</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>1</td>\n",
       "      <td>16</td>\n",
       "      <td>108</td>\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>1</td>\n",
       "      <td>3</td>\n",
       "      <td>38</td>\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>5</td>\n",
       "      <td>18</td>\n",
       "      <td>266</td>\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>15</td>\n",
       "      <td>265</td>\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>10</td>\n",
       "      <td>246</td>\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": [
       "   Nuls  Blancs  Abstentions  ARTHAUD  ROUSSEL  MACRON  LASSALLE  LE PEN  \\\n",
       "0     1      16          108        3        6     150        18     149   \n",
       "1     1       3           38        2        7      50        10      23   \n",
       "2     5      18          266        4       30     159        24     237   \n",
       "3     6      15          265        6       13     201        19     210   \n",
       "4     8      10          246        8       18     229        28     227   \n",
       "\n",
       "   ZEMMOUR  MÉLENCHON  HIDALGO  JADOT  PÉCRESSE  POUTOU  DUPONT-AIGNAN  \n",
       "0       43         66        5     30        26       3             21  \n",
       "1       14         41        3     10         8       3              0  \n",
       "2       69        216       15     25        40       8             13  \n",
       "3       68        194       19     46        42       4             20  \n",
       "4       74        227       16     65        35       3             19  "
      ]
     },
     "execution_count": 41,
     "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": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 42,
     "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": 43,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((69670, 15), (69670, 5))"
      ]
     },
     "execution_count": 43,
     "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": 44,
   "metadata": {},
   "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": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([69670, 15])"
      ]
     },
     "execution_count": 45,
     "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": 46,
   "metadata": {},
   "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": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_loader = DataLoader(train_set, batch_size=32, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "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": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([32, 15]), torch.Size([32, 5]))"
      ]
     },
     "execution_count": 49,
     "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": 50,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([1175., 1043.,  634.,  547.,  640., 1019., 1319.,  648.,  343.,  639.,\n",
       "          591.,  828.,   85.,  662., 1007.,  945., 1086.,  872.,  288.,  133.,\n",
       "         1132.,  224.,   36.,  956.,  454.,  728.,  919.,  909.,  689.,  108.,\n",
       "         1032.,  946.]),\n",
       " tensor([1176., 1043.,  634.,  547.,  640., 1021., 1319.,  648.,  343.,  640.,\n",
       "          591.,  828.,   85.,  662., 1008.,  945., 1086.,  872.,  289.,  133.,\n",
       "         1133.,  224.,   36.,  956.,  455.,  730.,  918.,  912.,  689.,  108.,\n",
       "         1032.,  945.]))"
      ]
     },
     "execution_count": 50,
     "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": 51,
   "metadata": {},
   "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": 51,
     "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": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([13934, 15]), torch.Size([13934, 5]))"
      ]
     },
     "execution_count": 52,
     "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": 53,
   "metadata": {
    "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.DoubleTensor\")\n",
    "torch.set_default_tensor_type(\"torch.FloatTensor\")\n",
    "\n",
    "class TransfertVoix(torch.nn.Module):\n",
    "    def __init__(self, N_1er, N_2eme):#, device=None):\n",
    "        super(TransfertVoix, self).__init__()\n",
    "        #if device is None: device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "        #M = torch.randn((N_1er, N_2eme))\n",
