2022-06-08_transfert-des-voix.ipynb

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    "tl;dr : *On essaie ici de deviner le transfert des voix entre les choix effectués entre deux scrutins d'un vote (ici les élections présidentielles 2022 en France) par une méthode d'[apprentissage automatique](https://fr.wikipedia.org/wiki/Apprentissage_automatique).*\n",
    "\n",
    "\n",
    "[![DOI](https://zenodo.org/badge/488514016.svg)](https://zenodo.org/badge/latestdoi/488514016)\n",
    "\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](https://fr.wikipedia.org/wiki/Apprentissage_automatique) pour inférer des structures à première vue cachées dans la masse des 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 du report de voix entre les choix de vote au premier tour et ceux qui sont effectués au deuxième tour*.\n",
    "\n",
    "Pour cela, parmi les outils mathématiques de l'apprentissage automatique, nous allons utiliser des probabilités. Cette théorie va nous permettre d'exprimer le fait que les résultats tels qu'ils sont obtenus peuvent présenter une variabilité mais que celle-ci réelle résulte de préférences de chaque individu dans la population votante. En particulier, on peut considérer que chaque individu va avoir une préférence, graduée entre $0=0\\%$ et $1=100\\%$ pour chacun des choix (candidats, nul, blanc, abstention) au premier et second tour. Ainsi, les votes effectués vont correspondre à la réalisation de ces préférences. \n",
    "\n",
    "Bien sûr, le vote reste secret et on n'a pas accès au vote de chaque individu et encore moins à ses préférences. Mais comme chaque bureau de vote présente des variabilités liées au contexte local et qui fait que cette population locale 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. **En exploitant les irrégularités locales, bureau de vote par bureau de vote, nous allons pouvoir prédire (le mieux possible) le report des votes individuel (de chaque individu tel qu'il passe d'un vote à un autre, par exemple de \"Hidalgo\" à \"Macron\").** Nous allons en particulier montrer une prédiction très correcte des données du second tour à partir de ceux du premier, montrant la plausibilité d'une telle hypothèse :\n",
    "\n",
    "![Prédiction du transfert des voix](https://raw.githubusercontent.com/laurentperrinet/2022-05-04_transfert-des-voix/main/2022-06-08_prediction_transfert-des-voix_bce.png \"Prédiction du transfert des voix\")\n",
    "\n",
    "C'est à ma connaissance une contribution originale (jusqu'à ce qu'une bonne âme veuille bien me donner un lien vers une méthode existante similaire qui me permette de correctement la citer...) que nous allons exploiter ici. Cette prédiction, si elle est efficace (et on va montrer qu'elle est en moyenne correctement prédite avec moins de 2 points de pourcentages d'erreur près), 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",
    "Nous allons dans la suite montrer comment on peut estimer 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",
    "![Transfert des voix](https://raw.githubusercontent.com/laurentperrinet/2022-05-04_transfert-des-voix/main/2022-06-06_transfert-des-voix.png \"Transfert des voix\")\n",
    "\n",
    "Comme on le verra plus bas, ce tableau montre des tendances claires, par exemple que si on a voté \"Macron\", \"Jadot\", \"Hidalgo\" ou \"Pécresse\" au premier tour, alors on va certainement voter \"Macron\" au deuxième tour. Ces électeurs se montrent particulièrement consensuels et suivent le « pacte républicain » mis en place pour faire un « barrage » au Front National (en suivant le terme consacré). 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.\n",
    "\n",
    "Connaissant les couleurs politiques d'autres candidats du premier tour, on peut être surpris que les électeurs de \"Arthaud\", \"Roussel\", \"Lassalle\" ou \"Poutou\" 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.** \n",
    "\n",
    "En résumé, cette analyse donne des tendances en fonction des choix exprimés au premier tour:\n",
    "\n",
    "![Transfert des voix](https://raw.githubusercontent.com/laurentperrinet/2022-05-04_transfert-des-voix/main/2022-06-08_transfert-des-voix_tendances.png \"Tendances présidentielle 2022\")\n",
    "qui montre une nette séparation des groupes de vote.\n",
    "\n",
    "<!-- TEASER_END -->"
   ]
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   "source": [
    "Grâce à l'ouverture des données sur https://www.data.gouv.fr/ (notamment utilisées 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 les résultats donnés sont indiqués pour *chacun* des bureaux de vote. \n",
    "\n",
