2022-06-01_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,
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   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut directement enregistrer à partir de l'adresse des données puis extraire ses données numériques depuis le tableau Excel grâce a la [fonction suivante](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.read_excel.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
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   "source": [
    "fname = '/tmp/T1.xlsx'\n",
    "\n",
    "if not os.path.isfile(fname):\n",
    "    url = 'https://static.data.gouv.fr/resources/election-presidentielle-des-10-et-24-avril-2022-resultats-definitifs-du-1er-tour/20220414-152612/resultats-par-niveau-burvot-t1-france-entiere.xlsx' # XLSX\n",
    "    import urllib.request\n",
    "    urllib.request.urlretrieve(url, fname)\n",
    "\n",
    "T1 = pd.read_excel(fname)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut avoir une première idée de ces données et du nombre total de bureaux de vote :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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   "outputs": [
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       "      <th>Libellé de la circonscription</th>\n",
       "      <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",
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       "      <td>56.70</td>\n",
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       "      <td>231</td>\n",
       "      <td>Taipei</td>\n",
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       "      <td>942</td>\n",
       "      <td>55.12</td>\n",
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       "      <td>Nour-Soultan</td>\n",
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       "      <td>DUPONT-AIGNAN</td>\n",
       "      <td>Nicolas</td>\n",
       "      <td>1</td>\n",
       "      <td>0.85</td>\n",
       "      <td>1.96</td>\n",
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       "      <th>69680</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
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       "      <td>2ème circonscription</td>\n",
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       "      <td>Monterrey</td>\n",
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       "      <td>77.56</td>\n",
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       "      <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",
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       "      Code du département           Libellé du département  \\\n",
       "69677                  ZZ  Français établis hors de France   \n",
       "69678                  ZZ  Français établis hors de France   \n",
       "69679                  ZZ  Français établis hors de France   \n",
       "69680                  ZZ  Français établis hors de France   \n",
       "69681                  ZZ  Français établis hors de France   \n",
       "\n",
       "       Code de la circonscription Libellé de la circonscription  \\\n",
       "69677                           6          6ème circonscription   \n",
       "69678                          11         11ème circonscription   \n",
       "69679                          11         11ème circonscription   \n",
       "69680                           2          2ème circonscription   \n",
       "69681                           2          2ème circonscription   \n",
       "\n",
       "       Code de la commune Libellé de la commune Code du b.vote  Inscrits  \\\n",
       "69677                 229                Zurich           0001     24868   \n",
       "69678                 231                Taipei           0001      1709   \n",
       "69679                 233          Nour-Soultan           0001       117   \n",
       "69680                 234             Monterrey           0001       713   \n",
       "69681                 235      Bahamas (Nassau)           0001       136   \n",
       "\n",
       "       Abstentions  % Abs/Ins  ...  Unnamed: 95  Unnamed: 96  Unnamed: 97  \\\n",
       "69677        14101      56.70  ...           47         0.19         0.44   \n",
       "69678          942      55.12  ...           10         0.59         1.32   \n",
       "69679           64      54.70  ...            0         0.00         0.00   \n",
       "69680          553      77.56  ...            1         0.14         0.63   \n",
       "69681           78      57.35  ...            0         0.00         0.00   \n",
       "\n",
       "       Unnamed: 98  Unnamed: 99   Unnamed: 100  Unnamed: 101  Unnamed: 102  \\\n",
       "69677           12            M  DUPONT-AIGNAN       Nicolas           189   \n",
       "69678           12            M  DUPONT-AIGNAN       Nicolas            10   \n",
       "69679           12            M  DUPONT-AIGNAN       Nicolas             1   \n",
       "69680           12            M  DUPONT-AIGNAN       Nicolas             1   \n",
       "69681           12            M  DUPONT-AIGNAN       Nicolas             1   \n",
       "\n",
       "       Unnamed: 103  Unnamed: 104  \n",
       "69677          0.76          1.77  \n",
       "69678          0.59          1.32  \n",
       "69679          0.85          1.96  \n",
       "69680          0.14          0.63  \n",
       "69681          0.74          1.82  \n",
       "\n",
       "[5 rows x 105 columns]"
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     },
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   ],
   "source": [
    "T1.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les données sont organisées suivant des colonnes qui vont représenter les différents choix et aussi d'autres métadonnées. Il va falloir faire quelques hypothèses pour récupérer les données utiles…"
   ]
  },
  {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Code du département', 'Libellé du département',\n",
       "       'Code de la circonscription', 'Libellé de la circonscription',\n",
       "       'Code de la commune', 'Libellé de la commune', 'Code du b.vote',\n",
       "       'Inscrits', 'Abstentions', '% Abs/Ins',\n",
       "       ...\n",
       "       'Unnamed: 95', 'Unnamed: 96', 'Unnamed: 97', 'Unnamed: 98',\n",
       "       'Unnamed: 99', 'Unnamed: 100', 'Unnamed: 101', 'Unnamed: 102',\n",
       "       'Unnamed: 103', 'Unnamed: 104'],\n",
       "      dtype='object', length=105)"
      ]
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     "execution_count": 5,
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   ],
   "source": [
    "T1.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Première colonne concerne les nuls, blancs et abstention, que l'on peut enregistrer dans un nouveau tableau :"
   ]
  },
  {
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       "      <th>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",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Nuls  Blancs  Abstentions\n",
       "0     1      16          108\n",
       "1     1       3           38\n",
       "2     5      18          266\n",
       "3     6      15          265\n",
       "4     8      10          246"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1 = T1[['Nuls', 'Blancs', 'Abstentions']].copy()\n",
    "df_1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.287846Z",
     "iopub.status.busy": "2022-06-03T10:36:12.287360Z",
     "iopub.status.idle": "2022-06-03T10:36:12.289648Z",
     "shell.execute_reply": "2022-06-03T10:36:12.289980Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nuls</th>\n",
       "      <th>Blancs</th>\n",
       "      <th>Abstentions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>18</td>\n",
       "      <td>266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>15</td>\n",
       "      <td>265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69677</th>\n",
       "      <td>31</td>\n",
       "      <td>40</td>\n",
       "      <td>14101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69678</th>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69679</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69680</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69681</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>69682 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Nuls  Blancs  Abstentions\n",
       "0         1      16          108\n",
       "1         1       3           38\n",
       "2         5      18          266\n",
       "3         6      15          265\n",
       "4         8      10          246\n",
       "...     ...     ...          ...\n",
       "69677    31      40        14101\n",
       "69678     2       8          942\n",
       "69679     0       2           64\n",
       "69680     2       0          553\n",
       "69681     0       3           78\n",
       "\n",
       "[69682 rows x 3 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extraction des résultats de vote"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les 23 premières colonnes correspondent aux métadonnées :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.293530Z",
     "iopub.status.busy": "2022-06-03T10:36:12.293011Z",
     "iopub.status.idle": "2022-06-03T10:36:12.295441Z",
     "shell.execute_reply": "2022-06-03T10:36:12.295807Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Code du département', 'Libellé du département',\n",
       "       'Code de la circonscription', 'Libellé de la circonscription',\n",
       "       'Code de la commune', 'Libellé de la commune', 'Code du b.vote',\n",
       "       'Inscrits', 'Abstentions', '% Abs/Ins', 'Votants', '% Vot/Ins',\n",
       "       'Blancs', '% Blancs/Ins', '% Blancs/Vot', 'Nuls', '% Nuls/Ins',\n",
       "       '% Nuls/Vot', 'Exprimés', '% Exp/Ins', '% Exp/Vot', 'N°Panneau',\n",
       "       'Sexe'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T1.columns[:23]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les colonnes suivant la colonne numéro 23 vont concerner les résultats candidats par candidats :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.298790Z",
     "iopub.status.busy": "2022-06-03T10:36:12.298321Z",
     "iopub.status.idle": "2022-06-03T10:36:12.300061Z",
     "shell.execute_reply": "2022-06-03T10:36:12.300419Z"
    }
   },
   "outputs": [],
   "source": [
    "col_start = 23\n",
    "col_par_cdt = 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut extraire les noms des candidats présents au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.304633Z",
     "iopub.status.busy": "2022-06-03T10:36:12.304079Z",
     "iopub.status.idle": "2022-06-03T10:36:12.306179Z",
     "shell.execute_reply": "2022-06-03T10:36:12.306510Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Nom                   ARTHAUD\n",
       "Unnamed: 30           ROUSSEL\n",
       "Unnamed: 37            MACRON\n",
       "Unnamed: 44          LASSALLE\n",
       "Unnamed: 51            LE PEN\n",
       "Unnamed: 58           ZEMMOUR\n",
       "Unnamed: 65         MÉLENCHON\n",
       "Unnamed: 72           HIDALGO\n",
       "Unnamed: 79             JADOT\n",
       "Unnamed: 86          PÉCRESSE\n",
       "Unnamed: 93            POUTOU\n",
       "Unnamed: 100    DUPONT-AIGNAN\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "candidats = T1.iloc[0][col_start::col_par_cdt]\n",
    "candidats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut par exemple extraire les résultats pour le premier bureau de vote et donner le nombre de suffrages exprimés pour chaque candidat :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.310725Z",
     "iopub.status.busy": "2022-06-03T10:36:12.310134Z",
     "iopub.status.idle": "2022-06-03T10:36:12.312410Z",
     "shell.execute_reply": "2022-06-03T10:36:12.312743Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Voix              3\n",
       "Unnamed: 32       6\n",
       "Unnamed: 39     150\n",
       "Unnamed: 46      18\n",
       "Unnamed: 53     149\n",
       "Unnamed: 60      43\n",
       "Unnamed: 67      66\n",
       "Unnamed: 74       5\n",
       "Unnamed: 81      30\n",
       "Unnamed: 88      26\n",
       "Unnamed: 95       3\n",
       "Unnamed: 102     21\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "résultats = T1.iloc[0][(col_start+2)::col_par_cdt]\n",
    "résultats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grâce à ces connaissances, nous allons pouvoir maintenant récolter les données pour chaque candidat et pour tous les bureaux de vote en utilisant la fonction suivante :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.316699Z",
     "iopub.status.busy": "2022-06-03T10:36:12.316132Z",
     "iopub.status.idle": "2022-06-03T10:36:12.326095Z",
     "shell.execute_reply": "2022-06-03T10:36:12.326528Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# colonne 25  résultats= [3 2 4 ... 0 0 0]\n",
      "# colonne 32  résultats= [ 6  7 30 ...  1  1  1]\n",
      "# colonne 39  résultats= [150  50 159 ...  25  96  25]\n",
      "# colonne 46  résultats= [18 10 24 ...  1  1  0]\n",
      "# colonne 53  résultats= [149  23 237 ...   3   4   3]\n",
      "# colonne 60  résultats= [43 14 69 ...  7 18 17]\n",
      "# colonne 67  résultats= [ 66  41 216 ...   9  19   2]\n",
      "# colonne 74  résultats= [ 5  3 15 ...  0  2  0]\n",
      "# colonne 81  résultats= [30 10 25 ...  4 10  0]\n",
      "# colonne 88  résultats= [26  8 40 ...  0  5  6]\n",
      "# colonne 95  résultats= [3 3 8 ... 0 1 0]\n",
      "# colonne 102  résultats= [21  0 13 ...  1  1  1]\n"
     ]
    }
   ],
   "source": [
    "for i_candidat, candidat in enumerate(candidats):\n",
    "    i_col = col_start + i_candidat*col_par_cdt + 2\n",
    "    print('# colonne', i_col, ' résultats=', T1.iloc[:, i_col].values)\n",
    "    df_1[candidat] = T1.iloc[:, i_col].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous avons récolté les données utiles dans un nouveau tableau :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.329823Z",
     "iopub.status.busy": "2022-06-03T10:36:12.329342Z",
     "iopub.status.idle": "2022-06-03T10:36:12.337673Z",
     "shell.execute_reply": "2022-06-03T10:36:12.338034Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 69682 entries, 0 to 69681\n",
      "Data columns (total 15 columns):\n",
      " #   Column         Non-Null Count  Dtype\n",
      "---  ------         --------------  -----\n",
      " 0   Nuls           69682 non-null  int64\n",
      " 1   Blancs         69682 non-null  int64\n",
      " 2   Abstentions    69682 non-null  int64\n",
      " 3   ARTHAUD        69682 non-null  int64\n",
      " 4   ROUSSEL        69682 non-null  int64\n",
      " 5   MACRON         69682 non-null  int64\n",
      " 6   LASSALLE       69682 non-null  int64\n",
      " 7   LE PEN         69682 non-null  int64\n",
      " 8   ZEMMOUR        69682 non-null  int64\n",
      " 9   MÉLENCHON      69682 non-null  int64\n",
      " 10  HIDALGO        69682 non-null  int64\n",
      " 11  JADOT          69682 non-null  int64\n",
      " 12  PÉCRESSE       69682 non-null  int64\n",
      " 13  POUTOU         69682 non-null  int64\n",
      " 14  DUPONT-AIGNAN  69682 non-null  int64\n",
      "dtypes: int64(15)\n",
      "memory usage: 8.0 MB\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "print(df_1.info())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ceci nous permet par exemple d'extraire les résultats pour un candidat donné et pour tous les bureaux de vote :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.341537Z",
     "iopub.status.busy": "2022-06-03T10:36:12.340834Z",
     "iopub.status.idle": "2022-06-03T10:36:12.343667Z",
     "shell.execute_reply": "2022-06-03T10:36:12.344061Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0         3\n",
       "1         3\n",
       "2         8\n",
       "3         4\n",
       "4         3\n",
       "         ..\n",
       "69677    47\n",
       "69678    10\n",
       "69679     0\n",
       "69680     1\n",
       "69681     0\n",