    "        #self.M = torch.nn.Parameter(M, requires_grad=True)#.to(device)\n",
    "        self.lin = torch.nn.Linear(N_2eme, N_1er, bias=False)\n",
    "\n",
    "    def forward(self, p_1):\n",
    "        M = torch.softmax(self.lin.weight, axis=0)\n",
    "        #p_2_pred = torch.matmul(p_1, M)\n",
    "        p_2_pred = torch.matmul(p_1, M)\n",
    "        return p_2_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": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15, 5)"
      ]
     },
     "execution_count": 54,
     "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": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "trans = TransfertVoix(N_1er, N_2eme)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[-0.0973, -0.0630, -0.3426,  0.2832,  0.0974],\n",
      "        [ 0.2189,  0.1229,  0.4423, -0.0693, -0.0343],\n",
      "        [ 0.3343, -0.1700,  0.1350, -0.0829,  0.3481],\n",
      "        [-0.4079, -0.0950, -0.3319, -0.3767,  0.0367],\n",
      "        [-0.1743,  0.0671, -0.3659, -0.1458,  0.1345],\n",
      "        [-0.3771, -0.3872, -0.0496,  0.1809,  0.1484],\n",
      "        [ 0.2655,  0.0022,  0.2620, -0.1870, -0.2444],\n",
      "        [ 0.2651, -0.2130,  0.0011,  0.4150, -0.3718],\n",
      "        [-0.3110,  0.2348, -0.1896,  0.0694,  0.0020],\n",
      "        [ 0.3316,  0.2567,  0.0343, -0.3827,  0.3035],\n",
      "        [ 0.0583,  0.0108, -0.3183, -0.1000, -0.2057],\n",
      "        [-0.2068,  0.1093, -0.1301, -0.4237, -0.3099],\n",
      "        [-0.3077, -0.3108,  0.2086,  0.1166,  0.2375],\n",
      "        [-0.3387, -0.4209,  0.2650,  0.3309, -0.2711],\n",
      "        [-0.2849, -0.2669,  0.2762, -0.1752,  0.2988]], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "for p in trans.parameters():print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([15, 5])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans.lin.weight.shape"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-22T15:14:03.579763Z",
     "iopub.status.busy": "2022-05-22T15:14:03.579510Z",
     "iopub.status.idle": "2022-05-22T15:14:03.589311Z",
     "shell.execute_reply": "2022-05-22T15:14:03.588646Z"
    }
   },
   "source": [
    "torch.softmax(trans.M, 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": "raw",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-05-22T15:14:03.593698Z",
     "iopub.status.busy": "2022-05-22T15:14:03.593484Z",
     "iopub.status.idle": "2022-05-22T15:14:03.601021Z",
     "shell.execute_reply": "2022-05-22T15:14:03.600358Z"
    }
   },
   "source": [
    "torch.softmax(trans.M, axis=0).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": 58,
   "metadata": {},
   "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": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([13934, 15]),\n",
       " tensor([1.0000, 1.0000, 1.0000,  ..., 1.0000, 1.0000, 1.0000]))"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_1.shape, p_1.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([13934, 15]), torch.Size([15, 5]))"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_1.shape, trans.lin.weight.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([13934, 5])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.matmul(p_1, torch.softmax(trans.lin.weight, axis=0)).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.0779, 0.0632, 0.0680, 0.0723, 0.0711],\n",
       "        [0.0737, 0.0608, 0.0664, 0.0751, 0.0709],\n",
       "        [0.0852, 0.0652, 0.0693, 0.0665, 0.0783],\n",
       "        ...,\n",
       "        [0.0742, 0.0642, 0.0670, 0.0688, 0.0738],\n",
       "        [0.0797, 0.0620, 0.0682, 0.0721, 0.0738],\n",
       "        [0.0875, 0.0682, 0.0690, 0.0635, 0.0808]],\n",
       "       grad_fn=<ReshapeAliasBackward0>)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.tensordot(p_1, torch.softmax(trans.lin.weight, axis=0), dims=1)"
   ]
  },
  {
   "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": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.0772, 0.0640, 0.0674, 0.0708, 0.0723], grad_fn=<MeanBackward1>),\n",
       " tensor(0.3516, grad_fn=<SumBackward0>))"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_2_pred = trans(n_1/sum_1[:, None])\n",
    "p_2_pred.mean(axis=0), p_2_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": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.0184, 0.0501, 0.2548, 0.3704, 0.3063]), tensor(1.))"