    "Nous allons faire deux hypothèses que nous allons expliciter mathématiquement : \n",
    "\n",
    "1. Tout d'abord, nous allons estimer que pour chaque individu, il existe une préférence pour les choix du premier tour ainsi que pour les choix du deuxième tour. \n",
    "\n",
    " - On note par exemple les différentes alternatives au premier tour comme $i \\in \\{ \\text{'Nul'}, \\text{'Abstention'}, \\ldots, \\text{'Macron'}, \\text{'Poutou'} \\}$ et au deuxième tour  $j \\in \\{ \\text{'Nul'}, \\text{'Abstention'}, \\ldots, \\text{'Macron'}, \\text{'Le Pen'} \\}$. \n",
    " \n",
    " - Le vote de chaque individu se modélise mathématiquement par un [processus de Bernoulli](https://fr.wikipedia.org/wiki/Processus_de_Bernoulli) relatif à ces préférences : 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), alors $\\sum_i p^k_i = 1$ et $\\sum_j q^k_j = 1$, ce qui revient à dire qu'à chaque scrutin un individu effectue un et un seul choix.\n",
    " \n",
    " - Avec une telle modélisation, on peut prédire les résultats du vote, car les préférences de chaque individu pour tel ou tel choix doit se révèle nécessairement au niveau de la population totale. Plus précisément, le théorème central limite indique que la moyenne observée (c'est-à-dire les moyennes de vote observées pour les différents choix) 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).\n",
    "\n",
    "2. 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.\n",
    "\n",
    " - En effet, les préférences peuvent évoluer avec chaque invidu mais que la transition est homogène au sein de la population (par exemple \"une personne qui choisit de s'abstenir s'abstiendra\"). C'est une hypothèse *a priori* grossière, mais assez générale pour refléter les tendances au niveau de la population globale, et nous allons la tester. \n",
    "\n",
    " - Cette hypothèse est basée sur la modélisation d'une séquence de deux événements aléatoires comme dans un [processus 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. Mathématiquement, 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. \n",
    "\n",
    " - Il est important de noter qu'il existe une contrainte  pour chaque colonne de cette matrice de transition, de sorte que la somme des différents éléments sur les différentes lignes de la matrice pour chaque colonne est égale 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 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 *quantitatif* des reports de vote qui vont être effectivement effectués entre les deux tours."
   ]
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   "source": [
    "## Méthodes\n",
    "\n",
    "### Calcul libre\n",
    "\n",
    "Ce post est une exploration, un travail de recherche dont les méthodes essaient de suivre la méthode scientifique le plus fidélement possible:\n",
    "\n",
    " - À ce titre, il est écrit dans un format qui permet de reproduire *entièrement* les résultats: les données et les algorithmes sont librement disponibles: le format choisi est un [notebook jupyter](https://fr.wikipedia.org/wiki/Jupyter) avec le language python. Aussi, les librairies utilisées sont toutes open-source et donc utilisables librement.\n",
    " - De plus, nous avons consigné les différentes versions de ce post dans une \"archive\" github : https://github.com/laurentperrinet/2022-05-04_transfert-des-voix. Ceci permet de vérifier le cheminement (parfois tortueux) suivi pour arriver à des résultats qui semblent valides. \n",
    "\n",
    "### Collecte des données\n",
    "\n",
    "La première partie de ce travail consiste à collecter les données et elle est représentée 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 librairies python : `numpy` pour le traitement de données numériques puis `pandas` pour la représentation de ces données sous forme de tableau tableaux.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:22:46.946555Z",
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   "outputs": [],
   "source": [
    "datetime = '2022-06-08'\n",
    "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 (en format \"Excel (xlsx)\") 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": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:22:47.259823Z",
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     "shell.execute_reply": "2022-06-09T15:22:47.261528Z"
    }
   },
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:22:47.265767Z",
     "iopub.status.busy": "2022-06-09T15:22:47.265070Z",
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     "shell.execute_reply": "2022-06-09T15:23:57.993240Z"
    }
   },
   "outputs": [],
   "source": [