       "Name: POUTOU, Length: 69682, dtype: int64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1['POUTOU']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En particulier, on a le nombre suivant de bureaux de vote :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.347178Z",
     "iopub.status.busy": "2022-06-03T10:36:12.346626Z",
     "iopub.status.idle": "2022-06-03T10:36:12.348793Z",
     "shell.execute_reply": "2022-06-03T10:36:12.349202Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69682"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et on peut calculer pour chaque alternative le nombre total de choix ainsi que le nombre total de choix dans les data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.352444Z",
     "iopub.status.busy": "2022-06-03T10:36:12.351931Z",
     "iopub.status.idle": "2022-06-03T10:36:12.358095Z",
     "shell.execute_reply": "2022-06-03T10:36:12.358394Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Nuls               247151\n",
       " Blancs             543609\n",
       " Abstentions      12824169\n",
       " ARTHAUD            197094\n",
       " ROUSSEL            802422\n",
       " MACRON            9783058\n",
       " LASSALLE          1101387\n",
       " LE PEN            8133828\n",
       " ZEMMOUR           2485226\n",
       " MÉLENCHON         7712520\n",
       " HIDALGO            616478\n",
       " JADOT             1627853\n",
       " PÉCRESSE          1679001\n",
       " POUTOU             268904\n",
       " DUPONT-AIGNAN      725176\n",
       " dtype: int64,\n",
       " 48747876)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.sum(), df_1.sum().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Par exemple, on note qu'environ 13 millions de personnes se sont abstenues, alors que environ 10 millions de personnes ont voté pour Macron."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans le reste, nous allons complétement ignorer les votes 'Nuls' et 'Abstebnsions'. En effet, des expériencesz précedentes (cf github) ont montré que ces valuers sont moins prédictibles. Pour celà, nous utilisons la fonction [`DataFrame.drop`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.drop.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.361666Z",
     "iopub.status.busy": "2022-06-03T10:36:12.361188Z",
     "iopub.status.idle": "2022-06-03T10:36:12.363375Z",
     "shell.execute_reply": "2022-06-03T10:36:12.363701Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Nuls', 'Blancs', 'Abstentions', 'ARTHAUD', 'ROUSSEL', 'MACRON',\n",
       "       'LASSALLE', 'LE PEN', 'ZEMMOUR', 'MÉLENCHON', 'HIDALGO', 'JADOT',\n",
       "       'PÉCRESSE', 'POUTOU', 'DUPONT-AIGNAN'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.366941Z",
     "iopub.status.busy": "2022-06-03T10:36:12.366470Z",
     "iopub.status.idle": "2022-06-03T10:36:12.379599Z",
     "shell.execute_reply": "2022-06-03T10:36:12.379953Z"
    }
   },
   "outputs": [],
   "source": [
    "df_1 = df_1.drop(columns=['Nuls', 'Blancs', 'Abstentions'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.383747Z",
     "iopub.status.busy": "2022-06-03T10:36:12.383126Z",
     "iopub.status.idle": "2022-06-03T10:36:12.385390Z",
     "shell.execute_reply": "2022-06-03T10:36:12.385732Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['ARTHAUD', 'ROUSSEL', 'MACRON', 'LASSALLE', 'LE PEN', 'ZEMMOUR',\n",
       "       'MÉLENCHON', 'HIDALGO', 'JADOT', 'PÉCRESSE', 'POUTOU', 'DUPONT-AIGNAN'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sous un format graphique on peut représenter ainsi les résultats du vote au premier tour et pour cela nous allons utiliser la librairie `matplotlib`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.388735Z",
     "iopub.status.busy": "2022-06-03T10:36:12.388264Z",
     "iopub.status.idle": "2022-06-03T10:36:12.925022Z",
     "shell.execute_reply": "2022-06-03T10:36:12.925397Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:12.929454Z",
     "iopub.status.busy": "2022-06-03T10:36:12.928952Z",
     "iopub.status.idle": "2022-06-03T10:36:13.079506Z",
     "shell.execute_reply": "2022-06-03T10:36:13.079964Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13, 5))\n",
    "k = df_1.sum()/df_1.sum().sum()\n",
    "ax = k.plot.bar(ax=ax)\n",
    "ax.set_xlabel('Choix 1er tour')\n",
    "ax.set_ylabel('Pourcentage');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque le fort taux d'abstention qui a été observé au premier tour, ainsi que les deux candidats qui se distinguent par le plus grand nombre de voix et qui sont sélectionnés pour le second tour."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Données du 2ème tour"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons maintenant répéter la même opération pour les données obtenues au deuxième tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:13.083959Z",
     "iopub.status.busy": "2022-06-03T10:36:13.083482Z",
     "iopub.status.idle": "2022-06-03T10:36:34.474332Z",
     "shell.execute_reply": "2022-06-03T10:36:34.474748Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Code du département</th>\n",
       "      <th>Libellé du département</th>\n",
       "      <th>Code de la circonscription</th>\n",
       "      <th>Libellé de la circonscription</th>\n",
       "      <th>Code de la commune</th>\n",
       "      <th>Libellé de la commune</th>\n",
       "      <th>Code du b.vote</th>\n",
       "      <th>Inscrits</th>\n",
       "      <th>Abstentions</th>\n",
       "      <th>% Abs/Ins</th>\n",
       "      <th>...</th>\n",
       "      <th>Voix</th>\n",
       "      <th>% Voix/Ins</th>\n",
       "      <th>% Voix/Exp</th>\n",
       "      <th>Unnamed: 28</th>\n",
       "      <th>Unnamed: 29</th>\n",
       "      <th>Unnamed: 30</th>\n",
       "      <th>Unnamed: 31</th>\n",
       "      <th>Unnamed: 32</th>\n",
       "      <th>Unnamed: 33</th>\n",
       "      <th>Unnamed: 34</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>69677</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>6</td>\n",
       "      <td>6ème circonscription</td>\n",
       "      <td>229</td>\n",
       "      <td>Zurich</td>\n",
       "      <td>0001</td>\n",
       "      <td>24867</td>\n",
       "      <td>13153</td>\n",
       "      <td>52.89</td>\n",
       "      <td>...</td>\n",
       "      <td>10166</td>\n",
       "      <td>40.88</td>\n",
       "      <td>88.88</td>\n",
       "      <td>2</td>\n",
       "      <td>F</td>\n",
       "      <td>LE PEN</td>\n",
       "      <td>Marine</td>\n",
       "      <td>1272</td>\n",
       "      <td>5.12</td>\n",
       "      <td>11.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69678</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>11</td>\n",
       "      <td>11ème circonscription</td>\n",
       "      <td>231</td>\n",
       "      <td>Taipei</td>\n",
       "      <td>0001</td>\n",
       "      <td>1703</td>\n",
       "      <td>928</td>\n",
       "      <td>54.49</td>\n",
       "      <td>...</td>\n",
       "      <td>611</td>\n",
       "      <td>35.88</td>\n",
       "      <td>82.23</td>\n",
       "      <td>2</td>\n",
       "      <td>F</td>\n",
       "      <td>LE PEN</td>\n",
       "      <td>Marine</td>\n",
       "      <td>132</td>\n",
       "      <td>7.75</td>\n",
       "      <td>17.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69679</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>11</td>\n",
       "      <td>11ème circonscription</td>\n",
       "      <td>233</td>\n",
       "      <td>Nour-Soultan</td>\n",
       "      <td>0001</td>\n",
       "      <td>117</td>\n",
       "      <td>64</td>\n",
       "      <td>54.70</td>\n",
       "      <td>...</td>\n",
       "      <td>39</td>\n",
       "      <td>33.33</td>\n",
       "      <td>78.00</td>\n",
       "      <td>2</td>\n",
       "      <td>F</td>\n",
       "      <td>LE PEN</td>\n",
       "      <td>Marine</td>\n",
       "      <td>11</td>\n",
       "      <td>9.40</td>\n",
       "      <td>22.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69680</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>2</td>\n",
       "      <td>2ème circonscription</td>\n",
       "      <td>234</td>\n",
       "      <td>Monterrey</td>\n",
       "      <td>0001</td>\n",
       "      <td>715</td>\n",
       "      <td>510</td>\n",
       "      <td>71.33</td>\n",
       "      <td>...</td>\n",
       "      <td>181</td>\n",
       "      <td>25.31</td>\n",
       "      <td>89.60</td>\n",
       "      <td>2</td>\n",
       "      <td>F</td>\n",
       "      <td>LE PEN</td>\n",
       "      <td>Marine</td>\n",
       "      <td>21</td>\n",
       "      <td>2.94</td>\n",
       "      <td>10.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69681</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>2</td>\n",
       "      <td>2ème circonscription</td>\n",
       "      <td>235</td>\n",
       "      <td>Bahamas (Nassau)</td>\n",
       "      <td>0001</td>\n",
       "      <td>137</td>\n",
       "      <td>78</td>\n",
       "      <td>56.93</td>\n",
       "      <td>...</td>\n",
       "      <td>35</td>\n",
       "      <td>25.55</td>\n",
       "      <td>68.63</td>\n",
       "      <td>2</td>\n",
       "      <td>F</td>\n",
       "      <td>LE PEN</td>\n",
       "      <td>Marine</td>\n",
       "      <td>16</td>\n",
       "      <td>11.68</td>\n",
       "      <td>31.37</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 35 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Code du département           Libellé du département  \\\n",
       "69677                  ZZ  Français établis hors de France   \n",
       "69678                  ZZ  Français établis hors de France   \n",
       "69679                  ZZ  Français établis hors de France   \n",
       "69680                  ZZ  Français établis hors de France   \n",
       "69681                  ZZ  Français établis hors de France   \n",
       "\n",
       "       Code de la circonscription Libellé de la circonscription  \\\n",
       "69677                           6          6ème circonscription   \n",
       "69678                          11         11ème circonscription   \n",
       "69679                          11         11ème circonscription   \n",
       "69680                           2          2ème circonscription   \n",
       "69681                           2          2ème circonscription   \n",
       "\n",
       "       Code de la commune Libellé de la commune Code du b.vote  Inscrits  \\\n",
       "69677                 229                Zurich           0001     24867   \n",
       "69678                 231                Taipei           0001      1703   \n",
       "69679                 233          Nour-Soultan           0001       117   \n",
       "69680                 234             Monterrey           0001       715   \n",
       "69681                 235      Bahamas (Nassau)           0001       137   \n",
       "\n",
       "       Abstentions  % Abs/Ins  ...   Voix  % Voix/Ins  % Voix/Exp  \\\n",
       "69677        13153      52.89  ...  10166       40.88       88.88   \n",
       "69678          928      54.49  ...    611       35.88       82.23   \n",
       "69679           64      54.70  ...     39       33.33       78.00   \n",
       "69680          510      71.33  ...    181       25.31       89.60   \n",
       "69681           78      56.93  ...     35       25.55       68.63   \n",
       "\n",
       "       Unnamed: 28  Unnamed: 29  Unnamed: 30  Unnamed: 31  Unnamed: 32  \\\n",
       "69677            2            F       LE PEN       Marine         1272   \n",
       "69678            2            F       LE PEN       Marine          132   \n",
       "69679            2            F       LE PEN       Marine           11   \n",
       "69680            2            F       LE PEN       Marine           21   \n",
       "69681            2            F       LE PEN       Marine           16   \n",
       "\n",
       "       Unnamed: 33  Unnamed: 34  \n",
       "69677         5.12        11.12  \n",
       "69678         7.75        17.77  \n",
       "69679         9.40        22.00  \n",
       "69680         2.94        10.40  \n",
       "69681        11.68        31.37  \n",
       "\n",
       "[5 rows x 35 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fname = '/tmp/T2.xlsx'\n",
    "\n",
    "if not os.path.isfile(fname):\n",
    "    url = 'https://static.data.gouv.fr/resources/election-presidentielle-des-10-et-24-avril-2022-resultats-definitifs-du-2nd-tour/20220428-142301/resultats-par-niveau-burvot-t2-france-entiere.xlsx' # XLSX\n",
    "    import urllib.request\n",
    "    urllib.request.urlretrieve(url, fname)\n",
    "\n",
    "T2 = pd.read_excel(fname)\n",
    "\n",
    "T2.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On vérifie que les données sont une nouvelle fois organisé suivant la même structure :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.478485Z",
     "iopub.status.busy": "2022-06-03T10:36:34.478003Z",
     "iopub.status.idle": "2022-06-03T10:36:34.480136Z",
     "shell.execute_reply": "2022-06-03T10:36:34.480461Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Code du département', 'Libellé du département',\n",
       "       'Code de la circonscription', 'Libellé de la circonscription',\n",
       "       'Code de la commune', 'Libellé de la commune', 'Code du b.vote',\n",
       "       'Inscrits', 'Abstentions', '% Abs/Ins', 'Votants', '% Vot/Ins',\n",
       "       'Blancs', '% Blancs/Ins', '% Blancs/Vot', 'Nuls', '% Nuls/Ins',\n",
       "       '% Nuls/Vot', 'Exprimés', '% Exp/Ins', '% Exp/Vot', 'N°Panneau', 'Sexe',\n",
       "       'Nom', 'Prénom', 'Voix', '% Voix/Ins', '% Voix/Exp', 'Unnamed: 28',\n",
       "       'Unnamed: 29', 'Unnamed: 30', 'Unnamed: 31', 'Unnamed: 32',\n",
       "       'Unnamed: 33', 'Unnamed: 34'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.483889Z",
     "iopub.status.busy": "2022-06-03T10:36:34.483405Z",
     "iopub.status.idle": "2022-06-03T10:36:34.485791Z",
     "shell.execute_reply": "2022-06-03T10:36:34.486117Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Code du département', 'Libellé du département',\n",
       "       'Code de la circonscription', 'Libellé de la circonscription',\n",
       "       'Code de la commune', 'Libellé de la commune', 'Code du b.vote',\n",
       "       'Inscrits', 'Abstentions', '% Abs/Ins', 'Votants', '% Vot/Ins',\n",
       "       'Blancs', '% Blancs/Ins', '% Blancs/Vot', 'Nuls', '% Nuls/Ins',\n",
       "       '% Nuls/Vot', 'Exprimés', '% Exp/Ins', '% Exp/Vot', 'N°Panneau',\n",
       "       'Sexe'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.columns[:23]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.489513Z",
     "iopub.status.busy": "2022-06-03T10:36:34.488952Z",
     "iopub.status.idle": "2022-06-03T10:36:34.490928Z",
     "shell.execute_reply": "2022-06-03T10:36:34.491257Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Nom', 'Prénom', 'Voix', '% Voix/Ins', '% Voix/Exp', 'Unnamed: 28',\n",
       "       'Unnamed: 29', 'Unnamed: 30', 'Unnamed: 31', 'Unnamed: 32',\n",
       "       'Unnamed: 33', 'Unnamed: 34'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.columns[23:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.495182Z",
     "iopub.status.busy": "2022-06-03T10:36:34.494642Z",
     "iopub.status.idle": "2022-06-03T10:36:34.496938Z",
     "shell.execute_reply": "2022-06-03T10:36:34.497277Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Nom              MACRON\n",
       "Prénom         Emmanuel\n",
       "Voix                237\n",
       "% Voix/Ins        36.86\n",
       "% Voix/Exp        52.67\n",
       "Unnamed: 28           2\n",
       "Unnamed: 29           F\n",
       "Unnamed: 30      LE PEN\n",
       "Unnamed: 31      Marine\n",
       "Unnamed: 32         213\n",
       "Unnamed: 33       33.13\n",
       "Unnamed: 34       47.33\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2.iloc[0, 23:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.501363Z",
     "iopub.status.busy": "2022-06-03T10:36:34.500877Z",
     "iopub.status.idle": "2022-06-03T10:36:34.503030Z",
     "shell.execute_reply": "2022-06-03T10:36:34.503364Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Nom            MACRON\n",