      ]
     },
     "execution_count": 64,
     "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": "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": 65,
   "metadata": {},
   "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",
    "p_2_average = (p_2*sum_2[:, None]).sum(axis=0)/sum_2.sum()\n",
    "ax.plot(p_2_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": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Nuls            1.651714\n",
       " Blancs          4.582147\n",
       " Abstentions    28.010677\n",
       " MACRON         38.497926\n",
       " LE PEN         27.257536\n",
       " dtype: float64,\n",
       " tensor([ 1.6140,  4.5410, 28.3805, 38.4217, 27.0429]))"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k*100, p_2_average*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.1137)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F.binary_cross_entropy(p_2_average, p_2_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. Mathémamatiquement, 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": 68,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch.nn.functional as F\n",
    "\n",
    "learning_rate = 0.02\n",
    "beta1, beta2 = 0.9, 0\n",
    "# beta1, beta2 = 0.9, 0.999\n",
    "num_epochs = 2 ** 5 + 1\n",
    "batch_size = 2 ** 9\n",
    "do_optim = True\n",
    "do_optim = False\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[ind_nonzero] = 1.\n",
    "        p_pred[ind_nonzero] = 1.\n",
    "        kl_div = p * (p.log() - p_pred.log())\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='kl',\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_2_pred = trans(p_1)\n",
    "            weight = sum_2 / 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_2_pred, p_2, 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_2_pred = trans(p_1)\n",
    "        weight = sum_2 / test_set_size # normalise par rapport à la taille du test dataset\n",
    "        loss_test = pdf_loss(p_2_pred, p_2, weight, loss_type=loss_type)\n",
    "\n",
    "    return trans, loss_train, loss_test, p_1.detach().numpy(), p_2.detach().numpy(), p_2_pred.detach().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='kl'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/laurent/.local/lib/python3.10/site-packages/torch/cuda/__init__.py:82: UserWarning: CUDA initialization: The NVIDIA driver on your system is too old (found version 10010). Please update your GPU driver by downloading and installing a new version from the URL: http://www.nvidia.com/Download/index.aspx Alternatively, go to: https://pytorch.org to install a PyTorch version that has been compiled with your version of the CUDA driver. (Triggered internally at  ../c10/cuda/CUDAFunctions.cpp:112.)\n",
      "  return torch._C._cuda_getDeviceCount() > 0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 0 / 33 - Loss: 4.27850e+02\n",
      "Iteration: 1 / 33 - Loss: 1.66217e+02\n",
      "Iteration: 2 / 33 - Loss: 1.48012e+02\n",
      "Iteration: 3 / 33 - Loss: 1.41567e+02\n",
      "Iteration: 4 / 33 - Loss: 1.38025e+02\n",
      "Iteration: 5 / 33 - Loss: 1.35697e+02\n",
      "Iteration: 6 / 33 - Loss: 1.34092e+02\n",
      "Iteration: 7 / 33 - Loss: 1.32972e+02\n",
      "Iteration: 8 / 33 - Loss: 1.32175e+02\n",
      "Iteration: 9 / 33 - Loss: 1.31593e+02\n",
      "Iteration: 10 / 33 - Loss: 1.31155e+02\n",
      "Iteration: 11 / 33 - Loss: 1.30815e+02\n",
      "Iteration: 12 / 33 - Loss: 1.30545e+02\n",
      "Iteration: 13 / 33 - Loss: 1.30326e+02\n",
      "Iteration: 14 / 33 - Loss: 1.30144e+02\n",
      "Iteration: 15 / 33 - Loss: 1.29992e+02\n",
      "Iteration: 16 / 33 - Loss: 1.29862e+02\n",