    "fname = '/tmp/T1.xlsx'\n",
    "\n",
    "if not os.path.isfile(fname):\n",
    "    url = 'https://static.data.gouv.fr/resources/election-presidentielle-des-10-et-24-avril-2022-resultats-definitifs-du-1er-tour/20220414-152612/resultats-par-niveau-burvot-t1-france-entiere.xlsx' # XLSX\n",
    "    import urllib.request\n",
    "    urllib.request.urlretrieve(url, fname)\n",
    "\n",
    "T1 = pd.read_excel(fname)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut avoir une première idée de ces données et du nombre total de bureaux de vote :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
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    }
   },
   "outputs": [
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       "      <th>Code du département</th>\n",
       "      <th>Libellé du département</th>\n",
       "      <th>Code de la circonscription</th>\n",
       "      <th>Libellé de la circonscription</th>\n",
       "      <th>Code de la commune</th>\n",
       "      <th>Libellé de la commune</th>\n",
       "      <th>Code du b.vote</th>\n",
       "      <th>Inscrits</th>\n",
       "      <th>Abstentions</th>\n",
       "      <th>% Abs/Ins</th>\n",
       "      <th>...</th>\n",
       "      <th>Unnamed: 95</th>\n",
       "      <th>Unnamed: 96</th>\n",
       "      <th>Unnamed: 97</th>\n",
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       "      <td>56.70</td>\n",
       "      <td>...</td>\n",
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       "      <td>0.44</td>\n",
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       "      <td>11</td>\n",
       "      <td>11ème circonscription</td>\n",
       "      <td>231</td>\n",
       "      <td>Taipei</td>\n",
       "      <td>0001</td>\n",
       "      <td>1709</td>\n",
       "      <td>942</td>\n",
       "      <td>55.12</td>\n",
       "      <td>...</td>\n",
       "      <td>10</td>\n",
       "      <td>0.59</td>\n",
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       "      <td>11ème circonscription</td>\n",
       "      <td>233</td>\n",
       "      <td>Nour-Soultan</td>\n",
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       "      <td>117</td>\n",
       "      <td>64</td>\n",
       "      <td>54.70</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>12</td>\n",
       "      <td>M</td>\n",
       "      <td>DUPONT-AIGNAN</td>\n",
       "      <td>Nicolas</td>\n",
       "      <td>1</td>\n",
       "      <td>0.85</td>\n",
       "      <td>1.96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69680</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
       "      <td>2</td>\n",
       "      <td>2ème circonscription</td>\n",
       "      <td>234</td>\n",
       "      <td>Monterrey</td>\n",
       "      <td>0001</td>\n",
       "      <td>713</td>\n",
       "      <td>553</td>\n",
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       "      <td>2</td>\n",
       "      <td>2ème circonscription</td>\n",
       "      <td>235</td>\n",
       "      <td>Bahamas (Nassau)</td>\n",
       "      <td>0001</td>\n",
       "      <td>136</td>\n",
       "      <td>78</td>\n",
       "      <td>57.35</td>\n",
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       "      <td>Nicolas</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]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T1.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les données sont organisées suivant des colonnes qui vont représenter les différents choix et aussi d'autres métadonnées. Il va falloir faire quelques recherches simples pour récupérer ces données utiles…"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:23:58.041180Z",
     "iopub.status.busy": "2022-06-09T15:23:58.040594Z",
     "iopub.status.idle": "2022-06-09T15:23:58.042782Z",
     "shell.execute_reply": "2022-06-09T15:23:58.043119Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Code du département', 'Libellé du département',\n",
       "       'Code de la circonscription', 'Libellé de la circonscription',\n",
       "       'Code de la commune', 'Libellé de la commune', 'Code du b.vote',\n",
       "       'Inscrits', 'Abstentions', '% Abs/Ins',\n",
       "       ...\n",
       "       'Unnamed: 95', 'Unnamed: 96', 'Unnamed: 97', 'Unnamed: 98',\n",
       "       'Unnamed: 99', 'Unnamed: 100', 'Unnamed: 101', 'Unnamed: 102',\n",
       "       'Unnamed: 103', 'Unnamed: 104'],\n",
       "      dtype='object', length=105)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T1.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ainsi, la première colonne concerne les nuls, blancs et abstention, que l'on peut enregistrer dans un nouveau tableau :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:23:58.048311Z",