       "Unnamed: 30    LE PEN\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col_start = 23\n",
    "col_par_cdt = 7\n",
    "candidats = T2.iloc[0][col_start::col_par_cdt]\n",
    "candidats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Une fois cette vérification faite nous pouvons extraire les données dans un nouveau tableau :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.507811Z",
     "iopub.status.busy": "2022-06-03T10:36:34.507294Z",
     "iopub.status.idle": "2022-06-03T10:36:34.512035Z",
     "shell.execute_reply": "2022-06-03T10:36:34.512363Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nuls</th>\n",
       "      <th>Blancs</th>\n",
       "      <th>Abstentions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>42</td>\n",
       "      <td>146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>23</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>71</td>\n",
       "      <td>322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18</td>\n",
       "      <td>45</td>\n",
       "      <td>313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>21</td>\n",
       "      <td>87</td>\n",
       "      <td>303</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Nuls  Blancs  Abstentions\n",
       "0     5      42          146\n",
       "1     3      23           45\n",
       "2    22      71          322\n",
       "3    18      45          313\n",
       "4    21      87          303"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_2 = T2[['Nuls', 'Blancs', 'Abstentions']].copy()\n",
    "#df_1 = df_1.rename(columns={\"Nuls\": \"1_Nuls\", \"Abstentions\": \"1_Abstentions\"})\n",
    "df_2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous vérifions aussi que nous avons le même nombre de bureaux de vote :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.515510Z",
     "iopub.status.busy": "2022-06-03T10:36:34.515029Z",
     "iopub.status.idle": "2022-06-03T10:36:34.517299Z",
     "shell.execute_reply": "2022-06-03T10:36:34.517627Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69682"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.521684Z",
     "iopub.status.busy": "2022-06-03T10:36:34.520846Z",
     "iopub.status.idle": "2022-06-03T10:36:34.523740Z",
     "shell.execute_reply": "2022-06-03T10:36:34.524082Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25 [237  94 360 ...  39 181  35]\n",
      "32 [213  48 355 ...  11  21  16]\n"
     ]
    }
   ],
   "source": [
    "for i_candidat, candidat in enumerate(candidats):\n",
    "    i_col = col_start + i_candidat*col_par_cdt + 2\n",
    "    print(i_col, T2.iloc[:, i_col].values)\n",
    "    df_2[candidat] = T2.iloc[:, i_col].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.529942Z",
     "iopub.status.busy": "2022-06-03T10:36:34.526918Z",
     "iopub.status.idle": "2022-06-03T10:36:34.532276Z",
     "shell.execute_reply": "2022-06-03T10:36:34.532606Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nuls</th>\n",
       "      <th>Blancs</th>\n",
       "      <th>Abstentions</th>\n",
       "      <th>MACRON</th>\n",
       "      <th>LE PEN</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>42</td>\n",
       "      <td>146</td>\n",
       "      <td>237</td>\n",
       "      <td>213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>23</td>\n",
       "      <td>45</td>\n",
       "      <td>94</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>71</td>\n",
       "      <td>322</td>\n",
       "      <td>360</td>\n",
       "      <td>355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18</td>\n",
       "      <td>45</td>\n",
       "      <td>313</td>\n",
       "      <td>426</td>\n",
       "      <td>327</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>21</td>\n",
       "      <td>87</td>\n",
       "      <td>303</td>\n",
       "      <td>449</td>\n",
       "      <td>353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69677</th>\n",
       "      <td>49</td>\n",
       "      <td>227</td>\n",
       "      <td>13153</td>\n",
       "      <td>10166</td>\n",
       "      <td>1272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69678</th>\n",
       "      <td>6</td>\n",
       "      <td>26</td>\n",
       "      <td>928</td>\n",
       "      <td>611</td>\n",
       "      <td>132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69679</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>64</td>\n",
       "      <td>39</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69680</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>510</td>\n",
       "      <td>181</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69681</th>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>78</td>\n",
       "      <td>35</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>69682 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Nuls  Blancs  Abstentions  MACRON  LE PEN\n",
       "0         5      42          146     237     213\n",
       "1         3      23           45      94      48\n",
       "2        22      71          322     360     355\n",
       "3        18      45          313     426     327\n",
       "4        21      87          303     449     353\n",
       "...     ...     ...          ...     ...     ...\n",
       "69677    49     227        13153   10166    1272\n",
       "69678     6      26          928     611     132\n",
       "69679     0       3           64      39      11\n",
       "69680     1       2          510     181      21\n",
       "69681     1       7           78      35      16\n",
       "\n",
       "[69682 rows x 5 columns]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De la même façon que pour le premier tour, nous pouvons représenter les résultats totaux obtenus au second tour de façon graphique :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.568465Z",
     "iopub.status.busy": "2022-06-03T10:36:34.559567Z",
     "iopub.status.idle": "2022-06-03T10:36:34.659719Z",
     "shell.execute_reply": "2022-06-03T10:36:34.660123Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13, 5))\n",
    "k = df_2.sum()/df_2.sum().sum()\n",
    "ax = k.plot.bar(ax=ax)\n",
    "ax.set_xlabel('Candidat')\n",
    "#ax.set_xlim(1, 10)\n",
    "#ax.set_xticks(np.arange(1, 10)+.5)\n",
    "#ax.set_xticklabels(np.arange(1, 10)) , rotation=45\n",
    "ax.set_ylabel('pourcentage');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.664011Z",
     "iopub.status.busy": "2022-06-03T10:36:34.663510Z",
     "iopub.status.idle": "2022-06-03T10:36:34.666958Z",
     "shell.execute_reply": "2022-06-03T10:36:34.667293Z"
    }
   },
   "outputs": [],
   "source": [
    "df_2 = df_2.drop(columns=['Nuls', 'Blancs', 'Abstentions'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nettoyage des données (non aux nans)\n",
    "\n",
    "Certains bureaux de vote n'ont pas de votants au premier ou au deuxieme. Ceci peut engendrer des problèmes numériques en générant des divisions par zéro, des `Not a Number (NaN)` dans le jargon informatique. Comme ceux-ci représentent un nombre très faible d'électeurs nous allons les ignorer par rapport au reste de la population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons d'abord compter le nombre de bureaux de vote qui n'ont aucun suffrage enregistré:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.671201Z",
     "iopub.status.busy": "2022-06-03T10:36:34.670729Z",
     "iopub.status.idle": "2022-06-03T10:36:34.675043Z",
     "shell.execute_reply": "2022-06-03T10:36:34.675375Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70, 97)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(df_1.sum(axis=1)==0).sum(), (df_2.sum(axis=1)==0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons \"effacer\" ces bureaux du vote en commençant par filtrer ceux qui n'ont aucun suffrage enregistré au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.679228Z",
     "iopub.status.busy": "2022-06-03T10:36:34.678711Z",
     "iopub.status.idle": "2022-06-03T10:36:34.689242Z",
     "shell.execute_reply": "2022-06-03T10:36:34.689597Z"
    }
   },
   "outputs": [],
   "source": [
    "df_2.drop(df_2.loc[df_1.sum(axis=1)==0].index, inplace=True)\n",
    "df_1.drop(df_1.loc[df_1.sum(axis=1)==0].index, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.693236Z",
     "iopub.status.busy": "2022-06-03T10:36:34.692720Z",
     "iopub.status.idle": "2022-06-03T10:36:34.697854Z",
     "shell.execute_reply": "2022-06-03T10:36:34.698185Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 58)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(df_1.sum(axis=1)==0).sum(), (df_2.sum(axis=1)==0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et maintenant répéter la même procédure sur les bureaux de vote qui n'ont aucun suffrage enregistré au second tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.702010Z",
     "iopub.status.busy": "2022-06-03T10:36:34.701514Z",
     "iopub.status.idle": "2022-06-03T10:36:34.713685Z",
     "shell.execute_reply": "2022-06-03T10:36:34.714032Z"
    }
   },
   "outputs": [],
   "source": [
    "df_1.drop(df_1.loc[df_2.sum(axis=1)==0].index, inplace=True)\n",
    "df_2.drop(df_2.loc[df_2.sum(axis=1)==0].index, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.717580Z",
     "iopub.status.busy": "2022-06-03T10:36:34.717083Z",
     "iopub.status.idle": "2022-06-03T10:36:34.721152Z",
     "shell.execute_reply": "2022-06-03T10:36:34.721495Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(df_1.sum(axis=1)==0).sum(), (df_2.sum(axis=1)==0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistiques de second ordre\n",
    "\n",
    "Comme cela est montré dans l'[article du Monde](https://www.lemonde.fr/les-decodeurs/article/2022/05/04/election-presidentielle-2022-quels-reports-de-voix-entre-les-deux-tours_6124672_4355770.html) on peut montrer la dépendance entre les choix qui sont effectués au premier tour et ceux qui sont effectués au deuxième tour. On va utiliser des représentations graphiques similaires à ceux de l'article pour d'une première part les répliquer et vérifier que la méthode est correct et d'un autre côté pour mieux comprendre comment nous pouvons tirer dans ses enseignements depuis ces observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.724911Z",
     "iopub.status.busy": "2022-06-03T10:36:34.724431Z",
     "iopub.status.idle": "2022-06-03T10:36:34.726155Z",
     "shell.execute_reply": "2022-06-03T10:36:34.726651Z"
    }
   },
   "outputs": [],
   "source": [
    "df_12 = pd.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.729884Z",
     "iopub.status.busy": "2022-06-03T10:36:34.729415Z",
     "iopub.status.idle": "2022-06-03T10:36:34.735066Z",
     "shell.execute_reply": "2022-06-03T10:36:34.735397Z"
    }
   },
   "outputs": [],
   "source": [
    "df_12['1_MÉLENCHON'] = df_1['MÉLENCHON'].copy()\n",
    "df_12['MACRON'] = df_2['MACRON'].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.738849Z",
     "iopub.status.busy": "2022-06-03T10:36:34.738362Z",
     "iopub.status.idle": "2022-06-03T10:36:34.744417Z",
     "shell.execute_reply": "2022-06-03T10:36:34.744754Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 69554 entries, 0 to 69681\n",
      "Data columns (total 2 columns):\n",
      " #   Column       Non-Null Count  Dtype\n",
      "---  ------       --------------  -----\n",
      " 0   1_MÉLENCHON  69554 non-null  int64\n",
      " 1   MACRON       69554 non-null  int64\n",
      "dtypes: int64(2)\n",
      "memory usage: 1.6 MB\n"
     ]
    }
   ],
   "source": [
    "df_12.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.748151Z",
     "iopub.status.busy": "2022-06-03T10:36:34.747638Z",
     "iopub.status.idle": "2022-06-03T10:36:34.751907Z",
     "shell.execute_reply": "2022-06-03T10:36:34.752238Z"
    }
   },
   "outputs": [],
   "source": [
    "df_12['1_MÉLENCHON'] = df_12['1_MÉLENCHON']/df_1.sum(axis=1)\n",
    "df_12['MACRON'] = df_12['MACRON']/df_2.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:34.755084Z",
     "iopub.status.busy": "2022-06-03T10:36:34.754611Z",
     "iopub.status.idle": "2022-06-03T10:36:35.096198Z",
     "shell.execute_reply": "2022-06-03T10:36:35.096627Z"
    }
   },
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:35.144522Z",
     "iopub.status.busy": "2022-06-03T10:36:35.125607Z",
     "iopub.status.idle": "2022-06-03T10:36:35.686877Z",
     "shell.execute_reply": "2022-06-03T10:36:35.687234Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.jointplot(x=df_12['1_MÉLENCHON'], y=df_12['MACRON'], kind='hist', height=8);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque effectivement une dépendance entre le choix. Un premier candidat effectué au premier tour et celui qui est effectué au second tour. Nous allons essayer d'inférer de façon plus précise cette dépendance grâce au modèle de transition que nous avons exposer au début de cet article."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modèle de prédiction du transfert des voix\n",
    "\n",
    "Tenant que nous avons récolté toutes les données pour les deux tours, et que nous avons une idée qu'il existe une dépendance entre les choix qui sont faits entre un tour et le suivant, nous allons pouvoir utiliser des librairies de tes apprentissage automatique machine Learning en anglais pour pouvoir insérer le report de voix entre les deux tours :. Pour cela nous allons utiliser un travail précédemment effectué appliquer à l'[exploration du comportement humain](https://laurentperrinet.github.io/sciblog/posts/2020-04-08-fitting-a-psychometric-curve-using-pytorch.html) ou alors pour [l'épidémiologie du Covid](https://laurentperrinet.github.io/sciblog/posts/2020-10-10-fitting-covid-data.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Formatage des données au format de la librairie `torch`\n",
    "\n",
    "Pendant un aperçu des résultats au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:35.695032Z",
     "iopub.status.busy": "2022-06-03T10:36:35.694415Z",
     "iopub.status.idle": "2022-06-03T10:36:35.696836Z",
     "shell.execute_reply": "2022-06-03T10:36:35.697171Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ARTHAUD</th>\n",
       "      <th>ROUSSEL</th>\n",
       "      <th>MACRON</th>\n",
       "      <th>LASSALLE</th>\n",
       "      <th>LE PEN</th>\n",
       "      <th>ZEMMOUR</th>\n",
       "      <th>MÉLENCHON</th>\n",
       "      <th>HIDALGO</th>\n",
       "      <th>JADOT</th>\n",
       "      <th>PÉCRESSE</th>\n",
       "      <th>POUTOU</th>\n",
       "      <th>DUPONT-AIGNAN</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>150</td>\n",
       "      <td>18</td>\n",
       "      <td>149</td>\n",
       "      <td>43</td>\n",
       "      <td>66</td>\n",
       "      <td>5</td>\n",
       "      <td>30</td>\n",
       "      <td>26</td>\n",
       "      <td>3</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>50</td>\n",
       "      <td>10</td>\n",
       "      <td>23</td>\n",
       "      <td>14</td>\n",
       "      <td>41</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>30</td>\n",
       "      <td>159</td>\n",
       "      <td>24</td>\n",
       "      <td>237</td>\n",
       "      <td>69</td>\n",
       "      <td>216</td>\n",
       "      <td>15</td>\n",
       "      <td>25</td>\n",
       "      <td>40</td>\n",
       "      <td>8</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>13</td>\n",
       "      <td>201</td>\n",
       "      <td>19</td>\n",
       "      <td>210</td>\n",
       "      <td>68</td>\n",
       "      <td>194</td>\n",
       "      <td>19</td>\n",
       "      <td>46</td>\n",
       "      <td>42</td>\n",
       "      <td>4</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>18</td>\n",
       "      <td>229</td>\n",
       "      <td>28</td>\n",
       "      <td>227</td>\n",
       "      <td>74</td>\n",
       "      <td>227</td>\n",
       "      <td>16</td>\n",
       "      <td>65</td>\n",
       "      <td>35</td>\n",
       "      <td>3</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ARTHAUD  ROUSSEL  MACRON  LASSALLE  LE PEN  ZEMMOUR  MÉLENCHON  HIDALGO  \\\n",
       "0        3        6     150        18     149       43         66        5   \n",