      "Iteration: 17 / 33 - Loss: 1.29750e+02\n",
      "Iteration: 18 / 33 - Loss: 1.29652e+02\n",
      "Iteration: 19 / 33 - Loss: 1.29566e+02\n",
      "Iteration: 20 / 33 - Loss: 1.29490e+02\n",
      "Iteration: 21 / 33 - Loss: 1.29422e+02\n",
      "Iteration: 22 / 33 - Loss: 1.29362e+02\n",
      "Iteration: 23 / 33 - Loss: 1.29307e+02\n",
      "Iteration: 24 / 33 - Loss: 1.29257e+02\n",
      "Iteration: 25 / 33 - Loss: 1.29212e+02\n",
      "Iteration: 26 / 33 - Loss: 1.29171e+02\n",
      "Iteration: 27 / 33 - Loss: 1.29133e+02\n",
      "Iteration: 28 / 33 - Loss: 1.29098e+02\n",
      "Iteration: 29 / 33 - Loss: 1.29065e+02\n",
      "Iteration: 30 / 33 - Loss: 1.29035e+02\n",
      "Iteration: 31 / 33 - Loss: 1.29007e+02\n",
      "Iteration: 32 / 33 - Loss: 1.28981e+02\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 936x216 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='l1'\n",
      "Iteration: 0 / 33 - Loss: 4.69381e+02\n",
      "Iteration: 1 / 33 - Loss: 2.82073e+02\n",
      "Iteration: 2 / 33 - Loss: 2.58255e+02\n",
      "Iteration: 3 / 33 - Loss: 2.49212e+02\n",
      "Iteration: 4 / 33 - Loss: 2.40622e+02\n",
      "Iteration: 5 / 33 - Loss: 2.35849e+02\n",
      "Iteration: 6 / 33 - Loss: 2.34086e+02\n",
      "Iteration: 7 / 33 - Loss: 2.33077e+02\n",
      "Iteration: 8 / 33 - Loss: 2.32440e+02\n",
      "Iteration: 9 / 33 - Loss: 2.31990e+02\n",
      "Iteration: 10 / 33 - Loss: 2.31618e+02\n",
      "Iteration: 11 / 33 - Loss: 2.31328e+02\n",
      "Iteration: 12 / 33 - Loss: 2.31077e+02\n",
      "Iteration: 13 / 33 - Loss: 2.30864e+02\n",
      "Iteration: 14 / 33 - Loss: 2.30638e+02\n",
      "Iteration: 15 / 33 - Loss: 2.30404e+02\n",
      "Iteration: 16 / 33 - Loss: 2.30138e+02\n",
      "Iteration: 17 / 33 - Loss: 2.29772e+02\n",
      "Iteration: 18 / 33 - Loss: 2.29117e+02\n",
      "Iteration: 19 / 33 - Loss: 2.27599e+02\n",
      "Iteration: 20 / 33 - Loss: 2.23613e+02\n",
      "Iteration: 21 / 33 - Loss: 2.20098e+02\n",
      "Iteration: 22 / 33 - Loss: 2.19303e+02\n",
      "Iteration: 23 / 33 - Loss: 2.18923e+02\n",
      "Iteration: 24 / 33 - Loss: 2.18627e+02\n",
      "Iteration: 25 / 33 - Loss: 2.18409e+02\n",
      "Iteration: 26 / 33 - Loss: 2.18237e+02\n",
      "Iteration: 27 / 33 - Loss: 2.18091e+02\n",
      "Iteration: 28 / 33 - Loss: 2.17978e+02\n",
      "Iteration: 29 / 33 - Loss: 2.17809e+02\n",
      "Iteration: 30 / 33 - Loss: 2.17722e+02\n",
      "Iteration: 31 / 33 - Loss: 2.17616e+02\n",
      "Iteration: 32 / 33 - Loss: 2.17540e+02\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='bce'\n",
      "Iteration: 0 / 33 - Loss: 2.62293e+02\n",
      "Iteration: 1 / 33 - Loss: 1.24821e+02\n",
      "Iteration: 2 / 33 - Loss: 1.06228e+02\n",
      "Iteration: 3 / 33 - Loss: 1.00527e+02\n",
      "Iteration: 4 / 33 - Loss: 9.80848e+01\n",
      "Iteration: 5 / 33 - Loss: 9.66743e+01\n",
      "Iteration: 6 / 33 - Loss: 9.57186e+01\n",
      "Iteration: 7 / 33 - Loss: 9.50739e+01\n",
      "Iteration: 8 / 33 - Loss: 9.45829e+01\n",
      "Iteration: 9 / 33 - Loss: 9.42193e+01\n",
      "Iteration: 10 / 33 - Loss: 9.39194e+01\n",
      "Iteration: 11 / 33 - Loss: 9.36971e+01\n",
      "Iteration: 12 / 33 - Loss: 9.34913e+01\n",
      "Iteration: 13 / 33 - Loss: 9.33172e+01\n",
      "Iteration: 14 / 33 - Loss: 9.31827e+01\n",
      "Iteration: 15 / 33 - Loss: 9.30773e+01\n",
      "Iteration: 16 / 33 - Loss: 9.29643e+01\n",
      "Iteration: 17 / 33 - Loss: 9.28672e+01\n",
      "Iteration: 18 / 33 - Loss: 9.27920e+01\n",
      "Iteration: 19 / 33 - Loss: 9.27223e+01\n",
      "Iteration: 20 / 33 - Loss: 9.26634e+01\n",
      "Iteration: 21 / 33 - Loss: 9.25883e+01\n",