     "iopub.status.busy": "2022-06-09T15:23:58.047832Z",
     "iopub.status.idle": "2022-06-09T15:23:58.053944Z",
     "shell.execute_reply": "2022-06-09T15:23:58.053423Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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",
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       "      <th>1</th>\n",
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       "      <td>3</td>\n",
       "      <td>38</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>18</td>\n",
       "      <td>266</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>15</td>\n",
       "      <td>265</td>\n",
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       "    <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": "2022-06-09T15:23:58.060279Z",
     "iopub.status.busy": "2022-06-09T15:23:58.059660Z",
     "iopub.status.idle": "2022-06-09T15:23:58.062168Z",
     "shell.execute_reply": "2022-06-09T15:23:58.062512Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nuls</th>\n",
       "      <th>Blancs</th>\n",
       "      <th>Abstentions</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>3</td>\n",
       "      <td>38</td>\n",
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       "    <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",
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       "      <td>10</td>\n",
       "      <td>246</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
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       "    <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",
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       "    <tr>\n",
       "      <th>69679</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>64</td>\n",
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       "    <tr>\n",
       "      <th>69680</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>553</td>\n",
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       "      <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": "2022-06-09T15:23:58.066352Z",
     "iopub.status.busy": "2022-06-09T15:23:58.065740Z",
     "iopub.status.idle": "2022-06-09T15:23:58.067834Z",
     "shell.execute_reply": "2022-06-09T15:23:58.068225Z"
    }
   },
   "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 candidat par candidat :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:23:58.071456Z",
     "iopub.status.busy": "2022-06-09T15:23:58.070983Z",
     "iopub.status.idle": "2022-06-09T15:23:58.072749Z",
     "shell.execute_reply": "2022-06-09T15:23:58.073136Z"
    }
   },
   "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": "2022-06-09T15:23:58.077588Z",
     "iopub.status.busy": "2022-06-09T15:23:58.076980Z",
     "iopub.status.idle": "2022-06-09T15:23:58.079124Z",
     "shell.execute_reply": "2022-06-09T15:23:58.079526Z"
    }
   },
   "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": "2022-06-09T15:23:58.083809Z",
     "iopub.status.busy": "2022-06-09T15:23:58.083239Z",
     "iopub.status.idle": "2022-06-09T15:23:58.085402Z",
     "shell.execute_reply": "2022-06-09T15:23:58.085728Z"
    }
   },
   "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 pouvons 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": "2022-06-09T15:23:58.089669Z",
     "iopub.status.busy": "2022-06-09T15:23:58.089168Z",
     "iopub.status.idle": "2022-06-09T15:23:58.099523Z",
     "shell.execute_reply": "2022-06-09T15:23:58.099859Z"
    }
   },
   "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": "2022-06-09T15:23:58.103175Z",
     "iopub.status.busy": "2022-06-09T15:23:58.102704Z",
     "iopub.status.idle": "2022-06-09T15:23:58.111935Z",
     "shell.execute_reply": "2022-06-09T15:23:58.112303Z"
    }
   },
   "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": [
    "Une fois ce nouveau tableau comilé, ceci nous permet par exemple d'extraire les résultats pour un candidat donné et pour chacun des bureaux de vote (indexé dans l'ordre du fichier) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:23:58.116805Z",
     "iopub.status.busy": "2022-06-09T15:23:58.116241Z",
     "iopub.status.idle": "2022-06-09T15:23:58.118375Z",
     "shell.execute_reply": "2022-06-09T15:23:58.118924Z"
    }
   },
   "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": "2022-06-09T15:23:58.122142Z",
     "iopub.status.busy": "2022-06-09T15:23:58.121640Z",
     "iopub.status.idle": "2022-06-09T15:23:58.123683Z",