       "1        2        7      50        10      23       14         41        3   \n",
       "2        4       30     159        24     237       69        216       15   \n",
       "3        6       13     201        19     210       68        194       19   \n",
       "4        8       18     229        28     227       74        227       16   \n",
       "\n",
       "   JADOT  PÉCRESSE  POUTOU  DUPONT-AIGNAN  \n",
       "0     30        26       3             21  \n",
       "1     10         8       3              0  \n",
       "2     25        40       8             13  \n",
       "3     46        42       4             20  \n",
       "4     65        35       3             19  "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous avons donc comptabilisé ces différentes alternatives au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:35.700890Z",
     "iopub.status.busy": "2022-06-03T10:36:35.700313Z",
     "iopub.status.idle": "2022-06-03T10:36:35.702582Z",
     "shell.execute_reply": "2022-06-03T10:36:35.702917Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df_1.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De sorte que sur les bureaux de vote que nous avons validé nous avons les deux tableaux suivants :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:35.706555Z",
     "iopub.status.busy": "2022-06-03T10:36:35.705989Z",
     "iopub.status.idle": "2022-06-03T10:36:35.708139Z",
     "shell.execute_reply": "2022-06-03T10:36:35.708636Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((69554, 12), (69554, 2))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1.values.shape, df_2.values.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons maintenant utiliser la librairie `torch` pour enregistrer ses données sous la forme d'une matrice (ou tenseur dans le jargon de cette librairie) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:35.711954Z",
     "iopub.status.busy": "2022-06-03T10:36:35.711484Z",
     "iopub.status.idle": "2022-06-03T10:36:36.174043Z",
     "shell.execute_reply": "2022-06-03T10:36:36.174457Z"
    }
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "\n",
    "X_1, X_2 = df_1.values, df_2.values\n",
    "x_1, x_2 = torch.Tensor(X_1), torch.Tensor(X_2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.178270Z",
     "iopub.status.busy": "2022-06-03T10:36:36.177669Z",
     "iopub.status.idle": "2022-06-03T10:36:36.179915Z",
     "shell.execute_reply": "2022-06-03T10:36:36.180245Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([69554, 12])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_1.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ainsi nous allons très facilement pouvoir représenter les données pour pouvoir les apprendre. Une pratique extrêmement importante dans l'apprentissage automatique et de séparer les données qui sont utilisés pour apprendre le modèle, avec celles qui sont utilisés pour tester ce modèle :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.184067Z",
     "iopub.status.busy": "2022-06-03T10:36:36.183600Z",
     "iopub.status.idle": "2022-06-03T10:36:36.188237Z",
     "shell.execute_reply": "2022-06-03T10:36:36.188538Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch.utils.data import TensorDataset, DataLoader\n",
    "\n",
    "dataset = TensorDataset(x_1, x_2)\n",
    "\n",
    "# Random split\n",
    "train_set_size = int(len(dataset) * 0.8)\n",
    "test_set_size = len(dataset) - train_set_size\n",
    "train_set, test_set = torch.utils.data.random_split(dataset, [train_set_size, test_set_size])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ainsi nous pourrons utiliser l'ensemble d'apprentissage au cours des différentes époques d'apprentissage utilisé plus bas :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.191844Z",
     "iopub.status.busy": "2022-06-03T10:36:36.191257Z",
     "iopub.status.idle": "2022-06-03T10:36:36.192943Z",
     "shell.execute_reply": "2022-06-03T10:36:36.193296Z"
    }
   },
   "outputs": [],
   "source": [
    "train_loader = DataLoader(train_set, batch_size=32, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.196387Z",
     "iopub.status.busy": "2022-06-03T10:36:36.195901Z",
     "iopub.status.idle": "2022-06-03T10:36:36.201168Z",
     "shell.execute_reply": "2022-06-03T10:36:36.201543Z"
    }
   },
   "outputs": [],
   "source": [
    "for n_1, n_2 in train_loader:\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En particulier nous allons couper les données de façon aléatoire puis il est représenté sous la forme de différents « paquet » dont la taille est fixé ici à 32, et nous verrons plus tard que si cette procédure permet d'accélérer l'apprentissage la taille du paquet n'a plus d'influence sur le résultat final."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.204993Z",
     "iopub.status.busy": "2022-06-03T10:36:36.204515Z",
     "iopub.status.idle": "2022-06-03T10:36:36.207077Z",
     "shell.execute_reply": "2022-06-03T10:36:36.207424Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([32, 12]), torch.Size([32, 2]))"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_1.shape, n_2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans chaque paquet nous pouvons compter le nombre de votes pour les différentes alternatives :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.210667Z",
     "iopub.status.busy": "2022-06-03T10:36:36.210162Z",
     "iopub.status.idle": "2022-06-03T10:36:36.214065Z",
     "shell.execute_reply": "2022-06-03T10:36:36.214394Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([261., 201., 948., 682., 728., 188., 311.,  68., 441.,  84.,  41., 592.,\n",
       "         450., 593., 889., 736., 496., 985., 356., 527., 228., 585., 624., 694.,\n",
       "         171., 248., 396., 938., 756., 770., 137., 737.]),\n",
       " tensor([285., 179., 867., 623., 692., 163., 283.,  59., 351.,  69.,  39., 491.,\n",
       "         329., 570., 844., 615., 433., 873., 332., 514., 278., 548., 551., 683.,\n",
       "         145., 214., 457., 860., 651., 681., 129., 696.]))"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_1, sum_2 = n_1.sum(axis=1), n_2.sum(axis=1)\n",
    "sum_1, sum_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons aussi vérifier que parmi toutes les et les alternatives on peut calculer des fréquences d'occurrence, et que comme chaque individu peut faire un seul un choix est un seul, la somme de ses fréquences d'occurrence pour chacun des paquets est égal à $1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.217484Z",
     "iopub.status.busy": "2022-06-03T10:36:36.217020Z",
     "iopub.status.idle": "2022-06-03T10:36:36.220400Z",
     "shell.execute_reply": "2022-06-03T10:36:36.220734Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,\n",
       "        1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,\n",
       "        1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,\n",
       "        1.0000, 1.0000, 1.0000, 1.0000, 1.0000])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(n_1/sum_1[:, None]).sum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pourrons aussi aisément utiliser les données qui sont représentés dans l'ensemble de test :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.225264Z",
     "iopub.status.busy": "2022-06-03T10:36:36.224226Z",
     "iopub.status.idle": "2022-06-03T10:36:36.228250Z",
     "shell.execute_reply": "2022-06-03T10:36:36.228601Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([13911, 12]), torch.Size([13911, 2]))"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_1, n_2 = dataset[test_set.indices]\n",
    "n_1.shape, n_2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modèle `torch` de transition de probabilités\n",
    "\n",
    "\n",
    "Maintenant que nous avons correctement formater les données, nous allons exprimer dans le langage de la librairie torche le modèle qui nous permet d'exprimer la transition entre les préférences au premier tour et les préférences au premier second tour. En particulier la matrice de transition sera définie par une matric `self.M` de telle sorte que quand on l'utilise, la contrainte qui fait que la somme des éléments colonne par colonne est bien égal à $1$ (utilisation de `torch.softmax(self.M, axis=1)`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.233404Z",
     "iopub.status.busy": "2022-06-03T10:36:36.232920Z",
     "iopub.status.idle": "2022-06-03T10:36:36.234681Z",
     "shell.execute_reply": "2022-06-03T10:36:36.235009Z"
    },
    "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=1)\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": 58,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.238347Z",
     "iopub.status.busy": "2022-06-03T10:36:36.237808Z",
     "iopub.status.idle": "2022-06-03T10:36:36.240037Z",
     "shell.execute_reply": "2022-06-03T10:36:36.240366Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12, 2)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N_1er, N_2eme = len(df_1.columns), len(df_2.columns)\n",
    "N_1er, N_2eme"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De telle sorte que nous allons pouvoir instancier un tel modèle, sachant que la matrice de transition sera choisi de façon totalement aléatoire et donc déconnecté des données à l'initialisation de cet apprentissage :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.243357Z",
     "iopub.status.busy": "2022-06-03T10:36:36.242890Z",
     "iopub.status.idle": "2022-06-03T10:36:36.244769Z",
     "shell.execute_reply": "2022-06-03T10:36:36.245251Z"
    }
   },
   "outputs": [],
   "source": [
    "trans = TransfertVoix(N_1er, N_2eme)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.248460Z",
     "iopub.status.busy": "2022-06-03T10:36:36.247920Z",
     "iopub.status.idle": "2022-06-03T10:36:36.250628Z",
     "shell.execute_reply": "2022-06-03T10:36:36.250982Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[ 0.1170,  0.1444],\n",
      "        [ 0.3141,  0.1127],\n",
      "        [-0.2527, -0.5902],\n",
      "        [ 0.3596, -0.1957],\n",
      "        [-0.2420, -0.3558],\n",
      "        [ 0.3933,  0.3463],\n",
      "        [ 0.2647,  0.4324],\n",
      "        [-0.6917,  0.3191],\n",
      "        [ 0.0184, -0.5614],\n",
      "        [ 0.3885, -0.4399],\n",
      "        [-0.6952,  0.6527],\n",
      "        [ 0.3665,  0.5490]], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "for p in trans.parameters():print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.253957Z",
     "iopub.status.busy": "2022-06-03T10:36:36.253484Z",
     "iopub.status.idle": "2022-06-03T10:36:36.255672Z",
     "shell.execute_reply": "2022-06-03T10:36:36.255997Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([12, 2])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans.lin.weight.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.259263Z",
     "iopub.status.busy": "2022-06-03T10:36:36.258761Z",
     "iopub.status.idle": "2022-06-03T10:36:36.261787Z",
     "shell.execute_reply": "2022-06-03T10:36:36.262117Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.4931, 0.5069],\n",
       "        [0.5502, 0.4498],\n",
       "        [0.5836, 0.4164],\n",
       "        [0.6354, 0.3646],\n",
       "        [0.5284, 0.4716],\n",
       "        [0.5118, 0.4882],\n",
       "        [0.4582, 0.5418],\n",
       "        [0.2668, 0.7332],\n",
       "        [0.6410, 0.3590],\n",
       "        [0.6960, 0.3040],\n",
       "        [0.2062, 0.7938],\n",
       "        [0.4545, 0.5455]], grad_fn=<SoftmaxBackward0>)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.softmax(trans.lin.weight, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous vérifions que la contrainte sur chaque colonne de la matrice de transition et bien vérifiée :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.265327Z",
     "iopub.status.busy": "2022-06-03T10:36:36.264818Z",
     "iopub.status.idle": "2022-06-03T10:36:36.267969Z",
     "shell.execute_reply": "2022-06-03T10:36:36.268305Z"
    },
    "tags": []
   },
   "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], grad_fn=<SumBackward1>)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.softmax(trans.lin.weight, axis=1).sum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exprimons maintenant pour chacun des bureaux de vote les probabilités de préférence qui sont exprimées localement :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.271737Z",
     "iopub.status.busy": "2022-06-03T10:36:36.271159Z",
     "iopub.status.idle": "2022-06-03T10:36:36.273453Z",
     "shell.execute_reply": "2022-06-03T10:36:36.273833Z"
    }
   },
   "outputs": [],
   "source": [
    "sum_1, sum_2 = n_1.sum(axis=1), n_2.sum(axis=1)\n",
    "p_1 = n_1/sum_1[:, None]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cette probabilité va pouvoir être multiplié par la matrice de transition de probabilité et nous vérifions dans les lignes suivantes la compatibilité entre les différentes dimensions des données représentées :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.277525Z",
     "iopub.status.busy": "2022-06-03T10:36:36.276951Z",
     "iopub.status.idle": "2022-06-03T10:36:36.279653Z",
     "shell.execute_reply": "2022-06-03T10:36:36.280151Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([13911, 12]),\n",
       " tensor([1.0000, 1.0000, 1.0000,  ..., 1.0000, 1.0000, 1.0000]))"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_1.shape, p_1.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.283507Z",
     "iopub.status.busy": "2022-06-03T10:36:36.282932Z",
     "iopub.status.idle": "2022-06-03T10:36:36.285184Z",
     "shell.execute_reply": "2022-06-03T10:36:36.285524Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([13911, 12]), torch.Size([12, 2]))"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_1.shape, trans.lin.weight.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.288451Z",
     "iopub.status.busy": "2022-06-03T10:36:36.287983Z",
     "iopub.status.idle": "2022-06-03T10:36:36.291841Z",
     "shell.execute_reply": "2022-06-03T10:36:36.292169Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([13911, 2])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.matmul(p_1, torch.softmax(trans.lin.weight, axis=1)).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ces différentes vérifications nous permettent de valider l'utilisation directe du modèle pour prédire la probabilité de préférence dans ce bureau de vote au second tour à partir de celle observée au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.295414Z",
     "iopub.status.busy": "2022-06-03T10:36:36.294884Z",
     "iopub.status.idle": "2022-06-03T10:36:36.298423Z",
     "shell.execute_reply": "2022-06-03T10:36:36.298750Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.5356, 0.4644], grad_fn=<MeanBackward1>),\n",
       " tensor(1., grad_fn=<SumBackward0>))"
      ]
     },
     "execution_count": 68,
     "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": 69,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.302016Z",
     "iopub.status.busy": "2022-06-03T10:36:36.301476Z",
     "iopub.status.idle": "2022-06-03T10:36:36.304662Z",
     "shell.execute_reply": "2022-06-03T10:36:36.305022Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.5478, 0.4522]), tensor(1.))"
      ]
     },
     "execution_count": 69,
     "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": 70,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.320585Z",
     "iopub.status.busy": "2022-06-03T10:36:36.310610Z",
     "iopub.status.idle": "2022-06-03T10:36:36.398795Z",
     "shell.execute_reply": "2022-06-03T10:36:36.399151Z"
    }
   },
   "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": 71,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.403665Z",
     "iopub.status.busy": "2022-06-03T10:36:36.403057Z",
     "iopub.status.idle": "2022-06-03T10:36:36.405836Z",
     "shell.execute_reply": "2022-06-03T10:36:36.406167Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(MACRON    58.548024\n",
       " LE PEN    41.451976\n",
       " dtype: float64,\n",
       " tensor([58.5693, 41.4307]))"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k*100, p_2_average*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.409480Z",