      "Iteration: 22 / 33 - Loss: 9.25450e+01\n",
      "Iteration: 23 / 33 - Loss: 9.25124e+01\n",
      "Iteration: 24 / 33 - Loss: 9.24385e+01\n",
      "Iteration: 25 / 33 - Loss: 9.24056e+01\n",
      "Iteration: 26 / 33 - Loss: 9.23546e+01\n",
      "Iteration: 27 / 33 - Loss: 9.23387e+01\n",
      "Iteration: 28 / 33 - Loss: 9.22807e+01\n",
      "Iteration: 29 / 33 - Loss: 9.22632e+01\n",
      "Iteration: 30 / 33 - Loss: 9.22190e+01\n",
      "Iteration: 31 / 33 - Loss: 9.22001e+01\n",
      "Iteration: 32 / 33 - Loss: 9.21654e+01\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for loss_type in ['kl', 'l1', 'bce']:\n",
    "    print(f'{loss_type=}')\n",
    "    trans, loss_train, loss_test, p_1, p_2, p_2_pred = fit_data(df_1, df_2, verbose=True, loss_type=loss_type)\n",
    "\n",
    "    fig, axs = plt.subplots(1, N_2eme, figsize=(13, 3))\n",
    "    for i_col, candidat in enumerate(df_2.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_2[:, i_col], y=p_2_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": 70,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.1374118e-01, 5.2406985e-02, 5.8245781e-04, 1.5348531e-04,\n",
       "        2.8790836e-04],\n",
       "       [1.6873121e-01, 5.4834433e-02, 6.0949643e-04, 1.5296642e-04,\n",
       "        3.2368774e-04],\n",
       "       [3.9545451e-03, 7.7638845e-03, 9.8640358e-01, 3.0245876e-01,\n",
       "        2.3873602e-01],\n",
       "       [2.0752308e-01, 5.9257355e-02, 6.9125189e-04, 1.2937325e-04,\n",
       "        3.3796829e-04],\n",
       "       [1.0322338e-01, 9.8209746e-02, 6.5528287e-04, 1.4694582e-04,\n",
       "        3.4401956e-04],\n",
       "       [4.4978666e-03, 4.0537443e-02, 2.5244886e-03, 6.9472229e-01,\n",
       "        2.9911168e-03],\n",
       "       [8.8826060e-02, 1.7443870e-01, 6.0413766e-04, 1.5500750e-04,\n",
       "        3.8378959e-04],\n",
       "       [8.0125639e-03, 5.0700415e-02, 1.7418023e-03, 3.6489472e-04,\n",
       "        7.5344723e-01],\n",
       "       [2.0998299e-02, 5.0607260e-02, 8.6484430e-04, 1.9532430e-04,\n",
       "        4.0654032e-04],\n",
       "       [6.8218340e-03, 7.1750537e-02, 1.8198136e-03, 7.3779927e-04,\n",
       "        9.9644100e-04],\n",
       "       [1.0262095e-01, 1.0899508e-01, 6.1617128e-04, 1.4907238e-04,\n",
       "        3.5480948e-04],\n",
       "       [2.1133253e-02, 6.9387034e-02, 8.1175403e-04, 1.7543290e-04,\n",
       "        3.8725961e-04],\n",
       "       [2.1237656e-02, 3.7165340e-02, 8.2221854e-04, 1.9284924e-04,\n",
       "        4.1793476e-04],\n",
       "       [6.9110282e-02, 8.2110688e-02, 6.0045120e-04, 1.2995779e-04,\n",
       "        2.9430969e-04],\n",
       "       [5.9567880e-02, 4.1835018e-02, 6.5210409e-04, 1.3584824e-04,\n",
       "        2.9095149e-04]], dtype=float32)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = torch.softmax(trans.lin.weight, axis=0).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": 71,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.0000001 , 0.99999994, 0.99999994, 1.        , 1.0000001 ],\n",
       "       dtype=float32),\n",
       " (15, 5))"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.sum(axis=0), 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 voir en fonction de chacun des choix FE au deuxième tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "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": 73,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11.4,  5.2,  0.1,  0. ,  0. ],\n",
       "       [16.9,  5.5,  0.1,  0. ,  0. ],\n",
       "       [ 0.4,  0.8, 98.6, 30.2, 23.9],\n",
       "       [20.8,  5.9,  0.1,  0. ,  0. ],\n",
       "       [10.3,  9.8,  0.1,  0. ,  0. ],\n",
       "       [ 0.4,  4.1,  0.3, 69.5,  0.3],\n",
       "       [ 8.9, 17.4,  0.1,  0. ,  0. ],\n",
       "       [ 0.8,  5.1,  0.2,  0. , 75.3],\n",
       "       [ 2.1,  5.1,  0.1,  0. ,  0. ],\n",
       "       [ 0.7,  7.2,  0.2,  0.1,  0.1],\n",
       "       [10.3, 10.9,  0.1,  0. ,  0. ],\n",
       "       [ 2.1,  6.9,  0.1,  0. ,  0. ],\n",
       "       [ 2.1,  3.7,  0.1,  0. ,  0. ],\n",
       "       [ 6.9,  8.2,  0.1,  0. ,  0. ],\n",
       "       [ 6. ,  4.2,  0.1,  0. ,  0. ]], dtype=float32)"
      ]
     },
     "execution_count": 73,
     "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": 74,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[68. , 75.1,  0.3, 77.5, 51. ,  0.6, 33.6,  1. , 28.7,  8.3, 48.2,\n",
       "        23. , 35.5, 45.4, 58.1],\n",
       "       [31.3, 24.4,  0.5, 22.1, 48.5,  5.4, 66. ,  6.2, 69.3, 87.4, 51.2,\n",
       "        75.5, 62.1, 53.9, 40.8],\n",
       "       [ 0.3,  0.3, 64.1,  0.3,  0.3,  0.3,  0.2,  0.2,  1.2,  2.2,  0.3,\n",
       "         0.9,  1.4,  0.4,  0.6],\n",
       "       [ 0.1,  0.1, 19.6,  0. ,  0.1, 93.2,  0.1,  0. ,  0.3,  0.9,  0.1,\n",
       "         0.2,  0.3,  0.1,  0.1],\n",
       "       [ 0.2,  0.1, 15.5,  0.1,  0.2,  0.4,  0.1, 92.5,  0.6,  1.2,  0.2,\n",
       "         0.4,  0.7,  0.2,  0.3]], dtype=float32)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MT = M.T\n",
    "MT /= MT.sum(axis=0)\n",
    "MT*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "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 = ['blueviolet', 'violet', '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": 76,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 27.7,  29.9,  99.6,  28.8,   0. ,  32.5,  42.5,  29.6,  31.2,\n",
       "         31.6,  30.6,  31.8],\n",
       "       [ 72.3,  70.1,   0.4,  71.2, 100. ,  67.5,  57.5,  70.4,  68.8,\n",
       "         68.4,  69.4,  68.2]], dtype=float32)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MT = M[3:, 3:].T\n",
    "MT /= MT.sum(axis=0)\n",
    "MT*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "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[3:]\n",
    "rows = df_2.columns[3:]\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": 78,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Total des voix au 1er tour= 48747864, dont Macron = 9783058 (soit une pourcentage de 20.07%), \n",
      "-> nombre de reports de Macron du 1er vers Le Pen au 2eme = 41940 personnes.\n",
      "\n"
     ]
    }
   ],
   "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": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAIN: Loss avec do_optim=False = 102.41 / Loss avec alternative choice do_optim=True = 143.32 \n",
      "TEST: Loss avec do_optim=False = 92.75 / Loss avec alternative choice do_optim=True = 127.94 \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": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "do_optim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour learning_rate= 2.00e-03, loss_train=1.58e+02 / loss_test=1.42e+02; le temps de calcul est 18.013 s\n",
      "Pour learning_rate= 4.31e-03, loss_train=1.87e+02 / loss_test=1.71e+02; le temps de calcul est 18.103 s\n",
      "Pour learning_rate= 9.28e-03, loss_train=1.45e+02 / loss_test=1.30e+02; le temps de calcul est 17.351 s\n",
      "Pour learning_rate= 2.00e-02, loss_train=1.43e+02 / loss_test=1.28e+02; le temps de calcul est 17.328 s\n",
      "Pour learning_rate= 4.31e-02, loss_train=1.42e+02 / loss_test=1.28e+02; le temps de calcul est 18.764 s\n",
      "Pour learning_rate= 9.28e-02, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 17.961 s\n",