     "shell.execute_reply": "2022-06-09T15:23:58.124102Z"
    }
   },
   "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": "2022-06-09T15:23:58.127160Z",
     "iopub.status.busy": "2022-06-09T15:23:58.126629Z",
     "iopub.status.idle": "2022-06-09T15:23:58.133165Z",
     "shell.execute_reply": "2022-06-09T15:23:58.133503Z"
    }
   },
   "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 pourrions aussi complétement ignorer les votes 'Nuls' et 'Abstentions'. En effet, durant nos expériences (cf github) nous avons pu obtenir des modèles pour lesquelles ces valeurs étaient moins prédictibles. Dans le cadre d'un \"débogage\", on peut vouloir enlever certaines colonnes. Pour cela, 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": "2022-06-09T15:23:58.137200Z",
     "iopub.status.busy": "2022-06-09T15:23:58.136591Z",
     "iopub.status.idle": "2022-06-09T15:23:58.139143Z",
     "shell.execute_reply": "2022-06-09T15:23:58.138797Z"
    }
   },
   "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": "markdown",
   "metadata": {},
   "source": [
    "Dans ce post, nous ne l'avons pas fait, mais il suffit de décommenter la ligne suivante pour impacter le reste des calculs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:23:58.141946Z",
     "iopub.status.busy": "2022-06-09T15:23:58.141482Z",
     "iopub.status.idle": "2022-06-09T15:23:58.143310Z",
     "shell.execute_reply": "2022-06-09T15:23:58.143853Z"
    }
   },
   "outputs": [],
   "source": [
    "# df_1 = df_1.drop(columns=['Nuls', 'Blancs'])#, 'Abstentions'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:23:58.147521Z",
     "iopub.status.busy": "2022-06-09T15:23:58.146955Z",
     "iopub.status.idle": "2022-06-09T15:23:58.149140Z",
     "shell.execute_reply": "2022-06-09T15:23:58.149623Z"
    }
   },
   "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": 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": "2022-06-09T15:23:58.152944Z",
     "iopub.status.busy": "2022-06-09T15:23:58.152440Z",
     "iopub.status.idle": "2022-06-09T15:23:58.777858Z",
     "shell.execute_reply": "2022-06-09T15:23:58.778225Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:23:58.782345Z",
     "iopub.status.busy": "2022-06-09T15:23:58.781729Z",
     "iopub.status.idle": "2022-06-09T15:23:58.948621Z",
     "shell.execute_reply": "2022-06-09T15:23:58.949027Z"
    }
   },
   "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 :\n",
    " - le fort taux d'abstention qui a été observé au premier tour, \n",
    " - ainsi que les deux candidats (\"Macron\", \"Le Pen\") 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": "2022-06-09T15:23:58.954102Z",
     "iopub.status.busy": "2022-06-09T15:23:58.953415Z",
     "iopub.status.idle": "2022-06-09T15:24:22.275340Z",
     "shell.execute_reply": "2022-06-09T15:24:22.275733Z"
    }
   },
   "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 organisées suivant une structure similaire :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:22.279840Z",
     "iopub.status.busy": "2022-06-09T15:24:22.279239Z",
     "iopub.status.idle": "2022-06-09T15:24:22.281330Z",
     "shell.execute_reply": "2022-06-09T15:24:22.281729Z"
    }
   },
   "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": "2022-06-09T15:24:22.285427Z",
     "iopub.status.busy": "2022-06-09T15:24:22.284817Z",
     "iopub.status.idle": "2022-06-09T15:24:22.287148Z",
     "shell.execute_reply": "2022-06-09T15:24:22.287480Z"
    }
   },
   "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": "2022-06-09T15:24:22.290980Z",
     "iopub.status.busy": "2022-06-09T15:24:22.290500Z",
     "iopub.status.idle": "2022-06-09T15:24:22.292726Z",
     "shell.execute_reply": "2022-06-09T15:24:22.293055Z"
    }
   },
   "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": "2022-06-09T15:24:22.297145Z",
     "iopub.status.busy": "2022-06-09T15:24:22.296567Z",
     "iopub.status.idle": "2022-06-09T15:24:22.298817Z",
     "shell.execute_reply": "2022-06-09T15:24:22.299208Z"
    }
   },
   "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": "2022-06-09T15:24:22.303620Z",
     "iopub.status.busy": "2022-06-09T15:24:22.303134Z",
     "iopub.status.idle": "2022-06-09T15:24:22.305222Z",
     "shell.execute_reply": "2022-06-09T15:24:22.305622Z"
    }
   },
   "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": "2022-06-09T15:24:22.310168Z",
     "iopub.status.busy": "2022-06-09T15:24:22.309598Z",
     "iopub.status.idle": "2022-06-09T15:24:22.314386Z",
     "shell.execute_reply": "2022-06-09T15:24:22.314714Z"
    },
    "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_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": "2022-06-09T15:24:22.317983Z",