     "iopub.status.busy": "2022-06-03T10:36:36.408884Z",
     "iopub.status.idle": "2022-06-03T10:36:36.411884Z",
     "shell.execute_reply": "2022-06-03T10:36:36.412220Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(1.3568)"
      ]
     },
     "execution_count": 72,
     "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. Mathématiquement, c'est une semi-normes car elle obéit à deux propriétés fondamentales: elle est toujours positive et est égale à zéro quand elle est appliquée à distributions identiques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.425856Z",
     "iopub.status.busy": "2022-06-03T10:36:36.425333Z",
     "iopub.status.idle": "2022-06-03T10:36:36.427323Z",
     "shell.execute_reply": "2022-06-03T10:36:36.427688Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch.nn.functional as F\n",
    "\n",
    "learning_rate = 0.01\n",
    "beta1, beta2 = 0.99, 0\n",
    "# beta1, beta2 = 0.9, 0.999\n",
    "num_epochs = 2 ** 9 + 1\n",
    "batch_size = 2 ** 8\n",
    "do_optim = False\n",
    "do_optim = True\n",
    "\n",
    "def pdf_loss(p_pred, p, weight, loss_type):\n",
    "    if loss_type=='kl':\n",
    "        ind_nonzero = (p==0) + (p_pred==0)\n",
    "        p[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='bce',\n",
    "    beta1=beta1,\n",
    "    beta2=beta2, \n",
    "    do_optim=do_optim, \n",
    "    split_ratio=.9, \n",
    "    seed=2022, # graine du générateur de nombre aléatoires utilisé dans le split test vs train\n",
    "    verbose=False\n",
    "):\n",
    "\n",
    "    device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "    N_1er, N_2eme = len(df_1.columns), len(df_2.columns)\n",
    "    trans = TransfertVoix(N_1er, N_2eme)\n",
    "    trans = trans.to(device)\n",
    "    trans.train()\n",
    "    \n",
    "    # apprentissage\n",
    "    if beta2==0: \n",
    "        optimizer = torch.optim.SGD(trans.parameters(), lr=learning_rate, momentum=beta1, nesterov=do_optim)\n",
    "    else:\n",
    "        optimizer = torch.optim.Adam(trans.parameters(), lr=learning_rate, betas=(beta1, beta2), amsgrad=do_optim)\n",
    "\n",
    "    if torch.cuda.is_available(): torch.cuda.empty_cache()    \n",
    "    # the data\n",
    "    X_1, X_2 = df_1.values, df_2.values\n",
    "    x_1, x_2 = torch.Tensor(X_1), torch.Tensor(X_2)\n",
    "\n",
    "    # split train and test\n",
    "    dataset = TensorDataset(x_1, x_2)\n",
    "    train_set_size = int(len(dataset) * split_ratio)\n",
    "    test_set_size = len(dataset) - train_set_size\n",
    "    train_set, test_set = random_split(dataset, [train_set_size, test_set_size], generator=torch.Generator().manual_seed(seed))\n",
    "    train_loader = DataLoader(train_set, batch_size=int(batch_size), shuffle=True)\n",
    "\n",
    "    for epoch in range(int(num_epochs)):\n",
    "        losses = []\n",
    "        for n_1, n_2 in train_loader:\n",
    "            n_1, n_2 = n_1.to(device), n_2.to(device)\n",
    "\n",
    "            sum_1, sum_2 = n_1.sum(axis=1), n_2.sum(axis=1)\n",
    "            p_1 = n_1/sum_1[:, None]\n",
    "            p_2 = n_2/sum_2[:, None]\n",
    "\n",
    "            p_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": 74,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:36:36.433172Z",
     "iopub.status.busy": "2022-06-03T10:36:36.432354Z",
     "iopub.status.idle": "2022-06-03T10:45:13.714945Z",
     "shell.execute_reply": "2022-06-03T10:45:13.715294Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='kl'\n",
      "Iteration: 0 / 513 - Loss: 9.57231e+00\n",
      "Iteration: 16 / 513 - Loss: 3.50453e+00\n",
      "Iteration: 32 / 513 - Loss: 3.42124e+00\n",
      "Iteration: 48 / 513 - Loss: 3.38734e+00\n",
      "Iteration: 64 / 513 - Loss: 3.37005e+00\n",
      "Iteration: 80 / 513 - Loss: 3.35837e+00\n",
      "Iteration: 96 / 513 - Loss: 3.35059e+00\n",
      "Iteration: 112 / 513 - Loss: 3.34545e+00\n",
      "Iteration: 128 / 513 - Loss: 3.34029e+00\n",
      "Iteration: 144 / 513 - Loss: 3.33679e+00\n",
      "Iteration: 160 / 513 - Loss: 3.33458e+00\n",
      "Iteration: 176 / 513 - Loss: 3.33250e+00\n",
      "Iteration: 192 / 513 - Loss: 3.33125e+00\n",
      "Iteration: 208 / 513 - Loss: 3.32932e+00\n",
      "Iteration: 224 / 513 - Loss: 3.32746e+00\n",
      "Iteration: 240 / 513 - Loss: 3.32667e+00\n",
      "Iteration: 256 / 513 - Loss: 3.32536e+00\n",
      "Iteration: 272 / 513 - Loss: 3.32448e+00\n",
      "Iteration: 288 / 513 - Loss: 3.32340e+00\n",
      "Iteration: 304 / 513 - Loss: 3.32300e+00\n",
      "Iteration: 320 / 513 - Loss: 3.32242e+00\n",
      "Iteration: 336 / 513 - Loss: 3.32164e+00\n",
      "Iteration: 352 / 513 - Loss: 3.32169e+00\n",
      "Iteration: 368 / 513 - Loss: 3.32107e+00\n",
      "Iteration: 384 / 513 - Loss: 3.32009e+00\n",
      "Iteration: 400 / 513 - Loss: 3.31978e+00\n",
      "Iteration: 416 / 513 - Loss: 3.31951e+00\n",
      "Iteration: 432 / 513 - Loss: 3.31997e+00\n",
      "Iteration: 448 / 513 - Loss: 3.31865e+00\n",
      "Iteration: 464 / 513 - Loss: 3.31856e+00\n",
      "Iteration: 480 / 513 - Loss: 3.31828e+00\n",
      "Iteration: 496 / 513 - Loss: 3.31797e+00\n",
      "Iteration: 512 / 513 - Loss: 3.31806e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='l1'\n",
      "Iteration: 0 / 513 - Loss: 5.63241e+01\n",
      "Iteration: 16 / 513 - Loss: 3.38772e+01\n",
      "Iteration: 32 / 513 - Loss: 3.37744e+01\n",
      "Iteration: 48 / 513 - Loss: 3.37384e+01\n",
      "Iteration: 64 / 513 - Loss: 3.37248e+01\n",
      "Iteration: 80 / 513 - Loss: 3.37110e+01\n",
      "Iteration: 96 / 513 - Loss: 3.37061e+01\n",
      "Iteration: 112 / 513 - Loss: 3.36955e+01\n",
      "Iteration: 128 / 513 - Loss: 3.37098e+01\n",
      "Iteration: 144 / 513 - Loss: 3.37006e+01\n",
      "Iteration: 160 / 513 - Loss: 3.36864e+01\n",
      "Iteration: 176 / 513 - Loss: 3.36876e+01\n",
      "Iteration: 192 / 513 - Loss: 3.36866e+01\n",
      "Iteration: 208 / 513 - Loss: 3.36881e+01\n",
      "Iteration: 224 / 513 - Loss: 3.36835e+01\n",
      "Iteration: 240 / 513 - Loss: 3.36772e+01\n",
      "Iteration: 256 / 513 - Loss: 3.36793e+01\n",
      "Iteration: 272 / 513 - Loss: 3.36906e+01\n",
      "Iteration: 288 / 513 - Loss: 3.36796e+01\n",
      "Iteration: 304 / 513 - Loss: 3.36787e+01\n",
      "Iteration: 320 / 513 - Loss: 3.36798e+01\n",
      "Iteration: 336 / 513 - Loss: 3.36746e+01\n",
      "Iteration: 352 / 513 - Loss: 3.36866e+01\n",
      "Iteration: 368 / 513 - Loss: 3.36722e+01\n",
      "Iteration: 384 / 513 - Loss: 3.36726e+01\n",
      "Iteration: 400 / 513 - Loss: 3.36811e+01\n",
      "Iteration: 416 / 513 - Loss: 3.36737e+01\n",
      "Iteration: 432 / 513 - Loss: 3.36815e+01\n",
      "Iteration: 448 / 513 - Loss: 3.36919e+01\n",
      "Iteration: 464 / 513 - Loss: 3.36778e+01\n",
      "Iteration: 480 / 513 - Loss: 3.36706e+01\n",
      "Iteration: 496 / 513 - Loss: 3.36723e+01\n",
      "Iteration: 512 / 513 - Loss: 3.36741e+01\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='bce'\n",
      "Iteration: 0 / 513 - Loss: 1.60668e+01\n",
      "Iteration: 16 / 513 - Loss: 6.85285e+00\n",
      "Iteration: 32 / 513 - Loss: 6.73786e+00\n",
      "Iteration: 48 / 513 - Loss: 6.69954e+00\n",
      "Iteration: 64 / 513 - Loss: 6.67866e+00\n",
      "Iteration: 80 / 513 - Loss: 6.67004e+00\n",
      "Iteration: 96 / 513 - Loss: 6.66102e+00\n",
      "Iteration: 112 / 513 - Loss: 6.65679e+00\n",
      "Iteration: 128 / 513 - Loss: 6.65285e+00\n",
      "Iteration: 144 / 513 - Loss: 6.65057e+00\n",
      "Iteration: 160 / 513 - Loss: 6.64744e+00\n",
      "Iteration: 176 / 513 - Loss: 6.64252e+00\n",
      "Iteration: 192 / 513 - Loss: 6.63991e+00\n",
      "Iteration: 208 / 513 - Loss: 6.63985e+00\n",
      "Iteration: 224 / 513 - Loss: 6.64057e+00\n",
      "Iteration: 240 / 513 - Loss: 6.63912e+00\n",
      "Iteration: 256 / 513 - Loss: 6.64614e+00\n",
      "Iteration: 272 / 513 - Loss: 6.63611e+00\n",
      "Iteration: 288 / 513 - Loss: 6.63701e+00\n",
      "Iteration: 304 / 513 - Loss: 6.63577e+00\n",
      "Iteration: 320 / 513 - Loss: 6.63332e+00\n",
      "Iteration: 336 / 513 - Loss: 6.63285e+00\n",
      "Iteration: 352 / 513 - Loss: 6.63122e+00\n",
      "Iteration: 368 / 513 - Loss: 6.63199e+00\n",
      "Iteration: 384 / 513 - Loss: 6.63126e+00\n",
      "Iteration: 400 / 513 - Loss: 6.63218e+00\n",
      "Iteration: 416 / 513 - Loss: 6.63631e+00\n",
      "Iteration: 432 / 513 - Loss: 6.63411e+00\n",
      "Iteration: 448 / 513 - Loss: 6.63081e+00\n",
      "Iteration: 464 / 513 - Loss: 6.62921e+00\n",
      "Iteration: 480 / 513 - Loss: 6.63107e+00\n",
      "Iteration: 496 / 513 - Loss: 6.63096e+00\n",
      "Iteration: 512 / 513 - Loss: 6.63181e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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CTi3AwIHQoQN89JGSgAhTIiAikfX883DSSdC4MWOGT2Z1Oy0PFxGRMrZvh9NOg4cfhiFD4IsvQD1EIk6JgIhEVloa9O0L337LlvrN/I5GRESiUWrJ7UCfew5eeglSUvyNJ04Yv+7alpWVZefOnevLe4tUFLfiqkisQ393pnshV/+Oob2fV3GYmx1FhtTsjdRc8jNrs453NloLxvDVBvf7Pv+03f3yb8/MYtexZtXc+whkeNQWDDgm03UsWhhjvrPWZvkdh980X4hUTmNnZVPnh+lsa9jMuSVoyVwBEAjxz9OEEFYSxXpt2L7MFboiICJhVfP3n/jXpd3pcvdgkrZvdTZqjaeIiJTR/MNRHD/0VNo9f4+zQXNFhVMiICJh0+CrT+n975NIKCpi0hPvU1Q1w++QREQk2hQWwtChHPnI9aw7uivf3/y43xHFLd0+VET2nbUc9PoTHDLyITYcdCRfPfw2O+rs73dUIiISbTZtgrPOgsmT+W3gUOb/+25ITPQ7qrilREBkH0VLYxavOoBQ389rjebmgjIXFDds4PeeZ/PYJS9RZNNgw+77zM3e7vp6h9ao6jrWIsO9DmDwcTVcx7zqJkREwq3Cm25VoFBqxiDI952QAH/9BaNG0XrQIFqHOZZYP84VTYmAiIQsff1qUrZtJrt5W2ZcNQybkEBRtntBsIiIxKmvvnJ6A2Rmwty5kKQ/QaOBagREJCT1fp7DaZd1p8d9F0MggE1MVKGXiIjsylp47DHo3h2GDXO2KQmIGkoERGSvNZ34LidfezJFaVWYdPdrzqVeERGRUhLy82DQILj5ZjjzTOe/ElWUkolIuZniYg598T4O+s9zrD7iOL689w3ya9TyOywRkagQTevTw72O3qtmLNi9+9M2rqXTLefDz9+xYMit/HLRjbCgACgI+TV3KgqEdvW5Inv7xAolAhI2Xicdr1/2UJtdxYJQi6vchNo0zOskN3pGjuvYuh273skhoShAx1/mM6/vJTxy7hMUFyTvVhS8cHOu6+ud0TDNdSzZuBcEV0ly/wF6e3qO61hqBd6IQsVrIiL/SNq+jSob1jD94TdY3e0Uv8MRF0oERGSPavy5lIIqGeyoWZePHxxLcUoqxdnJfoclIiJRptZPs9l0yFFsa9KCie9/RyBFN5CIZlrYKyKeGv3wNQP+3Y0TnrwagGKd1EVEpKxAgINHPEiPS3vT5H/vOZs0X0Q9XREQEVftPn6Zrs/fQnbjlky94kG/wxERkXIK95JEz2W827bBBRfAhx/C4MF0uPUiOqQ6SUAk+rkMOCbTdUzLNPeOEgGpEF5FP24niUg0yPIS6muG8n6h1g54HUcvXifin7JTdn+fokJOGXEjHSa8ypRDT+CWC58md2sG/Jbz93PMjs1BX69ew5au71UnpcB1LDM14DqWYNxrBJI8rmtW5ElfE4yIxKXly6FfP1iwAJ5+Gq6+WreSjiFKBERkN6k7ttLihym83OvfPNv3RgIJav8uIiJBLFoEq1fDhAlw4ol+RyN7SYmAiPytzqpFZO/XjB0ZtXju2W8Zu8H9E3wREYljCxbAIYdAr16wdClUr+53RBICFQuLCABtZo7nymu70POt+wAoqJrhc0QiIhJ1iorgmmugXTuYPt3ZpiQgZumKgOwm1H4AXuvXQ9mvMhT8hFIL4HVf/wHHuH/fXvfTz8l3X9ozKSeBQeMe57z37ubXA47g0W5D2bC55PnW/X9cSr3mQbf3ret+FaF2mnsdgFfxl4hIZRZN851bLAELyVty6HTnYPaf/RW/9b+ceYGW2JnZ5Be7/wGQHGJxm9ffDV5i5e+DaKFEQCSOJebv4N7hQ+g9/V0+63Q2Dw55ifyUKn6HJSIiUSZj+SKOu3kgVdesZPZtz7LslPP8DknCQImASBzLWPcHx/4wkRf638cbfW/UnR5ERCSo/WdPIXnbZr56/mM2HtbR73AkTJQIiMShjDXL2bp/U3KatOKMpxaQU72u3yGJiEi0sZaqa1ayvUFTfj9rCCt6nUlBZm2/o5IwUiIgEmdaTRpL90ev5OtrHueXPhcoCRARiWKh1g+E2q9m53r/hIJ8Ojx2PY2//oTxb04jd/8mFFavA0FKvbzKAArdS8NI9rhlTSTqxtyOSTzXFSgRiCKh/rK7FZd6NWEKWPffWq+CVC9eTatCaQ4WyvcMkJTg/n1X9C+72/t5HSuv+L3225jnXhD88oK1mECAq8c/Ta8vRzDnwKO4u2YW2T+tJW3jMtf9TGYj17EL2gT/3hqmF7vu4yXUnx8REQmvtE3r6XLb+dT7aTbzL7qZ3Hruc4HENiUCInGgat42Hn3rRrotmMJ7nfrz0Bl3UJi0e0dhERGJbzUX/UTX/xtAas4mpt7/Oiu7n+p3SBJBSgRE4sDhy3/k2F+m8eAZd/LOcQNVFCwiIkG1/Og1sJbPX5zIptaH+R2ORJgSAZFKrOqmdWyvtR/T2xzLSXd8zppaDfwOSURE9kKoS1r36j78gQCpOX+RX6suc68dxvxLbiWvVr1yv16eRx+BjGT3HYs9XjMSvRXiuRbAjRKBKBLqD6hbQY13oVBo69ALA+6/7KnuS9Q9X9OtyMh7Hb37e3k1NvESatFVkccxcVvv7xVjaqL7/5t5m9yX83yydscuj8/6ahSXj7mTy697l7S0KmQDaX+t2G2/gox6u23bqf/BTV3HMlOKXMfc6CS8u1AL+kREwiFxRy4d7v83mYsX8vmoKRSmZeyWBEjl5fHnlIjEoqSiQm5/+2bueusm5rTpzG+ND/E7JBERiUJV166ix2V9aPj1eJacOoiiKul+hyQVTFcERCqRGts28fiLl9Dx1294/cQrefrMOwkkJKKyYBERKa3OvJl0vnUQCQV5fPP4aNYe09MZ2JslRRLzlAiIVCJ9Zn1A+8WzuH3wc4zrfI7f4YiISDSylkNHPEhhegbfvDCOrc1a+x2R+ESJQAULd68AcK8R8Fq77sWriYfXun2vQiKv+8CH0gch1O8t1LX+ENr7ub2mV2HVtI3un99/9/23QbdXy8slvTiPcfs3Zd55D7GiZh3SF3759/jWhu1cX/Pcgxu7jjWs6l4HkO5SALZXBWqiugkRH0WiIDXc7+W1n1e9WbB+Qaa4mMT8HexIy+CLu18nkJRMQfWaUPjPc9zmpzSP+rXtRe5xVE1y3y/RY2r1mktCra3S+XZ3qhEQiWXWcv709/jo+QtpkLMOjGFF7YZ+RyUiIlEmeetmut/cn653DIJAgLxa9ZwkQOKaEgGRGJVSVMC9Hz/GtV++wpxmh/NXeqbfIYmISBTK+GMJfS7rSf25X7Oia19I0J9/4tDSIJEYVGfrXzz23n20W/0LL3a9gFeOG0jy9k1+hyUiIlGm/pwpdLnzImxSEp8/8xHrD+8MAb+jkmihREAkBl00bQwt1y/lxrPuYspBx/odjojIbipy/X2oKjKOUNe8h1oTt7UwgYSCfDoMu5at9Rox4cHRbN2/KRTCH9vdG/80rxa8NmxzgXscNVJCqwNw67WzJ9Hy81MZKBEIkdcvrdcvu1vzrD3xKuB1i8Wr6VaoQo3fi9uJwOs4ep48PE6aXoVVXicrr+6HRR6frAQr1gJYtNX9V2/G77+7jqUHLPnJqTzT6wreP6ofS/Zr/vfYtgaHuu7XuXkz17HG6QWuY17NzaKlkC7WqaGYiIRbQmEBpjiJQEoqnz7yPtvqNqCwaobfYUkU0iIxkRhgAgGu+t/zvDXyctLzcslLSdslCRAREQFIzd7ACVf3o9NLdwGQ3bS1kgBxpURAJMpVyd/OU2/ewJBJr/Bzw4MoSEr2OyQREYlCmb//xEmX9KDWrz+yvk17v8ORGKClQSJRrMGm1Tz3+rUcuG4Jj/S9kTHt/wUmAuuzRETCLJQlfZG4136o+3lxe02vnj9eS2u9lq162Zj3z+e5B077hF4PX0ZBenXGPjWBNa2PhOLg+xV6LGndlB/8M2KvPgKJHn1/vHoCVeZln7FCiUCIKvqE5LVfRf4iReK93GoBvE6akagf8KoD8KofyCl0v7D2mUtzsD9+neO6T/V1P//99b2fPEf9Tau48eQrmd34QGyi+69s40YHuo51qZvnOnZep0zXMa8Gcm4/r14/I16v59V0rjLTRCgi+6rqpvX0fuhS/jqgLZ/c+x9y69QHNXeUcihXImCM6Q08AyQCr1hrhwV5ztnAPTg/evOsteeGMU6RuJJYXExxYiKPdB1IWlEBK2vu73dIInukuUKkYiUUFRJISmZ7rXp88OhHrG95GMWpVfwOS2LIHmsEjDGJwHDgJKAtMMAY07bMc1oCtwKdrbUHA9eGP1SRyi+xuIhrvnmPB/83EmMDrM+opSRAYoLmCpGKVXX9avpfdQIHffYOAGsO6agkQPZaeYqFjwYWW2uXWmsLgDFAvzLPuRQYbq3NBrDWrg9vmCKVX8aOrTz/9s2cPX8Kq2vUxWNZpUg00lwhUkHqLJjDSZf0IHPVEvKq1/I7HIlh5Vka1BD4o9TjVUCHMs9pBWCM+RbnkvA91tr/hSXCGBTqmt9wFzRFoh4hEmu83WoBvOoACj3W+ieH2KBkW6H7a6Z4pMzLPRqzLMvZHHR7zT9m7/K4cc56HvnsNfbfls09/W7m4/Z9gu7Xp/0Rru/VoIp7PwAv4S6W8xKvdQBxQnOF7LNIzFuh8mrk5TYXhtq/x2veWlNmjmnzxRhOeOJqttWpzz23j+ePxm0hSGP5DPepiWTP4t7g38ShmYWu+3j1nAmVasoqRriKhZOAlkBXoBEw1RhzqLU2p/STjDFDgCEATZo0CdNbi8S2hECAhz9/nfTCPK751+XMcEkCRCqBcs0VoPlCJJi6i+fTe9hl/HH4cYy/603+KN7P75AkxpUnEVgNNC71uFHJttJWAbOstYXAMmPMIpyT/S63RrHWjgRGAmRlZWnhg8Q3azFYAgkJPNBtANlp1ViXoUu8ErPCNleA5guRXQQCkJDAhhbtGHf/aJYf3ZNAUnLQKwEie6M8F7HmAC2NMQcYY1KAc4BxZZ7zEc4nPBhj6uBc/l0avjBFKpfk4iL+b+p7XDL3MwB+rdtESYDEOs0VIhFQY/USzr3ieOr/7CwpXdqpj5MEiITBHq8IWGuLjDFDgc9w1nS+Zq392RhzHzDXWjuuZKyXMWYhTvuKm6y1f0UycJFYVXvLBp4Z/xKHrlvOa+17grVqEiYxT3OFRFqodQCh1kF5NcIKWLdztvs+G/PcF+3nFAR/vaY/fs1Z91+AxfB7ToBfc3ZNAH7L3uL6mnZH8Bo1gKMaN3Yda1K1KOh2r7q9UNfse/2/8eolJOFTrhoBa+0EYEKZbXeV+toC15f8i3sV3VDMTaiFNpH4xXzz2xzXsVSXc6P7ida7sMqrQ6PXiWx7kft+4zcFbwwGsGLJfNex6msX7vK41foVDPvkWTLztnHbyVczuVXZWkpodNDu23byKgiuW8WlhSSh//8Od0FWtPxuSGRorhAJE2s58pOX6fXiLfzZoBVP3jqW9fs39zsqqYTUWVikgqTnb+fZDx5lR3Iql/W/i9/2O8DvkEREJAq1nv4pvYffyO8devPo0FHsqFrd75CkklIiIBJpJUt/clOrcn+vS/llvwPYWL2u31GJiEi0KZkvFnXswyc3vMhPPc5hx45Uv6OSSkyJgEgEpRXmc8fnrzClZRaTWnXg2+aH+x2SiEhM8loi6LXs00uoPWmKXYa2Frrfg2V5rkeNQKGhwYqfOf+lqxl5w5tk12nIsmMvgHz4Yc1a1/2qrP3VdSwr63jXsTYZ7j0BMpIDQbenJ4d2kLW0M7opEYiASDQU8+L2Sxbqev5QG3l5/bJX8fhJc2va4lWo5fW9eTU2KduYpbRPN7rXAfy15AfXscz5/w26vV7uFh6cM4kW65fzXfMjKaj2z1WAolbHub5es7TgJ2GAJI+JyWs9v1e9SLgLsiJx0tdkISKV2WGzx3PJU4PJq1KNals2kF2nod8hSZxQIiASAYdsXM0D08aRAlx39l1Mb5Hld0giIhJtrKXb2Cfo/da9rDzwCIb/37vk1G7gd1QSR5QIiIRZw63ZPD1lLOurZjBk4MMsr+N+mzYREYlfx457gT5v3sOs487ijStfpDC1it8hSZxRIiASZqszavJM++581agl65QEiIiIizk9z6c4OYWJJ1yqfjLiC+Pc1rniZWVl2blz5/ry3vEi1CYqofKqLfBah+62n1cfAbdCLYCFOe4dF9cWuBdyzf3tZ9ex6itmuY4VVqtLtbxc7vjfS4zqeBq/lrrXc72j+gbd58Q67v0AvOoAaqR41U2EVlMRapFdtPQYqMyMMd9Za+N+XZnmCwF4e3qO65hXYW+o5z+vOWhTfvC5ZOEW989Xp27cDsDBy37gsk+f5KbLRpKf4lwBCBTkue6XsM29514g3f3c2Kl+HdexwzODNw0D92Jhr/o7r2Psdf4Otd+R7Gpf5gr3v4pEpFwab/qTV/9zB8ct+Y6mm1b7HY6IiESpPjP/yxvDTqHlqoXUzXG/G5BIRdHSIJF9cNQfv3DvF6MoTkjgyrPv4MfGbf0OSUREoowJBLj6vw9w6YRnmNvqGK7/92tkZ7h/Yi9SUZQIiITo8D9/5/HxL7C0dmNuOu0m1mTW8zskERGJQqe9fis9JjzP2OMv4KFzH6Yoyf121SIVSYlAFAn3GumKXlc9ekaOx+je3//eaz3o+h3uq9pWuazdBFj07ceuY5krZriO5TffvTHL9y3r8Urndbx2zsNsr1It6H7H1gzetMWrDqC2Rx8Br/WsofYRiJZ1mPFaByCyt6KpnibUJl+hnHe81qi79aMByC92f81kjwXShe6nYtfmYNM25QfdvqLThXybXJN3O/WH3Jzdxmv+9oXre2W3OdF1LNx1AOB9nEPh9TMS6vwTTb8DsU41AiJ7IXP7Zu4f9yS1tmVTnJDIa53Ock0CREQkfmX9Oo1b37oZrOWP/ZrzbudzdGcgiTpKBETKqeX65bz+5i10WTyHlhuW+x2OiIhEqTOnjOKlx0/n6F++pkZuxd7BT2RvaGmQSDkcv2gW94x/lm2pVblswP38Wr+F3yGJiEiUSSoq5KbRt3PO5FeY2q4nt172MtuqVvc7LBFXSgRE9qDHyt+4e/ZnLKjfkptPu4W/qmn9oYj4J5rWQHvFEkovG69as6QQ1zB43eN+nUe92eodwesAACYsXx90+zPDB3HCL9/w5jFn8lyPwQTW/fb3H1rVsle6vp5XHUCflu6NKQ/NdO9J4/V9e9UBhNJbpqJ/JqPpdyDWKRGIIuFuuuG1T6i8TixeYzuK3AdHTcsJun15rvuP56Rs97HNKxa4jlXf4VHYVif4p/wzq9VnVL22jDj9DgpS0nYbP6OOe9FVzZTgVWpJITa48TrGXsXV53UKbbLWyVZEpPw+aH8S37TqwKeH9fQ7FJFyUY2ASBB1t2Vzw9R3SS4uZGtaOs+d80DQJEBEROLbcT9P4bwprwMw68AjlQRITFEiIFLGweuW8fIHT9Dr97kcsEmdH0VEJAhruejLkbzw0iWcMucjkoqD3y5aJJppaZBIKScums3NX49hY3oNrjv5SpbVqu93SCIicSPBuK+NzC8O7dabmwvcP/Ncm+dRB/CH+7LJjDW/cccnT3Ly/C/4/OCu3NPvJhKzV5G6eY3rPrn12riOpdZp5DpWN9WjoYGHRI/DFUptR6jLl71ESx+beKZEIEaE2iwqlNcLdc24V5GX19r2NS4FWRM3uf945i+Z6zqW/tcy17HNTTu4jp0//T1unvw2s1sczbWDn2Vz+j/fa7+a7pNTPY+TdNWk8DZmCXdh3p5eU0REdpUQKObFN2/iiD8W8EK3C3mly3nqDyAxS4mASIlpbbuw3+Z1PNn3RooSk/0OR0REolAgIZGJ7Xrwn2POYHLbLn6HI7JPVCMgca3xxj+4/MuRYC1L9m/Bo6fdqiRARER203vuOLr8NAmA94/qqyRAKgUlAhK3OiyezejnL2Dgt2PYb/M6v8MREZEoZAIBrhr3GE+8eiXnTH0TbHiXfIr4SUuDKoFQim286gq81vN77VdsQ1sjucmlkGvbxlWu+9TYuNh1LL+6R4FvrUZgLed89Tq3jLmDZfu34Oqhb7KubjM61Mlw3a1emvvdIKqn7H0h13mdMl3HvGotvIRaP6AaARHxEur5w6u4N5Sapu0e/Wi8CmPX57l/5vmFRxgZS76lSkEed08cTtff5zDu0G48esJgMpZOJ+XPeUH3yTn0VNfXq9asnetYz8wi17F6acH70ewLr+Pv1ssmEgXBofRIkvBSIiBx54b37+XCz19kymG9uPXiF8it4p4AiIhIfErP385LY+6h+cY/eLLbBbzX/iQVBUulo0RA4s6cVp0oSkziuVNvJZDgfus4ERGJX7kpVZjb5GCe7zKQWQcc5nc4IhGhREDiwoHrl3PQmt/5oMkRTD2sF1MP6+V3SCIiEoVO+fotfmpxFKuN4Zlug/wORySilAhIpdfltxk88NGjbE2rxoReQ8lLrep3SCIiMSPU+qNUjwuubuvQvdaFD/9qi+tYjkf9wH//yHUdq/bb5L+/TgwUc/VXb9P/h8/4oF0Pnj7sWNf9Ahn7Bd3evvWhrvu0q17gOlavinutmVdNmdca+4BH3V601IZFoqeR7B0lAhUsEj/YoTaScuN2ggbY4XGyLQi4j/2Y435LzqmLlwTdnrlspus+Oc07u44l1WrgfGEtg8c/xVX/fYCFzQ7nuqvfpm+LOq771U1zP0nXSHE/KIUetcLJLjVqXv/PBhwT/hNckcf/m4qkE7uIRKOMvG088OlzdFjxE6OPPInnu5xLosdNKUQqCyUCUjlZy4MjL+fkGe8xscPp3H3x8+SnVPE7KhERiTL1tvzF8+8/SP3NG3ig1xA+PbQrAKogk3igREAqJ2P4vXFbnm1wB6+efL3u9CAiIkFlV63O0tqNeLDXEOY1auN3OCIVSomAVCqHrPyJjHVLmHPQcYzqc43f4YiIhMxtKV0kltFF4h7xofREeenrza5jXmvev/VYflq6DuBv1tLvpyl8U78ZW9PSubP7QACSt/7TXDL70H6ur9nqgOAJw/6p7mtFveoAvPoghNr3B9yXtIZ7SbGXUH9etVy0YigRqGCh/mCH0nQj1F90r5Ptpnz3xiwrt7v/OH29aoPrWEIg+Mlxc7u+rvskJu3+Xn1mvs+9r13DuiZteOSJadiE3WNtWNW9MViCcT9peo1V8fgtcqu38FqzH4l19AOOyQxpv3DTiV1E/JZcVMgtX77KyT9PpXZWH95q39PvkER8o0RAYp4JBLjqgwe5ZMIzzG11DO/dMTpoEiAiIvGtVu5mho17inZ/LuKVjqfz9qHuN54QiQdKBCSmpRTm8fiLF9P1x88Ye/wFPDxwGB1r1PA7LBERiTLNN/7Bkx88SuaOrdx28tVMbt1xl6VAIvFIiYDEtIKkVLZUzeShgcMY0/1iFQWLiEhQOVUyWJ9Rm1v6Xc9v+x3gdzgiUcFY63HT+AjKysqyc+fO9eW9K5twF5SNmpbjOuZVI/BnnvvN1r6ePsV1bHvD4A1Yjm9U13WfI36ZyubaDdjU4ECwdpcEoFHVYtf9anoUcnkp9vg1SU7Y+98hrwIvraOXnYwx31lrs/yOw2+aL8ovFnrVAGS7zCXfZ7sX/c7Mca/xSvp9WtDtxgY49Yvn+LJxa4oTEnabL7Ycdpbra9Zp6f6r16dO8L4zDdPd5x+v875X/x6vur2kEOYfgPxi99d0m9NCbf7lRfNdeOzLXKGF1BJzjpv4CoNvP4WTXrvD2aCrACIiUkZaQR7DPhjG7XO+oPuqRc5GzRciu9DSIIkZCUWFnPXKzRw/cSS/Zp3I+9e95HdIIiIShfbbvJ4nxz5Ai/XLGd7uWL5o3NrvkESikhIBiQlVtmVz6SMDaTP/a7449Rq+GnwfNlF9H0VEZFeHrvqFx99/kNSiAq47+y5+LN7kd0giUUuJgMSEouQ0kgoLeOOaEczqfh6Zif7UtoiIhFMoa/ojUQcQKq/38+p/47Ym/tc89xXLVb//wD0Q889+tiCXTVUyuOukK1hRqwG5+53oulujFoe7jp1SL991rNhl3b7X2vtUj3nLqw7Aq4/NjiL3/S7onOk65iWU5nJeNQ5etQVeQv05j6bfj1igRCCKVGSxzdvTc1zHvAqCF2x1L+SatepP1zHT7CjXsSPrVA+6vWFaEc2+n8KfrY+koEZ13n1yIiQk0JBiaqa4n3Vqp7kXa3nxOhGf1ynTdSyUZm8iIhI+iYFiOi2bxzcHtmdRvWZceO69WKMySJE90W+JRCdr6fje05x726kc9/YwZ5uahImISBnV8rfz2LineOTTZzlkzWIAJQEi5aQrAhJ1kgvyuOjFoRz79TssPO40pg663e+QREQkCjXOXsujnz5Lw80bGNbjQhbUb+F3SCIxpVyJgDGmN/AMkAi8Yq0d5vK8M4D3gaOstbrps+y1GtlruWZYf1r8PoevL7idaeferNu9icQQzRd7J5SlnZFY5+y1xNHr/vejZ+S4jq3b4X5Dh7UufWe2/DrddZ/03A27PM5avYj7Jr9DcUICF183lu9adQy634kNgi8/BWhbw70OwEvVhOA9abzqAAoDe3/vfvA+/qHWAXgtRXZ7P699oqnHgOoA9s4eEwFjTCIwHOgJrALmGGPGWWsXlnleBnANMCsSgcaDUIttQivscT+zbCpwv6Ra5BFj96b1XccW73B/zfY1/mnMUq0gjzq5G/nknrfYfuK/aEHw9f5eJ0YvXsfYS6gnwFBeTycxiVWaL6QiVc/fwbpqmdx6wgX84pIEiIi38iyiOxpYbK1daq0tAMYA/YI8737gESAvjPFJnGj04zeY4mK21W3Im6/PYclxff0OSUT2nuYLiaik4iIOXbsMgMnND+OSflexNqOWz1GJxK7yJAINgT9KPV5Vsu1vxpj2QGNr7fgwxiZxwAQCHPP6A5x5w8kcOv51AAJJ7ncmEpGopvlCIiZzxzaemvgKT098mXrbcgAoTlA/GZF9sc/FwsaYBOBJ4MJyPHcIMASgSZMm+/rWEuPS8rZx4/MX02HOOBb0Po+fe5/vd0giEkGaLyRULdcu4elxz1Nrx1Ye6nI266tl+h2SSKVQnkRgNdC41ONGJdt2ygAOAb4yTlHn/sA4Y0zfsgVg1tqRwEiArKwsdYQqI9z3nM8tdL/gs92jCUmNZPf/NbU8igSapRe5jh1QddfH1deuoN+951J7+ULmXPMwv511GTWNAf4pwAq1sMqr/mHAMZmuY6EWNHlxe001Q5FKSvNFBQi1d0kkija9etJ8uiHFdWzj78Hrw6ut+3W3bV2W/sgdk95ga5XqDB78DL80aL3bcw6s5R5j82oFrmNexb1eEl2mGa/6tVALgkOtbfNSkXNJqO+lhmIVozyJwBygpTHmAJwT+jnAuTsHrbWbgTo7HxtjvgJujOe7QMiepW9aR9Xs9Xz40PvsOK6b3+GISHhovpCwa7N+Bctr1efa8x5lY0Ztv8MRqVT2mAhYa4uMMUOBz3BuB/eatfZnY8x9wFxr7bhIBymVx36/fc+61u1Z0/ZoXn1rHkVpValH8NuwiUhs0Xwh4ZJaWECDrRtZVqsBL3c4hVHFfchREiASduWqEbDWTgAmlNl2l8tzu+57WFLZmOIijn/pdtp/+BLvP/IhK4/sTlFa1T3vKCIxRfOF7Ku627IZNnEEtbdvof+595CfnEJBkjoFi0SCOgtHkVDXb3qtiXdT4PEhfO1U98GNHj0GUlyGUrdmc9L9F9FgzhR+6f9v8jseS72kf97Dba1lkmcdgOuQZx2Al0isHazIZkFaFymVVXZucUj1NrHO7XsOtZ7M61h51R28+W2O69jcTe51AOtWLHQdSwoErylratJ5+qO7qFKQxy0DHmB9yy5/j/Vqu3ttwE5ejcESTWiL7L3W9OcXu8277vNxqHNaqH1zIrHGPty84gg1Rq9jGY/nkT1RIiARlblyEX1uP4eMtSuZcetzLDn5PL9DEhGRKPSveZ9z57gnWF+9Lpde8iJL9j/Q75BEKj0lAhJR+/3yHSm5W/jyuXFsaKfOjyIiEoS1nPDz1/zYtB03DHyEzemZfkckEheUCEj4WUvmH7+T06QVv504gGWdTyKtVnW/oxIRkSiTnpdL1YIdbKheh1vPvIO89FoUJaqppEhFUSIgYZVQkM/xT11Hy8n/5b2Xp5HTpCUF1TJJ052BRCRENdMT43INbyjfs9daf6+15js8esus3eHevXfSkpWuYzVWz3Mdy89sSKNNq3lqzD1sT6nChRc/TUFiIoe1aee6T+vq7v0AqiZVbKsJt/4DXv1v8BhL8KhjKPJ6TQ9ea+VD6UUxekaO6z5e8Xv93Hm9Zqj1fuHuyVTZKRGIgNCLft3HvH6R8ouDb88pcN+plkdBcJ5rERQcWM29aVjm5nV0vf186v00m3kX3ULRAQdQLWHPCYBbAVW0FDPt6f2i5Q+UaIlDRGRPjlr2I4+MvR9rDI+cdCXW6K5AIn5QIiBhUXvRPHrffi6pmzfx9X2vs6L7qX6HJCIi0cZaTp8/mWunjmZFnUZc3/9eVtVq4HdUInFLiYCExYGTPwAs/3thIptaH+Z3OCIiEoVSigs5/acpTG9xFHecfgu5qel+hyQS15QISOgCAdI3riG3XkPmXHInv507lPyadfyOSkREokyNHVvJS0ohPzmVq06/mfX7tyKQ4F57ICIVQ4lABESiIZR78xJIdTmXVksOrXjHa7+dDVYSd+TS4f5/U3vBXP739rcUVs+EqrVJJfi+oRTvRNO6fK2/F/FPvDYUC4XXuT230H1w2Tb3Pwc+WLDEdSx120bXsc0HnwhAy9W/8Px/LuK7lh247aJn2Ayc0qhG0H2OqJXn+npe86BXsy6vYluv/UL52Xp7ek5I7+VVI+i1X6jF4V7H0u01vV7PayxamnVKcKrOkb1Wde0qelzWh4Zfj+e3Af+mMCP4CV1EROJbt3mf859H+pFSVMDoroP8DkdEytAVAdkrdebNpPOtg0goyOObx0ez9piefockIiLRxloumfgc13z8CAubtOOqK15lfc36fkclImUoEZC90ubtZylMz+CbF8axtVlrv8MREZEoVGfbJgZ//hITs/px5wWPk59Sxe+QRCQIJQIhisT6da/9vNYBujWCCbXBSmKZlzPFxSTlbqWweiaz7noREwhQUGP3WL3WCHqp6J4AIhJb4rWhWChrtb3kFLivBv7vz8tcx9I2/+k6tqPugbs8rpGbzeaqmayu1ZixI75my/5NOc/sHnDD9ODNwby+N7cmXlDxa8bd5i23mj3wrlXwap7lNUd61d95/d1wXif393Pj1fwLl/rAPe0X6vcdj+eDSFGNgHhK3rqZLjf1p+sNZ2OKiijMqBE0CRARkfh2yIr5fPhIXy6e9DIAW+o3gyBJgIhEDyUC4ipj5WJ6XdqT/ed8zdKTB2KTdAFJRER296+5n/DmswMpTExmatvj/Q5HRMpJf9lJUPvPnkLnOy8ikJjE5Gc/YsMRnf0OSUREoowJBLh6/NMM+XIEcw48iusGP0t2tVp+hyUi5aREQHZjiopo//StbK/XkKmPjia3fhO/QxIRiTtu67+91lyv2+F+of/NP93HbFo11zFzUDfXsTu2zubsya+w4OQLmX3VY/RPTvl7rGZqwHW/UL43r/vpR8t68kj0EfISah+BUPYbcIz691RGSgRCFIkfUO9CnL1vKFbofg4OWnSVUFgA1kJqKtOeHENBjVoUpWeQVKoIqCIbg6iIWEQkOlXdsZXtVTLY0Opwxoz8hr8OaKt6AJEYpBoBASB10wa6XnUqWY9eD8D2Bk0pSs/wOSoREYk27RdO5cPrD6bLd58C8Ffzg5UEiMQoJQJC5u8L6HlxD2r+8iNrOnT3OxwREYlSp3/5MsOH/YvN1WqxrGEbv8MRkX2kpUFxruFXn9LhvisorFadyS+NJ/ugI5QdioiEkdcyx4BHu5dCl/vOZ+e7n6U/2pDiOla49jf3N6ua6TrUI7OYhKJCThl5M8eMf5lfs05k9M2v0Sq9BvtXDd4PYE/cjonXOvSKrgMI9/tFYrlrqD0lvPoPSHxRIhABoZ48vAqhvPZ7e3pO0O0XdM503QeA7Gw46WpodwjJH35Ir/rR1f5dhUIiItGh7cxPOWb8y3x9xrX8b9C92ESPzlkiEjOUCMSj/HxISYGaNWHSJGjbFtLS/I5KRESiTHJhPgALOp/KC499ycq2HX2OSETCSatA4s2qVdC5Mzz9tPO4fXslASIispsuCybzv3uOp96KhWCMkgCRSkiJQDyZOROysmDRImjZ0u9oREQkGlnLRV+MYPhLF/NXRh3yq1b3OyIRiRAtDQpRqHUA3s1S3N/Pq/mHWx+B0jE2nTCGIx++lh31GvDtiA/IqXMQuLxmqEVE0dLQRUQkmgpL84vdKzoTPYo9V2wLfnIvcCkiBti0Pdd1rEnT1q5jPWs7Rb+JBXn0ePIa2n4xhkVdT2PKTS/QrGYaUBh0v1CPpdecFopQC3G94g/3z0kkfu5CbSgmspMSgThQbcXvHPXAUDYc0ZkZD71OQY1a4HGnChERiU9H/PcF2n4xhukX3s7s824q6Q/g0Z1SRGKaEoHKrLgYEhPZ1rQlU59+nw3tO2OTkv2OSkREoowpLsYmJvL9mUNZ17o9f7Tv6ndIIlIBVCNQSaX/sZSeFxzPfrMmA7D+6K5KAkREZDfHTR/LwMuOJW3zJgLJKUoCROKIrghUQnXnTqXTbRdiMQSS3JvLiIhUVhVdl+TVGOy8TpmuY6Om5biOfb8l+BS9aIt7HcCRNdNdxzrVzt91QyBA1usP0f7Nx9nQrgP7pxaQX7V4t/0iUTcW7oZWXv+/I9HIK1qoMZjsKyUCIQp1kgm1aVi5WAsvvADXXAOtWzPhvrfIbXRA0KdGoogoWgqCVbQsIuItafs2uj10OQd88ym/9jmPn255jEBKqt9hiUgF09KgyuTzz2HoUDjpJJgxwzUJEBGR+HbM87fR9NsJTL/qYabe/JySAJE4pSsClYG1zp0devWCMWPgzDMhMRGovJdDRUQkBCXzxdxL7mBp99NZndV154CfUYmIT5QIxLoFC2DQIBg9Glq1gv79/Y5IRCTuBKz7esuRUze7ji3d5n4ThxUFwf8496oD6F4v33Ws7fg3aPjVp3z72H+w9euwvX4Xakbw1qBedROhCLUOQEtCRdwpEQhRqMVHXidGr8YgQQuCxo2DgQPZkVaNaTNWk5Ndd5fheD35xev3LSISjCkqIuv5Ozjo/RGs7didxPw8inQXORFBNQKxyVp4+GE49VRo04YvX/uSnDaH+x2ViIhEmZQtOfS46WwOen8Ei865gmmPj6EoPcPvsEQkSuiKQCwaORJuuw0GDIBXXyVvfp7fEYmISBTqctdF7Pfjt0z/v+dYfepAv8MRkSijRCAWXXABJCfDRReVtH9XIiAiIrv77sr7SNqRy4Z2HamigmARKcNY68+JISsry86dO9eX9/ZTyAVNc+bArbfCf/8LNWr4FocKskQqjjHmO2ttlt9x+C1a5guv89/6HYmuY7lF7oXES3Pd99tQGHy/42oVuu5zbbcMePppWLkSnnpqlzGdv0Uqp32ZK1QjEAveeQeOOw6WLIF16/yORkREolBiQT4MHgzXX+8kAkVFfockIlFOiUA0CwScqwADB0KHDjB7tnOLUBERkVKqblrPGTeeAqNGwV13wdixkKTVvyLiTWeJaHb77TBsGAwZAs89BykpfkckIiJRxhQXceb1fchYvwreew/OOsvvkEQkRigRiGZDh0Lz5nDJJSVFwSIiEkle6+jzi93Pw3/lu19gr5bk3rQr0ePU3r1O8FqAK7tW333j849Do0bQvr37C0aA6g5EYpsSgWjz1Vfw6qvO5d2GDeHSSyPyNqGeoHViFxGJAoEA3Hef88f/JZdA375+RyQiMUg1AtHkpZegZ0/47jvYuNHvaEREJBrl5sLZZ8O99zq1YyIiISpXImCM6W2M+c0Ys9gY839Bxq83xiw0xsw3xkwyxjQNf6iVlykq5IjHboIrroBevWDGDNhvP7/DEhHZK5orIq/auj/g2GPhww/hiSdgxAi/QxKRGLbHpUHGmERgONATWAXMMcaMs9YuLPW0H4Asa+12Y8wVwKNA/0gEXBkddf9Qmn42Fm66CR5+GBLd7ystIhKNom2uCHXt+g6Pe/4XBtzHaqa41wEUe7TraVyl2HWsTtquY8lbcjjp390pzN/BzMdHs7ZTT5ids8tzKnr5ppaLisS28tQIHA0sttYuBTDGjAH6AX+f3K21U0o9fyZwXjiDjDV7PQHdewOcezJjW58Cc7eUfz8RkeihuSLCCqtn8suF17P+qOPZekBrv8MRkUqgPEuDGgJ/lHq8qmSbm4uBicEGjDFDjDFzjTFzN2zYUP4oK6Px451CL3B6BFxwgb/xiIjsm7DNFaD5YidTXEy75++mzryZAPx+1hAlASISNmEtFjbGnAdkAY8FG7fWjrTWZllrs+rWrRvOt44d1sKjj8Ipp8DHH8OOHX5HJCJSofY0V4DmC4DkrZs57sZzOOg/z7H/rMl+hyMilVB5lgatBhqXetyoZNsujDEnALcDx1tr88MTXuWSkJ8HgwbBW285d3x4/XWoUsXvsEREwkFzRRjVXPU7J9xzDtVWL2PO/z3F0n6D/A5JRCqh8iQCc4CWxpgDcE7q5wDnln6CMeYIYATQ21q7PuxRxpig6/mthW7d4OuvnSVBd9yxW5Mw1QGISAyLqrnC63zqVceVnOBVLOz+fhnJ7oNJHtfez+uUufvGRYvg7B6QlASTJ3FUly4c5f4S5Rbrc4yal4mE3x6XBllri4ChwGfAL8B71tqfjTH3GWN2djB5DKgGjDXG/GiMGRexiGOVMTBkCLz/Ptx5pzoFi0ilorkijFq0cJpJzp4NXbr4HY2IVGLl6ixsrZ0ATCiz7a5SX58Q5rgqj3ffheJiOPdc55+ISCWluWIfFBTArbfCNddAkyZOLZmISISps3CkBALOJ//nnAOjRjlLg0RERMpavx569IAnn4QJE/b8fBGRMCnXFQHZS9u2ObcD/fBDuOQSGD58n5cCaW2kiEh4eJ0z3/w2x3UsOcH9A51kj4/Vkjz2Y9486NcP1q2D0aOdD48kKM11IuGnRCDctm+Hzp1hwQJ45hm46irVA4iIyG5qz5sJ158FmZnwzTeQleV3SCISZ7Q0KNyqVoXTT4eJE+Hqq5UEiIhIUJtbHAxnnQVz5igJEBFfKBEIl1dfdU7mAHffDb16+RuPiIhEncS87Rzy4gMk7silKD3D6SdTv77fYYlInNLSoH1VVAQ33ADPPus0Cxs1yu+IREQkRKmJod3YwaP9wD9r21etglNPhe+/56DTj4eufd13CpFXPZmXSKy/V22bSPSL+0Rgn05U2dnQvz988QVcd11Eb/emk6aISAybOdNJArZvh3Hj4OST/Y5IRESJQMj+/BOOPx5WrHCWBQ0e7HdEIiISjT7+GM4+Gxo1gkmT4OCD/Y5IRARQjUDo9tsPjjkGJk9WEiAiIu7atYNTTnE6BSsJEJEooisCe8NaePFF5/Jugwbw5pt+RyQiIntp9Iwc17EBx4RpGeaWLTByJNxwA2NnAze9DIuBxbsuRw33ss9oWkYaTbGISHBxnwiU+0SVnw+XX+4UA69ZA/ffH9G4REQkRi1eDH37wqJF0LUrcKDfEYmIBKWlQeWxbh107+4kAXffDffe63dEIiISjSZPhqOPduaNL75QfwARiWpxf0Vgj375BU48ETZuhPfec5q/iIiIlPXqq3DZZdC6tXNnoAN1JUBEopuuCOxJ/frQpg18+62SABERcde8ubMkaMYMJQEiEhN0RSCYQABeeQUuuAAyM+Hzz/2OSEQkbmXnFvPuzOA9X/p3DF7n5dUjJimcH4Ft3AiffQYDB0K3bs6/Mrxq0Sqy6ZYafIlIWboiUFZurnO/58sug//8x+9oREQkWi1Y4NQDXHqp01tGRCTGKBEobeVKOPZY+PBDeOIJ9QcQEZHgxo1zesnk5cFXXzm3lBYRiTFKBHaaNQuOOgqWLoVPP4Xrrwdj/I5KRESizWOPOf1k2rSBOXOcqwIiIjFINQI7ZWZCkyZOk7CDDvI7GhERKVEzPdG1FiAU+7wePj0d+veH116DKlX8jSVK30tEYkN8XxEoKoLRo52Owa1bO+3flQSIiEhZq1c7PQIArrgC3nlnn5MAERG/xe8VgZwcOOcc524P9epBjx5aCiQiIrubPdtZCmSts3xUCYCIVBLxeUVg0SLo2BEmTYKRI50kQEREpKx33oEuXSA11bmVtJIAEalE4u+KwJdfOo3BkpKcRKBLF78jEhGRMNvn9fDWwm23wbBhzjzx/vtQt254ghMRiRLxd0WgqAiaNXPu9KAkQERE3GRnw5Ah8MUXSgJEpFKKjysCBQXOfZ579YLevaFnT0hM9DsqERGJNkuXOr0B2raF4cMhIUH1YyJSaVX+KwLr1zs1AH36wOLFzjYlASIiUtZXXzk9Ac4/31kalJioJEBEKrXKnQjMn++c1OfOhbffhhYt/I5IRESi0YgRztXiunVhzBglACISFypvIvDRR9Cpk1MT8M03zq1CRURESisshKFD4fLLneWjM2dCy5Z+RyUiUiEqbyKweDEcfLBTFJyV5Xc0IiISjax1rh7feCOMGwc1avgdkYhIhalcxcLbt8Mvv8CRR8INN8DVV0NKit9RiYhItFm40GkmWaeOc1eg1FS/IxIRqXCV54rAqlVw3HHOGs/Nm531nUoCRESkrPHjnaaSV17pPFYSICJxqnJcEZg502n/vn270wVSl3ZFRCqN7Nxixs7KDjq2V43DrIXHH4dbboEjjnC+FhGJY7F/ReDNN+H44yE9HWbMgJNP9jsiERGJNnl5MGgQ3Hyz013+m2+gcWO/oxIR8VXsJwKTJkHnzjB7tlMcLCIiUtbWrTBtGtx3n3N70KpV/Y5IRMR3sbk0aMsW+OsvOOAAGDnS6fyYnOx3VCIiEm1+/hlatXL6A8yfD9Wq+R2RiEjUiL1EYPFi6NvX+eN/3jwVeYmIVHI10xP3rhZgp3ffhYsucu4id//9SgJERMqIraVBkyc7nYLXrYPnnnPav4uIiJQWCMCddzqNJI88Eq66yu+IRESiUmwkAtbC8OFO18cGDZwmYd26+R2ViIhEm23b4Mwz4YEH4OKLnTqyevX8jkpEJCrFRiJQVOTcHahPH5g+HZo39zsiERGJRsuWOX/8P/00vPyy+smIiHiI7hqBjRshKQkyM+F//4Pq1bUcSEREdrd4MbRoAYceCkuXQu3afkckIhL1oveKwE8/wVFHwYUXOo9r1lQSICIiu3vlFWjbFt5+23msJEBEpFyiMxH4+GPo1Any8+G22/yORkREolFREVxzDVx6KXTvroaSIiJ7KboSAWvhoYfgtNOgTRunKPjoo/2OSkREok12tlM39uyzcN118OmnzjJSEREpt+iqEdi0ybk70DnnwKuvQpUqfkckIiLR6NtvYepUZ64YPNjvaEREYpJviUB2bjFjZ2UDkPrXevIza0NiImkvfc4pJ7cFY/wKTUREokjp+SJt41ry6uwPdTuTNvY7TjnlYJ+jExGJXeVaGmSM6W2M+c0Ys9gY839BxlONMe+WjM8yxjQrbwA1f/6OnoO6csiIBwHIq9dASYCISIyK2HxhLS3fGU6f04+g1k+zgZL5QkREQrbHRMAYkwgMB04C2gIDjDFtyzztYiDbWtsCeAp4pDxv3viz9+l2xckEklNY2evMvYtcRESiSsTmCxsg64GhHP7snazp3IvNLXQVQEQkHMpzReBoYLG1dqm1tgAYA/Qr85x+wBslX78P9DDG+2P9Khv+pOPdQ9h08JF8+dqXbGlRdq4QEZEYE5H5ImPlYg4YP5qfL76ZGQ++TnGV9LAHLiISj8pTI9AQ+KPU41VAB7fnWGuLjDGbgdrARrcXTdu0gSWnDuKHGx7BJqvzo4hIJRCR+SIpbwe89x4Hn3UWuhYgIhI+FVosbIwZAgwpeZjf4qM3FvDRG167xIM6eEyAcUTHwaHj4NBxcLT2OwC/lJ0vzNlnL/Azniih3wuHjoNDx8Gh47APc0V5EoHVQONSjxuVbAv2nFXGmCSgBvBX2Rey1o4ERgIYY+Zaa7NCCboy0XFw6Dg4dBwcOg4OY8xcv2PYS5ovIkjHwaHj4NBxcOg47NtcUZ4agTlAS2PMAcaYFOAcYFyZ54wDBpV8fSYw2VprQw1KRERikuYLEZEYsscrAiVrOIcCnwGJwGvW2p+NMfcBc62144BXgbeMMYuBTTgnfxERiSOaL0REYku5agSstROACWW23VXq6zzgrL1875F7+fzKSsfBoePg0HFw6Dg4Yu44aL6IKB0Hh46DQ8fBoeOwD8fA6IqsiIiIiEj8KVdnYRERERERqVwinghErN18jCnHcbjeGLPQGDPfGDPJGNPUjzgjbU/HodTzzjDGWGNMpbwTQHmOgzHm7JKfiZ+NMe9UdIwVoRy/F02MMVOMMT+U/G708SPOSDLGvGaMWW+MCXp7TON4tuQYzTfGtK/oGCuC5gqH5gqH5gqH5gqH5gpHROYLa23E/uEUiy0BmgMpwDygbZnn/Bt4qeTrc4B3IxmTH//KeRy6AVVLvr4iXo9DyfMygKnATCDL77h9+nloCfwA1Cx5XM/vuH06DiOBK0q+bgss9zvuCByHLkB7YIHLeB9gImCAjsAsv2P26WdBc4XVXFHmeZorNFfsfE6lnytKvrewzxeRviIQkXbzMWiPx8FaO8Vau73k4Uyc+29XNuX5eQC4H3gEyKvI4CpQeY7DpcBwa202gLV2fQXHWBHKcxwsUL3k6xrAnxUYX4Ww1k7FuXuOm37Am9YxE8g0xtSvmOgqjOYKh+YKh+YKh+YKh+aKEpGYLyKdCARrN9/Q7TnW2iJgZ7v5yqQ8x6G0i3Eyuspmj8eh5DJWY2vt+IoMrIKV5+ehFdDKGPOtMWamMaZ3hUVXccpzHO4BzjPGrMK5E81VFRNaVNnb80cs0lzh0Fzh0Fzh0Fzh0FxRfns9X5Tr9qFScYwx5wFZwPF+x1LRjDEJwJPAhT6HEg2ScC75dsX5xG+qMeZQa22On0H5YAAwylr7hDHmGJz7zx9irQ34HZiInzRXaK4oobnCobkiRJG+IrA37eYxHu3mY1x5jgPGmBOA24G+1tr8CoqtIu3pOGQAhwBfGWOW46xvG1cJi8DK8/OwChhnrS201i4DFuGc7CuT8hyHi4H3AKy1M4A0oE6FRBc9ynX+iHGaKxyaKxyaKxyaKxyaK8pvr+eLSCcCajfv2ONxMMYcAYzAObFXxjV+sIfjYK3dbK2tY61tZq1thrP+ta+1dq4/4UZMeX4vPsL5hAdjTB2cy79LKzDGilCe47AS6AFgjDkI5+S+oUKj9N844IKSu0F0BDZba9f4HVSYaa5waK5waK5waK5waK4ov72eLyK6NMiq3TxQ7uPwGFANGFtS/7bSWtvXt6AjoJzHodIr53H4DOhljFkIFAM3WWsr1aef5TwONwAvG2OuwykGu7Cy/fFnjBmNM5HXKVnfejeQDGCtfQlnvWsfYDGwHbjIn0gjR3OFQ3OFQ3OFQ3OFQ3PFPyIxX6izsIiIiIhIHFJnYRERERGROKREQEREREQkDikREBERERGJQ0oERERERETikBIBEREREZE4pERAYpIxxhpj3i71OMkYs8EY82mZ531kjJkZZP8bjTG/GmN+NMbMMcZcULL9K2PMb8aYeSXbDy+1Tw1jzJvGmMXGmCUlX9coGWtWEtNVpZ7/vDHmwvB/9yIiEipjzLYg2+4xxqwumRN2/sss85xmxpgdJWMLjTEvGWMSymzf+W/nnLLcGPPfUq9xpjFmVKS/R5HyUiIgsSoXOMQYU6XkcU/KdM8rOYkfCdQwxjQvtf3ykucfba09HKcJiSm160Br7WHACzj37N7pVWCptbaFtfZAYBnwSqnx9cA1JQ1PREQktjxlrT281L+cIM9ZUjJvtAPaAqeW3l7q35ul9jnSGNM2opGLhEiJgMSyCcC/Sr4eAIwuM3468Akwhl2bD90GXGGt3QJgrd1irX0jyOvPABoCGGNa4CQV95cavw/IMsYcWPJ4AzCJf7qfiohIJWStLQKmAy3K8fQngNsjG5FIaJQISCwbA5xjjEnD+XRmVpnxncnB6JKvMcZUBzKsteVpwd4bp307OJ/8/GitLd45WPL1j8DBpfZ5BLjRGJO4t9+MiIj46rpSS3umeD3RGFMV52ryTyWbDiyzNOi4Uk9/D2hf8oGSSFRJ8jsAkVBZa+cbY5rh/JE/ofSYMWY/oCUwzVprjTGFxphDgJXleOn/lCzvqQYcvpcxLTXGzALO3Zv9RETEd09Zax/fw3MONMb8CFjgY2vtxJJ5aOeSoWCKcZaZ3gpMDFOsImGhKwIS68YBj7P7sqCzgZrAMmPMcqAZMKBkOdC20jUDQQwEmgNvAM+VbFsIHG6M+ft3puTrw0vGSnsIuIVd6w5ERCT27awFOMJae89e7PcW0AVoHJmwREKjREBi3WvAvdban8psHwD0ttY2s9Y2w1nfv7NO4GFgeMkyIYwx1Xbe4WEna60F7gQ6GmPaWGsXAz8Ad5R62h3A9yVjpff9FSc5OCUc36CIiMQ2a20h8BRwnd+xiJSmREBimrV2lbX22dLbSi7TNgVmlnreMmCzMaYD8CIwBZhjjFkAfAMEgrz2Dpwir5tKNl0MtCq5degSoFXJtmAeBBrtw7cmIiKRUdUYs6rUv+tLtl9XZp1/s714zbI1AlcHec6raEm2RBnjfPApIiIiIiLxRFcERERERETikBIBEREREZE4pERARERERCQOKREQEREREYlDSgREREREROKQEgERERERkTikREBEREREJA4pERARERERiUP/D2/w2S4y+h7aAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 936x360 with 2 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, 5))\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 en niveaux 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": 75,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:45:13.720304Z",
     "iopub.status.busy": "2022-06-03T10:45:13.719671Z",
     "iopub.status.idle": "2022-06-03T10:45:13.721991Z",
     "shell.execute_reply": "2022-06-03T10:45:13.722347Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.9962241e-03, 9.9600381e-01],\n",
       "       [3.1071994e-01, 6.8928009e-01],\n",
       "       [9.9987340e-01, 1.2655793e-04],\n",