      "Pour learning_rate= 2.00e-01, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 18.905 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": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  64  256  576 1024 1600 2304]\n",
      "Pour batch_size= 64, loss_train=1.43e+02 / loss_test=1.28e+02; le temps de calcul est 33.471 s\n",
      "Pour batch_size= 256, loss_train=1.43e+02 / loss_test=1.28e+02; le temps de calcul est 22.230 s\n",
      "Pour batch_size= 576, loss_train=1.43e+02 / loss_test=1.28e+02; le temps de calcul est 19.089 s\n",
      "Pour batch_size= 1024, loss_train=1.43e+02 / loss_test=1.28e+02; le temps de calcul est 18.282 s\n",
      "Pour batch_size= 1600, loss_train=1.43e+02 / loss_test=1.28e+02; le temps de calcul est 21.440 s\n",
      "Pour batch_size= 2304, loss_train=1.43e+02 / loss_test=1.28e+02; le temps de calcul est 22.662 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": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.  1.  1.  0.9 0.8 0.5 0. ]\n"
     ]
    }
   ],
   "source": [
    "beta1s = 1 - (1 - beta1) * np.logspace(-1, 1, 7, base=10)\n",
    "print(beta1s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.  1.  1.  0.9 0.8 0.5 0. ]\n",
      "Pour beta1= 9.90e-01, loss_train=1.43e+02 / loss_test=1.27e+02; le temps de calcul est 20.630 s\n",
      "Pour beta1= 9.78e-01, loss_train=1.43e+02 / loss_test=1.27e+02; le temps de calcul est 20.413 s\n",
      "Pour beta1= 9.54e-01, loss_train=1.42e+02 / loss_test=1.28e+02; le temps de calcul est 22.102 s\n",
      "Pour beta1= 9.00e-01, loss_train=1.43e+02 / loss_test=1.28e+02; le temps de calcul est 20.730 s\n",
      "Pour beta1= 7.85e-01, loss_train=1.45e+02 / loss_test=1.29e+02; le temps de calcul est 21.522 s\n",
      "Pour beta1= 5.36e-01, loss_train=1.50e+02 / loss_test=1.34e+02; le temps de calcul est 21.176 s\n",
      "Pour beta1= 2.22e-16, loss_train=1.59e+02 / loss_test=1.42e+02; le temps de calcul est 25.643 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": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour beta2= 9.95e-01, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 23.884 s\n",
      "Pour beta2= 9.89e-01, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 20.925 s\n",
      "Pour beta2= 9.77e-01, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 19.262 s\n",
      "Pour beta2= 9.50e-01, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 19.146 s\n",
      "Pour beta2= 8.92e-01, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 19.421 s\n",
      "Pour beta2= 7.68e-01, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 19.680 s\n",
      "Pour beta2= 5.00e-01, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 20.084 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",
    "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": 86,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  5  17  37  65 101 145]\n",
      "Pour num_epochs=5, loss_train=1.52e+02 / loss_test=1.35e+02; le temps de calcul est 3.038 s\n",
      "Pour num_epochs=17, loss_train=1.47e+02 / loss_test=1.31e+02; le temps de calcul est 10.242 s\n",
      "Pour num_epochs=37, loss_train=1.43e+02 / loss_test=1.28e+02; le temps de calcul est 22.016 s\n",
      "Pour num_epochs=65, loss_train=1.43e+02 / loss_test=1.28e+02; le temps de calcul est 38.514 s\n",
      "Pour num_epochs=101, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 60.395 s\n",
      "Pour num_epochs=145, loss_train=1.42e+02 / loss_test=1.27e+02; le temps de calcul est 86.965 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');"
   ]
  }
 ],
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