       "       [2.5982315e-02, 9.7401774e-01],\n",
       "       [6.3018633e-05, 9.9993694e-01],\n",
       "       [2.4161758e-01, 7.5838244e-01],\n",
       "       [8.0003268e-01, 1.9996735e-01],\n",
       "       [9.9656457e-01, 3.4354762e-03],\n",
       "       [9.9965453e-01, 3.4542981e-04],\n",
       "       [9.9781239e-01, 2.1875487e-03],\n",
       "       [2.7940370e-02, 9.7205961e-01],\n",
       "       [1.4365434e-03, 9.9856347e-01]], dtype=float32)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = torch.softmax(trans.lin.weight, axis=1).detach().numpy()\n",
    "M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On vérifie dans un premier temps que la contrainte est toujours bien respectée :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:45:13.726656Z",
     "iopub.status.busy": "2022-06-03T10:45:13.726152Z",
     "iopub.status.idle": "2022-06-03T10:45:13.728310Z",
     "shell.execute_reply": "2022-06-03T10:45:13.728638Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.        , 1.        , 0.99999994, 1.        , 0.99999994,\n",
       "        1.        , 1.        , 1.        , 0.99999994, 0.99999994,\n",
       "        1.        , 1.        ], dtype=float32),\n",
       " array([1.        , 1.        , 0.99999994, 1.        , 0.99999994,\n",
       "        1.        , 1.        , 1.        , 0.99999994, 0.99999994,\n",
       "        1.        , 1.        ], dtype=float32),\n",
       " (12, 2))"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.sum(axis=1), M.sum(axis=1), M.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons nous inspirer d'[un graphique de la galerie matplotlib](https://matplotlib.org/stable/gallery/misc/table_demo.html#sphx-glr-gallery-misc-table-demo-py) pour représenter la la proportion des report de voir en fonction de chacun des choix FE au deuxième tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:45:13.761986Z",
     "iopub.status.busy": "2022-06-03T10:45:13.735384Z",
     "iopub.status.idle": "2022-06-03T10:45:13.978195Z",
     "shell.execute_reply": "2022-06-03T10:45:13.978689Z"
    },
    "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": 78,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:45:13.982685Z",
     "iopub.status.busy": "2022-06-03T10:45:13.982116Z",
     "iopub.status.idle": "2022-06-03T10:45:13.984572Z",
     "shell.execute_reply": "2022-06-03T10:45:13.984904Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.4,  99.6],\n",
       "       [ 31.1,  68.9],\n",
       "       [100. ,   0. ],\n",
       "       [  2.6,  97.4],\n",
       "       [  0. , 100. ],\n",
       "       [ 24.2,  75.8],\n",
       "       [ 80. ,  20. ],\n",
       "       [ 99.7,   0.3],\n",
       "       [100. ,   0. ],\n",
       "       [ 99.8,   0.2],\n",
       "       [  2.8,  97.2],\n",
       "       [  0.1,  99.9]], dtype=float32)"
      ]
     },
     "execution_count": 78,
     "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": 79,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:45:13.988863Z",
     "iopub.status.busy": "2022-06-03T10:45:13.988209Z",
     "iopub.status.idle": "2022-06-03T10:45:13.990468Z",
     "shell.execute_reply": "2022-06-03T10:45:13.990792Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.4,  31.1, 100. ,   2.6,   0. ,  24.2,  80. ,  99.7, 100. ,\n",
       "         99.8,   2.8,   0.1],\n",
       "       [ 99.6,  68.9,   0. ,  97.4, 100. ,  75.8,  20. ,   0.3,   0. ,\n",
       "          0.2,  97.2,  99.9]], dtype=float32)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MT = M.T\n",
    "MT /= MT.sum(axis=0)\n",
    "MT*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:45:14.028252Z",
     "iopub.status.busy": "2022-06-03T10:45:14.027730Z",
     "iopub.status.idle": "2022-06-03T10:45:14.243423Z",
     "shell.execute_reply": "2022-06-03T10:45:14.243769Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ByL6s6hIZya+/Y3JT8m+iZs2aqWrVqurfv7+k9NdUymdVVi655BJVqlRJs2fPTvUcymx/mf1GuvHGG/XDDz/ouuuu08KFC9WqVSsdOXJEUvrXxmvVqpWbp+S0kFm5ZSWr37Eny4t9+k12jjG5ocS+fft03333ZXvfOflNmfy8KlCggLp27arp06dnuf7u3btDY58888wzqZbdd999evrpp1M1sMpOGsktOL/88ssTzn9WwiJ46Xd//vmnPvvsMw0YMEDVq1fX008/rWnTpsnMQj9INm3apKVLl2rmzJN/433y5Mlat26dqlevrlq1amnfvn169913JQV+3KR8levPP/8MvUqUkeXLl6dqRpxfJD9AkzurTX69qn79+un+yv7TTz/prLPOUvHixdOdXynwykPy60IRERFq06aNHnnkEY0fPz5ULlLgdYchQ4Zo7ty5qebj+Dp37qx///vf6X6MT5s2TXv27FGNGjVUvXr10I/P4sWL66yzzkrVB2Za//vf//TTTz+pX79+oX506tevr7i4uFQ37qSkpAz7OLv//vv15JNPUnEO+uSTT7R3717FxMSoevXq+vLLL1P96CtVqpR69eqlSZMmqXnz5vriiy8kBV4RuuKKK/T000/r/vvvD/WfOHnyZL3xxhuqXr26OnfurJUrV2rDhg15cWhII/l5tnz5cj388MPZ3q5Pnz764osvQv025mcLFy7Uu+++e8Ldtlx//fUaNGhQpoHJ8uXLq2DBgpo7d67atm0bml+8eHEVLVo03T1x6dKlio6OlhR4Lqbsdylt/WHIkCFas2aN3n33XfXv3z/bfWWeLjJ7zuS2yMhIDR06VE8++WRoXnR0tFasWHFSLS8yqrekLNdkl156qQ4dOqTFixefXMbDWHJdOKt6fEaS6xrJgegOHTooLi5ODRo00NGjR0+oToGA49Ul0kouu+zc45CxlEHF//znP1mOvVC7dm398ssvWb6NtmDBAv38889q1KiRHnrooWzlIbPfSBUrVtRNN92kGTNmKDIyMtsNFPKDjMoto+fBvn379Msvv6h27doZ/o49XqzgePexk9nn6eCnn35SRESEypYtm61jTG4o8eabb6pkyZK5/psyMTEx1ZsFq1at0oYNG9SuXTtVr15dU6ZMyfBeGR0drWXLlkkKxIni4uJ0880368CBA6nWq1Onjho1apSq7/TspuFF60uCl6fAO++8oz59+ujnn3/Wli1btHXrVtWoUSPVD7XSpUvriSeeOOnWJ0lJSZo2bZpWrVqlLVu2aMuWLZoxY0boi9SmTRu99dZboS//xIkTM331b+XKlRo5cuQJtzoLJ0WKFNG4ceP07LPP6tixY+rdu7e+/PJLzZs3T1Lgr1p33HGHhg0bJinw14WZM2eGOqZOHjU2IiJC69evTxVciYuLU7Vq1XTgwAEtXLgw3Xxk30033aSHHnooXX83kydP1pw5c0LXwtKlS0N9VN13330aNGhQqIJ14MABvfnmm6m2d85p5MiRWrx4sdatWxcaOTHlDXjUqFFq0qSJateunWrbc889V/Xr19eHH37oxSGfdiZPnqxXXnklVBabN2/W3LlzFR8fr88++yzU187+/fu1adMmVa1aVcuWLQu9Qp6UlKSVK1eqWrVqoQ7Gt2/fHtrffffdl+OBe5C3ChYsqCFDhuT7V/f37NmjG2+8UW+++aaKFSt2Qttee+21GjZsmDp06JDpOo8++qiefPLJdK8g33333brjjjtCrzzPmzdPX375pXr16iVJuvjii/XWW29JCjz7pk2blmH9oXPnzmrWrFnY9fub2XPGC//4xz80b9487dq1S1LgDwLNmjXTQw89FKq/bdmyJdQPZ1aGDRume+65R7t375YUqGO88cYbuu2229Kt++CDD+qpp57KxSM5vZmZxo0bpx07dujyyy/PtB6fsvuGtO677z7deuutoVdazSwU2D+ROgUCsqpLpPX555/r5Zdf1sCBAyUd/x6HnCtSpIj69++vO++8M/THrl27dqVrjRUZGamxY8fqzTffDL0dmJGsfiPNmTMn1GXAb7/9pt27d6cbTA2ptW3bVvHx8aHfO4mJiRo6dKj+8Y9/qEiRImrevLm++uqr0IBuS5Ys0ZEjR1SlSpVM93m8+1idOnX066+/hgbO+vnnn7VixQo1atTIuwP12K5du/TPf/5Tt99+u5xznpy3lLLzmzIiIiLVmwWTJ0/Www8/HLpX/vrrr/r111/1888/p9pu2LBheuyxx1IN9JhZ/6cPPPBAqhaZ2U2jffv22rNnj1auXJlp/k9UZK7tCZmaPHmy7rnnnlTzunbtmi5Qec011+jhhx/WokWLUr0Slh2LFi1SpUqVVLFixdC81q1ba+3atdqxY4duvvlmrVu3TrGxsXLOqVmzZqnSX7RokRo3bqz4+HiVLVtW48aNS9U6Iz9q3LixGjZsGBoEacaMGRo8eLAGDRqkxMRE9enTR7fffrukwKtlt99+uy688EI551S2bFm98sorkgIP4MGDB2vv3r2KjIxU7dq19fLLL8vM9NRTT+mWW27RmWeeqaJFi4ZeJ5cCr+Il/2CUFGp5Nn/+/FQdVU+fPl3nnXee9yfEhypXrqw77rgj1bwtW7bo559/VqtWrULzatSooRIlSujbb7/VrbfeqgMHDqh58+YqWLCgChYsqKFDh6bb95lnnqmhQ4fq6aef1quvvqpXX31VgwcPDr2Cct555+nVV1/NMF8PPPCAGjdunItHenqIj49P9d287bbbNGfOnNAIlVJgBN8LL7xQH374oX755RfdfvvtioyMVFJSkgYMGKDmzZtrzpw5GjhwYOg1oBYtWuj222/Xk08+qWuvvTZVml27dtX1118f6sesYcOGoYEtunfvroYNG+qNN94IXT+SQi2MLrnkklAgp2HDhumC2PlR2jK86667JGV8P8ruaKzJr5Mnu+mmm9Jdt/379w/rV1ez48UXX9Tvv/+uW2+9NdX8nj17HvccFitWLF09I63zzz8/w/mDBw/Wnj17FBMTo4iICJUvX14zZswIvQL93HPP6ZZbbtG4ceNkZurbt2+qDt1TGjFihHr16qWBAwced6Ch00VGz5lkU6dOTfVK1PPPP6+KFStq/fr1qa6j5MD83Xffnep7/t1336XaX6FChXTHHXfozjvvDM175ZVXNHToUNWuXVtnnnmmSpcuraeffvq4+e7cubO2b9+u888/X845FStWTG+99ZYqVKiQbt2OHTuqTJkyx91nuLv77rs1cuRIxcfHq1WrVlqwYIEKFSqUaT0+eX5G5X3rrbfq4MGDatmypc444wydddZZuuCCC0J1gxOpU+Rnx44dU8GCBbOsS0h/X4vx8fGqUaOG3n333dAbZMe7x+HEJL+WnOzyyy/XE088oVGjRunBBx9U/fr1VbhwYRUtWjTDbhoqVKignj17asKECRo+fHiG+3vggQcy/Y306aef6s4771ThwoUlBbrjKF++vNatWxfq8zLZgw8+mOFIzPmNc07vv/++brvtNo0cOVJJSUnq2LFjqJ/lcuXK6bnnnlPHjh2VlJSks846S5MnTz7uczyr+9gZZ5yht956SzfeeKMOHz6sggUL6pVXXlGJEiW8Pdhclvz9TEhIUGRkpPr06ROqG3tx3tI60d+UU6ZM0axZs1LNu/baazVlypRU/XbHxMToueeeU9++fbVv375Q14MZjaQeHR2tJk2ahFpqZjeN5PxfffXV2c7/8bj89mqjc87y2zGfbpxzvHLrc5SR/1FG/kcZ+R9l5H+Ukf9RRv7n1zJasWKFBg4cmC7Qnx/5tYzwN8rI/ygj/wuWUYYdiobHn8UBAAAAAGHhxRdfVM+ePfN9q3wAQECWr40XcoV/S9CRcqcqM6dC4TMKh9UoV+GocGHKyO8oI/+jjPyPMvI/ysj/KCP/o4z8z89llFVfvvmJn8sIAZSR/1FG/le4cOGkzJZl2fIyQUfKjdcqZTRJUnN1Cn1+Tst1ls5WtFqnWq+hLlF1NUy3/TUaqnKqrkqqp6qKVh89pvFapdpqprKqrkqqq6qK1r2aHtrmaX2tFrpKpVVFpVVZLXSVntbXGq9VekRzJEnddG9o/dbqoRs0MlW6h48clpkxZTDNnj1bdevWVa1atTR69OhM13vnnXckSd9//73MTF9++aViYmLUtGlT/fjjjzIz7dmzR+3atVNiYuIJ5+Pw4fxdRocOHVLz5s3VsGFD1a9fXyNGjJCZ6T//+U+ob4xdu3Zlun2HDh1UokQJderUKdX8Xr16KSYmRvfdd19o3siRI/X+++9TRplMN954o8qUKaPo6OjQvN27d+uyyy5T7dq1ddlll+nPP/+UmSkpKSnUf0lMTIyWLl2a4T6XLFmiBg0aqFatWho8eLCSkpJkZho2bJhiYmLUp0+f0LqTJk3SmDFjTirv+aWMTnT65Zdf1KZNG0VFRal+/foaO3ZshustWLBAsbGxql+/vlq3bi0z0++//64LLrhA0dHRqa6b5L7lKKPcm473PDp8+LC6d++uWrVqqUWLFtq8ebPMeB7l9nS86yW5A/eMnknLly9Xq1atVL9+fcXExGjKlCmhZTyPcnf6v//7P9WvX1/R0dHq0aOHDh06pJ9++kktWrRQrVq11L17dx05ciTDbR9//HHVqlVLdevW1Zw5c2TGvc6LaezYsYqOjlb9+vVDz/W4uDi1atVKDRo00JVXXqm//vor3XbJ/dUnT8WKFQttn5v1hvxSRtTrTu/pZK8js4zvk2Y8j07FlJ269969e3XllVeGfv++9tprMgvcA5s0aaKYmBh9/fXXMjMlJCSobdu2OnjwIGWUi9Px6t6ff/65GjdurIiICE2fPj0034MyyjxGmdWGkmy8VmU4FdKZVkn17P/0vY3XKrtVz1sl1bNotQ6t85S+spIqZ+VUwx7WrND86zXcztX59rS+sfFaZU/rG7tBo2y8VlltNbO7NcXGa5X11qNWT61C2zVSO7tCt4Y+X6F/WmO1s/FaZY9ojhVTKSutKjZWy2y8Vllr9bAbNDJVvgOHjLSOHTtmNWvWtE2bNtmRI0esYcOGtmbNmnTr7du3zy666CJr2bKlff/992Zmdu2119rWrVtt0aJFdtddd5mZ2dChQ23BggUnlZf8XkZJSUm2f/9+MzM7evSotWjRwr755htbtmyZbd682apVq2a7du3KdPt58+bZzJkzrVOnTqF5K1assP79+5uZ2WWXXWZ79+61X3/91a688sqTymN+KaPPP//cli5datHR0aF5d999t40ePdrMzEaPHm3Dhg0zM7OPP/7YLr/8cktKSrJvvvnGWrRokeE+mzdvbt98840lJSXZ5ZdfbrNmzbK9e/faZZddZmZm/fv3t5UrV1p8fLxdeumldvTo0ZPKe34poxP166+/2tKlS80scD+rU6dOunvdnj17LCoqyn7++WczM9u5c6eZmT333HM2adIkO3jwoF188cVmZjZz5kx76KGHTiovlFHGsvM8mjBhgt1yyy1mZjZ58mTr3r27mfE8ym1ZXS+//PKLtW/f3qpWrZrhM2n9+vX2448/mpnZ9u3brXz58rZnzx6eR7ls27ZtVr16dYuPjzczs+uuu85ef/11u+6662zy5MlmZnbLLbfY888/n27bNWvWWMOGDe3w4cP2008/Wc2aNe3YsWPc63LZqlWrLDo62g4ePGgJCQnWtm1b27BhgzVr1swWLlxoZmavvvqqPfjgg1nu59ixY1auXDnbsmVLrtcb8ksZUa87feXkOsrsPsnz6NTITt37scceC117v//+u5199tl25MgRGzJkiC1atMi2bt1qXbp0MTOzcePG2euvv35SeaGMMpaduvfmzZttxYoV1qdPH5s+fXpovkdllGF8Mkd9XkbrIq3RF5KkpZqtZroi1fIVmq8YtVFTXaGlwZaRkvSp/qseelBn6ixJ0pk6S62UfhSiGorVX/pdkrRLv2ir1uoK3RJafoX+qV+0Vru0VZJ0lkqpnlrqW83IyWHlS999951q166tmjVrqlChQurRo4dmzEh/HocPH6577rknNMKbJBUsWFDx8fGKj49XwYIFtWnTJm3dulVt2rQ5hUcQPpxzOuuswLWRkJCghIQEOefUuHHjbI3u27ZtWxUrVizVvIIFC+rQoUNKSkpSQkKCIiIiNGLEiAxHFMPfWrdurVKlSqWaN2PGDPXr10+S1K9fv9Ao1jNmzFDfvn3lnFOrVq20d+9e7dixI9W2O3bs0L59+9SqVSs559S3b1998MEHKlCggBISEmRmoevomWee0eDBg1WwYMFTcqz5RYUKFdSkSRNJgRGao6KitH379lTrvP322+rSpYuqVq0qSSpbtqykv+91R44cUUREhI4dO6axY8dq2LBhp/Ygwlx2nkcpr8Nu3bpp/vz5MjOeR7ksq+tlyJAheuqppzJ9/apu3bqqU6eOJKlixYoqW7asdu3axfPIA8eOHdOhQ4d07NgxxcfHq0KFCvrss89Co+ymfFalNGPGDPXo0UNnnHGGatSoodq1a+u7777jXpfLfvjhB7Vs2VJFihRRZGSkLr74Yr333nv68ccf1bp1a0lSu3bt9O6772a5n/nz56tWrVqqVq0a9YaTRL3u9JXT6yjtfbJixYo8j06R7NS9nXPav3+/zEwHDhxQqVKlFBkZma5et3fvXn344Yfq27dvXhxK2MpO3bt69epq2LBhutHUT2UZ5Sh42VSXa6nmKEFHtF0/qpoaplq+RLPUVFeoqa7QEgWGUz+kAzqsgyqtKsfd/w/6Sg11qSRphzapkuqpgCJSZD5ClVRPO7QxNK+dbtJ8TVSSEnNyaPnO9u3bVaXK32VSuXLldDeVZcuWaevWrerUqVOq+ffdd5/69u2r0aNH6/bbb9cDDzxA59o5lJiYqEaNGqls2bJq166dWrZsmaP9RUVFqUyZMmrSpImuuuoqbdy4UUlJSaEHCbJv586dqlChgiSpfPny2rlzp6TsXUPbt29X5cqV061TrFgxdezYUY0bN1aFChVUokQJffvtt7rmmmu8P6B8bMuWLVq+fHm66+vHH3/Unj171KZNGzVt2lRvvvmmJKlXr16aMWOG2rVrp/vvv1/PP/+8+vTpoyJFiuRF9sNWdq+l5HUiIyNVokQJ7d69m+eRh1JeLzNmzFClSpUUGxubrW2/++47HT16VLVq1eJ5lMsqVaqkf//736patWro+dG0aVOVLFlSkZGBru0zuoakzK817nW5q0GDBlq0aJF2796t+Ph4zZo1S1u3blV0dHTox+H06dO1devWLPczZcoU9ezZU5KoN+Qi6nWnh5xcRxndJ9u3b8/zKA9kVve+/fbb9cMPP6hixYqKiYnRc889pwIFCmjQoEF6/PHH1a9fP91///0aOXKk7r///nQBNORMdu53mTmVZZTlgD3HU0n1tFvbtUSzFK2LUi3bpz+0S7+olprIySlCBfWrNuhsVTjufifqXiUqQUcUr3s1/YTyVFpVVF0xoWApckdSUpLuuusuvfHGG+mWNWrUSIsXL5YkffHFF6pQoYLMTNdff70KFiyoZ599VuXKhdW4T56LiIhQXFyc9u7dq2uvvVarV69WgwYNcrTPsWPHhv5/1VVX6aWXXtJjjz2mFStWqF27dho4cGAOc53/OOdyrdPnYcOGhVq1DBgwQI8++qheeeUVffrpp2rYsKEefPDBXEkHAQcOHFDXrl01duxYFS9ePNWyY8eOaenSpZo/f74OHTqk8847T61atVLdunX18ccfS5L27NmjJ554Qu+//74GDhyoPXv2aOjQoTrvvPPy4nAQxPPIGymvl8jISD3++OP69NNPs7Xtjh071KdPH02cODFUkeV5lHv27NmjGTNmaPPmzSpZsqSuu+46zZkz5/gbZqFEiRLc63JRVFSU7rnnHrVv315FixZVo0aNFBERoddee0133HGHRo4cqc6dO6tQoUKZ7uPo0aOaOXOmRo8eHZpHvSH3Ua/zr5xcRxndJ9966y3dcMMNPI9Ooazq3p988okaNWqkzz77TJs2bVK7du100UUXqWrVqlq4cKEkaePGjdq2bZuioqLUp08fHT16VCNHjlTdunXz4GiQ7FSWUY7DoQ3VRu/rWTVN88r4Mn2ieO3TQ7pcI9RBf2q7lmi2ztRZOkNF9Icy/+tiPz2hhzVbLdRZ0xV4SFdQLW3XeiXp78GHkpSk7VqvCqqVavv2GqC5ek0my+nh5RuVKlVK9Zeqbdu2qVKlSqHP+/fv1+rVq9WmTRtVr15dixcvVufOnbVkyZLQOmamUaNGafjw4XrkkUf01FNPaeDAgRo3btwpPZZwUrJkSV1yySU5/iGS0owZM9S0aVMdOHBAmzZt0rRp0/TOO+8oPj4+19IIZ+XKlQu9NrRjx47QK8XHu4aS19m2bVuW6yxfvlxmpnr16mn69OmaNm2aNm3apA0bNnh1SPlOQkKCunbtqt69e6tLly7plleuXFkdOnRQ0aJFVbp0abVu3VorVqxItc7IkSP1wAMPaPLkybrwwgs1ceJEPfzww6foCMJbdq+l5HWOHTumv/76S+ecc05oOc+j3JP2etm0aZM2b96s2NhYVa9eXdu2bVOTJk3022+/pdt237596tSpkx577DG1atUq3XKeRzk3b9481ahRQ2XKlFHBggXVpUsXffXVV9q7d6+OHTsmKeNrSMretca9Lnf0799fS5cu1RdffKGzzz5bdevW1bnnnqtPP/1US5cuVc+ePUODMmZk9uzZatKkSYZ/fKHekDPU604fJ3sdZXSf/Prrr1Otw/PIW8ere7/++uvq0qWLnHOqXbu2atSooXXr1qVaJ/ltmnHjxmnAgAF66qmneMU/l2TnfpcdXpdRjoOXrXStOupWVVLqaOpSzdZtekGP6hM9qk80TFO1TLMlBYKL0/SYDumAJOmI4vWtZqba3snpSt2uzVqp3/STyqiqKutcfaKXQut8opdUWVEqo6qpti2vmiqvmlqtz3N6ePlG8+bNtWHDBm3evFlHjx7VlClT1Llz59DyEiVK6I8//tCWLVu0ZcsWtWrVSjNnzlSzZs1C67z55pvq2LGjSpUqpfj4eBUoUEAFChTgpn+Cdu3apb1790qSDh06pLlz5+rcc8/NlX0nJCSE+q06dOhQ6K/LiYmJOnr0aK6kEe46d+6siRMnSpImTpyoq6++OjT/zTfflJlp8eLFKlGiROg1pGQVKlRQ8eLFtXjxYpmZ3nzzzdD2yYYPH66RI0cqISFBiYmB7i+4jnKPmal///6KiorSXXfdleE6V199tb788stQv0jffvutoqKiQss3bNigbdu2qU2bNqF7nXNOhw4dOlWHEdaO9zySUl+H77zzji699NJUrWV4HuWOjK6XmJgY/f7776H6QOXKlbVs2TKVL18+1bZHjx7Vtddeq759+4b6XkyJ51HuqFq1qhYvXqz4+HiZmebPn6/69evrkksu0TvvvCMp9bMqpc6dO2vKlCk6cuSINm/erA0bNqhFixah5dzrcs/vvwf68P/ll1/03nvvqVevXqF5SUlJGjVqlP75z39muv3kyZNDr4ynRb0hZ6jXnT5O9jrK6D6Zsl7H88hb2al7V61aVfPnz5cU6Mph/fr1qlmzZmj5559/rooVK6pOnTrU6zyQnbr38ZySMspsJB/LxmjjaefdodcsWq3tEc2xEipr/9HKVMsrK8r+rf/Zf7TSrtYQK6vqVkG1rbLOtb56PN1o4+O1yq7Vv+08XRscvfxLa65OVlqVrbQqW3N1sqf0VWi08QqqHdruXr1jTo7Rxk/Axx9/bHXq1LGaNWvaqFGjzMxs+PDhNmPGjHTrXnzxxaHRxs3MDh48aG3atAmNoPfFF19YgwYNrEmTJrZu3boTykd+L6MVK1ZYo0aNLCYmxqKjo+2RRx4xs8BIx5UqVbKIiAirUKFCaHS877//PvR/M7MLL7zQSpcubYULF7ZKlSrZnDlzQsvGjBkTGvkrKSnJevToYQ0aNAiN7pZd+aWMevToYeXLl7fIyEirVKmSvfLKK/bHH3/YpZdearVr17a2bdva7t27zSxwPm+77TarWbOmNWjQINX1ERsbG/r/999/b9HR0VazZk0bNGiQJSUlhZa9//77qUZzHTp0qDVo0MB69ep1wnnPL2V0ohYtWmSSLCYmxmJjYy02NtY+/vhje+GFF+yFF14IrffUU09ZVFSURUdH25gxY1Lt47rrrguNorxz504777zzrH79+vbOO++cUF4oo8wd73l06NAh69atm9WqVcuaN29umzZtCm3L8yj3ZHa9pFStWrXQaOMpn0eTJk2yyMjI0HaxsbG2fPny0HY8j3LPiBEjrF69ehYdHW033HCDHT582DZt2mTNmze3WrVqWbdu3ezw4cNmZjZjxgwbPnx4aNtRo0ZZzZo1rW7dujZr1qxU++Vel3suvPBCi4qKsoYNG9q8efPMzGzs2LFWp04dq1Onjt1zzz2h+sD27dvtiiuuCG174MABK1WqlO3duzfdfnOr3pBfyoh63ektJ9dRRvfJZDyPvJWduvf27dutXbt21qBBA4uOjrZJkyaFtk9KSrLLLrssdG2uXbvWGjdubDExMfbll1+eUF4oo8wdr+793XffWaVKlaxIkSJWqlQpq1+/fmhbD8oow/ikCyzPmHPOxmtV7kVKfeB2xSirY0bec85RRj5HGfkfZeR/lJH/UUb+Rxn5H2Xkf5SR/1FG/kcZ+R9l5H/BMsqw82GGaQIAAAAAAADgS1mONl4golDS7YkxYRXgLFy4cK6NIgdvUEb+Rxn5H2Xkf5SR/1FG/kcZ+R9l5H+Ukf9RRv5HGfkfZeR/hQsXTspsWZaByaTEowXaP/qRMpoiChVON69mm546o1gpFStfIzRdct+UVOtcNORVFYgspGLla6homSqq3OxytXt4Zqr5yVODLkPU/tGPVLhkWZWtf35oHw2vv1cVG7XNMF/Hmw4fPpxlP5/5YRo7dqyio6NVv359jRkzRmamuLg4tWrVSg0aNNCVV16pv/76K8Nt9+zZo65du6pevXo699xz9fXXX8vMNGzYMMXExKhPnz6hdSdNmhTa/4lMlFHG53n58uVq2bKlYmNj1bRpU3377bcZbjts2DBFR0crOjpaU6ZMCc3v1auXYmJidN9994XmjRw5Uu+//z5llIvT7NmzVbduXdWqVUujR4/O8Nx1795dtWrVUosWLbR582aZmb788kvFxMSoadOm+vHHH0Pfg3bt2ikxMZEyOokpo3td9+7dFRsbq9jYWFWrVk2xsbGZbn/s2DE1atRInTp1Cs3jOjrx6cYbb1SZMmUUHR0dmrd7925ddtllql27ti677DL9+eefMjMlJSVp8ODBqlWrlmJiYrR06dIM97lkyRI1aNBAtWrV0uDBg5WUlCSz3H0W5acyymxat25d6HqJjY1VsWLFNGbMGD300EOqWLFiaP7HH3+c4fb/93//p/r16ys6Olo9evTQoUOHZMZ1lJvTL7/8ojZt2igqKkr169fX2LFjZZb5NZZ2euONN1S7dm3Vrl1bb7zxRuicdujQQdHR0ZowYUJo3YEDB2Z6TVJGJzcdr87wwgsvqEGDBoqNjdUFF1ygNWvWyIw6g5/KiHpd3k/HK6Nnn31WUVFRiomJ0aWXXqotW7bILPCMa9KkiWJiYkK/aRMSEtS2bVsdPHiQMjqJ6WTr3pk9y8yIM5yKMspuLCijbT0oo0xjlLneqrLaedfovNv+E5oKnnlWunXOLFU+uHy8Duzaqt/XLU4zPzBVbNQ2tM2+XzfqwO+/5HZ2853Vq1frv//9r7777jutWLFCH330kTZu3KgBAwboiSee0KpVq3Tttdfq6aefznD7O++8U5dffrnWrVunFStWKCoqSn/99ZeWLVumlStXqlChQlq1apUOHTqk119/XYMGDTrFRxgeMjrPw4YN00MPPaS4uDg9+uijGjZsWLrtPv74Yy1btkxxcXH69ttv9cwzz2jfvn1auXKlzjzzTK1cuVLff/+9/vrrL+3YsUPffvutrrnmmlN/gGEqMTFRgwYN0uzZs7V27VpNnjxZa9euTbXOq6++qrPPPlsbN27UkCFDdM8990iSnn32Wc2aNUtjx47Viy++KEkaNWqU7r//fhUoEFYN4E+JzO51U6dOVVxcnOLi4tS1a1d16dIl030899xzqUaj5Do6Of/4xz80Z86cVPOeeOIJtW3bVhs2bFDbtm31xBNPSJJmz56tDRs2aMOGDXr55Zd16623ZrjPW2+9Vf/9739D686ZM4dnkQfq1asXul6WLl2qIkWK6Nprr5UkDRkyJLSsY8eO6bbdvn27xo0bpyVLlmj16tVKTEzUlClTuI5yWWRkpJ599lmtXbtWixcv1oQJE7R27dpMr7GU/vzzTz3yyCP69ttv9d133+mRRx7Rnj179Mknn+jCCy/UypUrNWnSJEnSihUrlJiYqCZNmpzqQwxb2akz9OrVS6tWrVJcXJyGDRsWGqmXOsOpQb3O/7JTRo0bN9aSJUu0cuVKdevWLfQb6qWXXtJzzz2nWbNm6ZlnnpEkvfDCC7rhhhtUpEiRU34sp7uc1L0ze5ZRt8tdOYkFZbbtqSyjPL1zFoiIUMkqUYrf/etx161+/rX66YuppyBX4e2HH35Qy5YtVaRIEUVGRuriiy/We++9px9//FGtW7eWJLVr107vvvtuum3/+usvffHFF+rfv78kqVChQipZsqQKFCighIQEmZni4+NVsGBBPfPMMxo8eLAKFix4So8vHGR2np1z2rdvX2idihUrptt27dq1at26tSIjI1W0aFE1bNhQc+bMUcGCBXXo0CElJSUpISFBERERGjFihB555JFTemzh7rvvvlPt2rVVs2ZNFSpUSD169NCMGTNSrTNjxgz169dPktStWzfNnz9fZqaCBQsqPj4+dA1t2rRJW7duVZs2bfLgSE5/md3rkpmZpk2bpp49e2a4/bZt2/Txxx9rwIABoXlcRyendevWKlWqVKp5Ka+Dfv366YMPPgjN79u3r5xzatWqlfbu3asdO3ak2nbHjh3at2+fWrVqJeec+vbtqw8++IBnkcfmz5+vWrVqqVq1atne5tixYzp06JCOHTum+Ph4VaxYkesol1WoUCEUUCxWrJiioqK0ffv2TK+xlD755BO1a9dOpUqV0tlnn6127dqF6gzx8fGh60mShg8frpEjR56y48oPslNnKF68eOj/Bw8eDL3uSJ3h1KBe53/ZKaNLLrkkFIxs1aqVtm3bJin9dbR37159+OGH6tu37yk/jnCQk7p3Zs8y6na5KyexoMy2PZVllOvBy5+/+UDfPD9Y3zw/WN+/dl+W6yYePaw/f1qhs8pVlyQd+vO30LbfPD9Ye7asDq1brsGF2v/rpmwFOpG5Bg0aaNGiRdq9e7fi4+M1a9Ysbd26VdHR0aEb/fTp07V169Z0227evFllypTRjTfeqMaNG2vAgAE6ePCgihUrpo4dO6px48aqUKGCSpQoQQuKHMjsPI8dO1Z33323qlSpon//+98aPXp0um1jY2M1Z84cxcfH648//tCCBQu0detWRUVFqUyZMmrSpImuuuoqbdy4UUlJSbSgyGXbt29XlSpVQp8rV66s7du3Z7pOZGSkSpQood27d+u+++5T3759NXr0aN1+++164IEHNGrUqFOa/3CS2b0u2aJFi1SuXDnVqVMnw+3/9a9/6amnnkrVOoLrKPfs3LlTFSpUkCSVL19eO3fulJT9a6hy5crp1uFZ5K0pU6ak+sExfvx4NWzYUDfddJP27NmTbv1KlSrp3//+t6pWrRoqj/bt23MdeWjLli2hLmYyu8ZSyux6a9eunbZs2aJWrVrpjjvu0MyZM9WkSZMM/2iKk5ed+50kTZgwQbVq1dKwYcM0btw4SaLOcIpQr/O/7F5HyV599VVdccUVkqRBgwbp8ccfV79+/XT//fdr5MiRtIzNgZzWvZOlfJZRt8tdOYkFZbbtqSyjLAfsORnVzrtG1S/M/DU86e8gpeRU5tyWKlO3mQ7t2Rl6bTwjzhVQ9Qu7aPOi6TqnTtPczna+ERUVpXvuuUft27dX0aJF1ahRI0VEROi1117THXfcoZEjR6pz584qVKhQum2PHTumZcuW6T//+Y9atmypO++8U0888YRGjhypYcOGhZrgDxgwQI8++qheeeUVffrpp2rYsKEefPDBU32op63MzvNff/2lMWPGqGvXrpo2bZr69++vefPmpdq2ffv2+v7773X++eerTJkyOu+88xQRESFJGjt2bGi9q666Si+99JIee+wxrVixQu3atdPAgQNP5WEijUaNGmnx4kAXGl988YUqVKggM9P111+vggUL6tlnn1W5cuXyOJenj8zudckmT56caavLjz76SGXLllXTpk21cOHCVMu4jnKfcy7XOk/nWeSNo0ePaubMmaE/mt16660aPny4nHMaPny4hg4dqtdeey3VNnv27NGMGTO0efNmlSxZUtddd53eeust3XDDDVxHHjhw4IC6du2qsWPHpmqtJ534NRYZGam3335bkpSQkKAOHTpoxowZuuuuu/TLL7+ob9++6ty5c67mH5kbNGiQBg0apLffflujRo3SxIkTqTOcBigj/3nrrbe0ZMkSff7555KkqlWrhup5Gzdu1LZt2xQVFaU+ffro6NGjGjlypOrWrZuHOT695KTunSyjZxl1u9yTk1hQVuV7qsooT/6s8HffluNU+9Le2d6uQuyl2rNltY789YeHuQt//fv319KlS/XFF1/o7LPPVt26dXXuuefq008/1dKlS9WzZ0/VqlUr3XaVK1dW5cqV1bJlS0mBVyOWLVuWap3ly5fLzFSvXj1Nnz5d06ZN06ZNm7Rhw4ZTcmzhILPzPHHixFAfIdddd52+++67DLd/4IEHFBcXp7lz58rM0j10Z8yYoaZNm+rAgQPatGmTpk2bpnfeeUfx8fHeHlg+UKlSpVR/qdq2bZsqVaqU6TrHjh3TX3/9pXPOOSe03Mw0atQoDR8+XI888oieeuopDRw4MNTaAtmX0b1OCpz39957T9dff32G23311VeaOXOmqlevrh49euizzz7TDTfckGodrqOcKVeuXOh18B07dqhs2bKSsn8NJb/yldk6PIty1+zZs9WkSZPQD+1y5copIiJCBQoU0MCBAzN8Hs2bN081atRQmTJlVLBgQXXp0kVff/11qnW4jnJHQkKCunbtqt69e4fqCZldYyll53p7/vnn1bdvXy1evFglSpTQ1KlT9eyzz3p4NPlHds5/Sj169Ej3+j91Bm9Rr/O/7F5H8+bN02OPPaaZM2fqjDPOSLc8uWXsuHHjNGDAAD311FN0Z3ISTrbuLWX8LEuJul3uONlYUGbbpuR1GZ1WbaILRESq6vnX6OdvZhx/ZWTq999/lyT98ssveu+999SrV6/QvKSkJI0aNUr//Oc/021Xvnx5ValSRevXr5cU6P+qfv36qdZJ7hMpISFBiYmJkqQCBQrwQ+QEZHaeK1asGPpL4WeffZZhk/vExETt3r1bUmBwkZUrV6p9+/ah5QkJCRo7dqyGDRumQ4cOhVpiJCYm6ujRo14fWthr3ry5NmzYoM2bN+vo0aOaMmVKutYpnTt31sSJEyVJ77zzji699NJULWLefPNNdezYUaVKlVJ8fLwKFCjANXSSMrrXSYEK7Lnnnpvq1eOURo8erW3btmnLli2aMmWKLr30Ur311luh5VxHOZfyOpg4caKuvvrq0Pw333xTZhYKliS/+pqsQoUKKl68uBYvXiwz05tvvhnaPhnPotyVtrVEyn5I33//fTVo0CDdNlWrVtXixYsVHx8vM9P8+fNTDYDFdZQ7zEz9+/dXVFRUaDAXKfNrLKUOHTro008/1Z49e7Rnzx59+umn6tChQ2j5nj179NFHH6lv376h55FzTocOHfL+wPKB7NQZUv7g+/jjj9PV/agzeIt6nf9lp4yWL1+uW265RTNnzszwDzmff/65KlasqDp16lBGOXSyde/MnmUpUbfLHScbC8ps25S8LqOTfm08MeGIPn+mX+hztfOukRTo83LHygWh+Y16Pqgzz85ek/i/XycPqNiknaq1Sn3zqdykvTZ/zsA9OdG1a1ft3r1bBQsW1IQJE1SyZEk999xzmjBhgiSpS5cuuvHGGyVJv/76qwYMGKBZs2ZJkv7zn/+od+/eOnr0qGrWrKnXX389tN8PPvhAzZo1C/WJ1KhRI8XExKhhw4aKjY09xUd5esvoPF999dW68847dezYMRUuXFgvv/yyJGnJkiV68cUX9corryghIUEXXXSRpEAn72+99ZYiI/++zCdMmKB+/fqpSJEiatiwoeLj4xUTE6OOHTuqZMmSeXGoYSUyMlLjx49Xhw4dlJiYqJtuuknR0dEaMWKEmjVrps6dO6t///7q06ePateurVKlSmnKlCmh7ePj4/XGG2/o008/lSTddddd6tixowoVKhR6hQ/Zl9G9Tkrfd5+U/l6XFa6jE9OzZ08tXLhQf/zxhypXrqxHHnlE9957r7p3765XX31V1apV07Rp0yRJHTt21KxZs1S7dm0VKVIk1TOmUaNGiouLkxRoDfaPf/xDhw4d0hVXXBHqv0riWZTbDh48qLlz5+qll14KzRs2bJji4uLknFP16tVDy1JeRy1btlS3bt3UpEkTRUZGqnHjxrr55ptD++A6yh1fffWVJk2apJiYGDVq1EiS9Pjjj2d6jaWsM5QqVUrDhw9X8+bNJUkjRoxINbjWo48+qgceeEAFChRQhw4dNGHCBMXExGT6owYnJjt1hvHjx2vevHkqWLCgzj777FCQTKLOcCpQr/O/7JTR3XffrQMHDui6666TFPjj2syZMyX93TJ26tRAfOHmm29W7969dezYMb3wwgt5dlynq5Ote2f2LOvYsaMk6na5KSexoMzKVzo1ZeSSRxHMcKFz1v7Rj3IlIb/4dMSVyuqYkfecc5SRz1FG/kcZ+R9l5H+Ukf9RRv5HGfkfZeR/lJH/UUb+Rxn5X7CMMuyo+7R6bRwAAAAAAABA/pHla+MFIgvt/HTElWE1DFrhwoWTnHMEbX2MMvI/ysj/KCP/o4z8jzLyP8rI/ygj/6OM/I8y8j/KyP8oI/8rXLjwzsyWZfnaOAAAAAAAAADkFaLOAAAAAAAAAHyJ4CUAAAAAAAAAXyJ4CQAAAAAAAMCXCF4CAAAAAAAA8CWClwAAAAAAAAB86f8BJhRhfb+vGzcAAAAASUVORK5CYII=\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 = ['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": 81,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:45:14.248032Z",
     "iopub.status.busy": "2022-06-03T10:45:14.247469Z",
     "iopub.status.idle": "2022-06-03T10:45:14.249714Z",
     "shell.execute_reply": "2022-06-03T10:45:14.250040Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12.3,  0. , 17.4, 17.9, 13.5,  3.6,  0.1,  0. ,  0. , 17.4, 17.8]],\n",
       "      dtype=float32)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MT = M[1:, 1:].T\n",
    "MT /= MT.sum(axis=1)\n",
    "MT*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:45:14.277764Z",
     "iopub.status.busy": "2022-06-03T10:45:14.277268Z",
     "iopub.status.idle": "2022-06-03T10:45:14.483991Z",
     "shell.execute_reply": "2022-06-03T10:45:14.484427Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(16, 5))\n",
    "\n",
    "columns = df_1.columns[1:]\n",
    "rows = df_2.columns[1:]\n",
    "\n",
    "# named colors: https://matplotlib.org/stable/gallery/color/named_colors.html\n",
    "colors = ['steelblue', 'brown' ]\n",
    "n_rows = len(rows)\n",
    "\n",
    "index = np.arange(len(columns)) + 0.3\n",
    "bar_width = 0.4\n",
    "\n",
    "# Initialize the vertical-offset for the stacked bar chart.\n",
    "y_offset = np.zeros(len(columns))\n",
    "\n",
    "# Plot bars and create text labels for the table\n",
    "cell_text = []\n",
    "for row in range(n_rows):\n",
    "    ax.bar(index, MT[row]*100, bar_width, bottom=y_offset, color=colors[row], linewidth=1)\n",
    "    y_offset = y_offset + MT[row]*100\n",
    "    cell_text.append([f'{x*100:1.1f}%' for x in MT[row]])\n",
    "ax.set_ylim(0, 100)\n",
    "# Add a table at the bottom of the axes\n",
    "the_table = ax.table(cellText=cell_text, colLoc='center', \n",
    "                      rowLabels=rows, rowLoc='center',\n",
    "                      rowColours=colors,\n",
    "                      colLabels=columns,\n",
    "                      loc='bottom')\n",
    "the_table.auto_set_font_size(False)\n",
    "the_table.set_fontsize(10)\n",
    "# Adjust layout to make room for the table:\n",
    "plt.subplots_adjust(left=0.2, bottom=0.2)\n",
    "\n",
    "plt.ylabel(\"Pourcentage de report des voix\")\n",
    "plt.yticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.xticks([])\n",
    "plt.title(\"Report des voix exprimées connaissant le choix exprimé au 1er tour\")\n",
    "plt.savefig('2022-05-23_transfert-des-voix.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ce tableau donne le pourcentage de chances d'exprimer une voix pour un candidat ou pour l'autre en fonction du choix qu'on a exprimé au premier tour. \n",
    "\n",
    "Ce tableau montre des tendances claires, par exemple que si on a voté Macron, Jadot ou Pécresse au premier tour, alors on va certainement voter Macron au deuxième tour. Ses électeurs se montre particulièrement consensuel et suivent le « pacte républicain » mise en place pour faire un barrage au Front National. Il montre aussi que si on a voté Le Pen ou Dupont-Aignan au premier tour alors on va voter Le Pen au deuxième, un clair vote de suivi. (On pourra aussi remarquer les ~ 3 % des voix pour Macron au premier tour qui ont voté Le Pen au deuxième tour, soit tout de même environ 320k individus…)\n",
    "\n",
    "Connaissant les couleurs politiques d'autres candidats du premier tour, on peut être surpris que les électeurs de Arthaud, Roussel ou Hidalgo ont majoritairement choisi Le Pen au deuxième tour, signifiant alors un rejet du candidat Macron. Les électeurs de Zemmour sont aussi partagés, signifiant un rejet des deux alternatives. **Ce résultat est à prendre avec des pincettes car ces derniers candidats ont obtenu moins de votes et donc que le processus d'inférence est forcément moins précis car il y a moins de données disponibles.** Pour se rendre compte de la variabilité des résultats qu'on obtient là, je conseille au lecteur (*à l'électeur*) de relancer ces notebook en utilisant différents « graines » pour le générateur de nombre aléatoire qui permet de séparer les données (le paramètre `seed`)."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "tags": []
   },
   "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": 83,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:45:14.490185Z",
     "iopub.status.busy": "2022-06-03T10:45:14.489226Z",
     "iopub.status.idle": "2022-06-03T10:48:02.737662Z",
     "shell.execute_reply": "2022-06-03T10:48:02.738008Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAIN: Loss avec do_optim=True = 7.37e+00 / Loss avec alternative choice do_optim=False = 7.37e+00 \n",
      "TEST: Loss avec do_optim=True = 6.42e+00 / Loss avec alternative choice do_optim=False = 6.42e+00 \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:.2e} / Loss avec alternative choice do_optim={not do_optim} = {loss_train_alt:.2e} ')\n",
    "print(f'TEST: Loss avec {do_optim=} = {loss_test:.2e} / Loss avec alternative choice do_optim={not do_optim} = {loss_test_alt:.2e} ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:48:02.741603Z",
     "iopub.status.busy": "2022-06-03T10:48:02.741082Z",
     "iopub.status.idle": "2022-06-03T10:48:02.743421Z",
     "shell.execute_reply": "2022-06-03T10:48:02.743772Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "do_optim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T10:48:02.749666Z",
     "iopub.status.busy": "2022-06-03T10:48:02.749033Z",
     "iopub.status.idle": "2022-06-03T11:07:48.217680Z",
     "shell.execute_reply": "2022-06-03T11:07:48.218025Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour learning_rate= 1.00e-03, loss_train=7.44e+00 / loss_test=6.50e+00; le temps de calcul est 168.979 s\n",
      "Pour learning_rate= 2.15e-03, loss_train=7.40e+00 / loss_test=6.45e+00; le temps de calcul est 169.298 s\n",
      "Pour learning_rate= 4.64e-03, loss_train=7.38e+00 / loss_test=6.43e+00; le temps de calcul est 168.974 s\n",
      "Pour learning_rate= 1.00e-02, loss_train=7.36e+00 / loss_test=6.43e+00; le temps de calcul est 169.628 s\n",
      "Pour learning_rate= 2.15e-02, loss_train=7.36e+00 / loss_test=6.41e+00; le temps de calcul est 168.544 s\n",
      "Pour learning_rate= 4.64e-02, loss_train=7.36e+00 / loss_test=6.42e+00; le temps de calcul est 170.272 s\n",
      "Pour learning_rate= 1.00e-01, loss_train=7.41e+00 / loss_test=6.41e+00; le temps de calcul est 169.396 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": 86,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T11:07:48.224042Z",
     "iopub.status.busy": "2022-06-03T11:07:48.223435Z",
     "iopub.status.idle": "2022-06-03T11:28:12.544346Z",
     "shell.execute_reply": "2022-06-03T11:28:12.544758Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  32  128  288  512  800 1152]\n",
      "Pour batch_size= 32, loss_train=7.37e+00 / loss_test=6.42e+00; le temps de calcul est 373.005 s\n",
      "Pour batch_size= 128, loss_train=7.37e+00 / loss_test=6.42e+00; le temps de calcul est 191.633 s\n",
      "Pour batch_size= 288, loss_train=7.36e+00 / loss_test=6.43e+00; le temps de calcul est 164.645 s\n",
      "Pour batch_size= 512, loss_train=7.37e+00 / loss_test=6.42e+00; le temps de calcul est 150.185 s\n",
      "Pour batch_size= 800, loss_train=7.37e+00 / loss_test=6.42e+00; le temps de calcul est 173.134 s\n",
      "Pour batch_size= 1152, loss_train=7.36e+00 / loss_test=6.42e+00; le temps de calcul est 171.458 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": 87,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T11:28:12.548728Z",
     "iopub.status.busy": "2022-06-03T11:28:12.548210Z",
     "iopub.status.idle": "2022-06-03T11:28:12.550265Z",
     "shell.execute_reply": "2022-06-03T11:28:12.550593Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.  1.  1.  1.  1.  1.  0.9]\n"
     ]
    }
   ],
   "source": [
    "beta1s = 1 - (1 - beta1) * np.logspace(-1, 1, 7, base=10)\n",
    "print(beta1s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T11:28:12.557434Z",
     "iopub.status.busy": "2022-06-03T11:28:12.556836Z",
     "iopub.status.idle": "2022-06-03T11:48:19.779294Z",
     "shell.execute_reply": "2022-06-03T11:48:19.779803Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.  1.  1.  1.  1.  1.  0.9]\n",
      "Pour beta1= 9.99e-01, loss_train=7.68e+00 / loss_test=6.66e+00; le temps de calcul est 173.541 s\n",
      "Pour beta1= 9.98e-01, loss_train=7.36e+00 / loss_test=6.41e+00; le temps de calcul est 177.062 s\n",
      "Pour beta1= 9.95e-01, loss_train=7.36e+00 / loss_test=6.41e+00; le temps de calcul est 173.594 s\n",
      "Pour beta1= 9.90e-01, loss_train=7.36e+00 / loss_test=6.42e+00; le temps de calcul est 172.367 s\n",
      "Pour beta1= 9.78e-01, loss_train=7.37e+00 / loss_test=6.43e+00; le temps de calcul est 169.937 s\n",
      "Pour beta1= 9.54e-01, loss_train=7.40e+00 / loss_test=6.45e+00; le temps de calcul est 169.573 s\n",
      "Pour beta1= 9.00e-01, loss_train=7.44e+00 / loss_test=6.50e+00; le temps de calcul est 170.973 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": 89,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T11:48:19.785649Z",
     "iopub.status.busy": "2022-06-03T11:48:19.785021Z",
     "iopub.status.idle": "2022-06-03T12:08:53.279595Z",
     "shell.execute_reply": "2022-06-03T12:08:53.280029Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour beta2= 9.95e-01, loss_train=7.36e+00 / loss_test=6.41e+00; le temps de calcul est 174.342 s\n",
      "Pour beta2= 9.89e-01, loss_train=7.37e+00 / loss_test=6.43e+00; le temps de calcul est 174.180 s\n",
      "Pour beta2= 9.77e-01, loss_train=7.37e+00 / loss_test=6.42e+00; le temps de calcul est 174.248 s\n",
      "Pour beta2= 9.50e-01, loss_train=7.39e+00 / loss_test=6.44e+00; le temps de calcul est 187.365 s\n",
      "Pour beta2= 8.92e-01, loss_train=7.38e+00 / loss_test=6.44e+00; le temps de calcul est 174.715 s\n",
      "Pour beta2= 7.68e-01, loss_train=7.38e+00 / loss_test=6.44e+00; le temps de calcul est 173.954 s\n",
      "Pour beta2= 5.00e-01, loss_train=7.38e+00 / loss_test=6.43e+00; le temps de calcul est 174.397 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": 90,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-03T12:08:53.285870Z",
     "iopub.status.busy": "2022-06-03T12:08:53.285286Z",
     "iopub.status.idle": "2022-06-03T12:41:12.994609Z",
     "shell.execute_reply": "2022-06-03T12:41:12.994954Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  65  257  577 1025 1601 2305]\n",
      "Pour num_epochs=65, loss_train=7.42e+00 / loss_test=6.49e+00; le temps de calcul est 21.450 s\n",
      "Pour num_epochs=257, loss_train=7.37e+00 / loss_test=6.45e+00; le temps de calcul est 84.800 s\n",
      "Pour num_epochs=577, loss_train=7.37e+00 / loss_test=6.42e+00; le temps de calcul est 191.238 s\n",
      "Pour num_epochs=1025, loss_train=7.36e+00 / loss_test=6.41e+00; le temps de calcul est 339.828 s\n",
      "Pour num_epochs=1601, loss_train=7.36e+00 / loss_test=6.41e+00; le temps de calcul est 528.091 s\n",
      "Pour num_epochs=2305, loss_train=7.36e+00 / loss_test=6.41e+00; le temps de calcul est 774.004 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');"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "include_colab_link": true,
   "name": "Welcome To Colaboratory",
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}