     "iopub.status.busy": "2022-06-09T15:24:22.317409Z",
     "iopub.status.idle": "2022-06-09T15:24:22.319514Z",
     "shell.execute_reply": "2022-06-09T15:24:22.319840Z"
    }
   },
   "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": "2022-06-09T15:24:22.323518Z",
     "iopub.status.busy": "2022-06-09T15:24:22.323053Z",
     "iopub.status.idle": "2022-06-09T15:24:22.326249Z",
     "shell.execute_reply": "2022-06-09T15:24:22.326564Z"
    }
   },
   "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": "2022-06-09T15:24:22.331218Z",
     "iopub.status.busy": "2022-06-09T15:24:22.329514Z",
     "iopub.status.idle": "2022-06-09T15:24:22.335413Z",
     "shell.execute_reply": "2022-06-09T15:24:22.335771Z"
    }
   },
   "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": "2022-06-09T15:24:22.375363Z",
     "iopub.status.busy": "2022-06-09T15:24:22.373079Z",
     "iopub.status.idle": "2022-06-09T15:24:22.471612Z",
     "shell.execute_reply": "2022-06-09T15:24:22.472005Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13, 5))\n",
    "k = df_2.sum()/df_2.sum().sum()\n",
    "ax = k.plot.bar(ax=ax)\n",
    "ax.set_xlabel('Candidat')\n",
    "#ax.set_xlim(1, 10)\n",
    "#ax.set_xticks(np.arange(1, 10)+.5)\n",
    "#ax.set_xticklabels(np.arange(1, 10)) , rotation=45\n",
    "ax.set_ylabel('pourcentage');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On vérifie :\n",
    " - le fort taux d'abstention observé au second tour, \n",
    " - le candidat \"Macron\" résolte le plus de suffrages exprimés (mais aussi au total)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:22.475438Z",
     "iopub.status.busy": "2022-06-09T15:24:22.474946Z",
     "iopub.status.idle": "2022-06-09T15:24:22.476642Z",
     "shell.execute_reply": "2022-06-09T15:24:22.477090Z"
    }
   },
   "outputs": [],
   "source": [
    "# à décommenter si on veut tester des prédictions sur les choix exprimés \n",
    "# df_2 = df_2.drop(columns=['Nuls', 'Blancs']])\n",
    "# df_2 = df_2.drop(columns=['Abstentions']) (en plus, sans les 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": "2022-06-09T15:24:22.480869Z",
     "iopub.status.busy": "2022-06-09T15:24:22.480400Z",
     "iopub.status.idle": "2022-06-09T15:24:22.496134Z",
     "shell.execute_reply": "2022-06-09T15:24:22.496478Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 11)"
      ]
     },
     "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": "2022-06-09T15:24:22.500807Z",
     "iopub.status.busy": "2022-06-09T15:24:22.500117Z",
     "iopub.status.idle": "2022-06-09T15:24:22.515069Z",
     "shell.execute_reply": "2022-06-09T15:24:22.515428Z"
    }
   },
   "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": "2022-06-09T15:24:22.519307Z",
     "iopub.status.busy": "2022-06-09T15:24:22.518797Z",
     "iopub.status.idle": "2022-06-09T15:24:22.524048Z",
     "shell.execute_reply": "2022-06-09T15:24:22.524434Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 2)"
      ]
     },
     "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": "2022-06-09T15:24:22.528514Z",
     "iopub.status.busy": "2022-06-09T15:24:22.527872Z",
     "iopub.status.idle": "2022-06-09T15:24:22.542764Z",
     "shell.execute_reply": "2022-06-09T15:24:22.543128Z"
    }
   },
   "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": "2022-06-09T15:24:22.546814Z",
     "iopub.status.busy": "2022-06-09T15:24:22.546328Z",
     "iopub.status.idle": "2022-06-09T15:24:22.551128Z",
     "shell.execute_reply": "2022-06-09T15:24:22.551696Z"
    }
   },
   "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": "2022-06-09T15:24:22.555393Z",
     "iopub.status.busy": "2022-06-09T15:24:22.554923Z",
     "iopub.status.idle": "2022-06-09T15:24:22.556542Z",
     "shell.execute_reply": "2022-06-09T15:24:22.557037Z"
    }
   },
   "outputs": [],
   "source": [
    "df_12 = pd.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:22.562941Z",
     "iopub.status.busy": "2022-06-09T15:24:22.560228Z",
     "iopub.status.idle": "2022-06-09T15:24:22.565461Z",
     "shell.execute_reply": "2022-06-09T15:24:22.565959Z"
    }
   },
   "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": "2022-06-09T15:24:22.569861Z",
     "iopub.status.busy": "2022-06-09T15:24:22.569277Z",
     "iopub.status.idle": "2022-06-09T15:24:22.575106Z",
     "shell.execute_reply": "2022-06-09T15:24:22.575442Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 69670 entries, 0 to 69681\n",
      "Data columns (total 2 columns):\n",
      " #   Column       Non-Null Count  Dtype\n",
      "---  ------       --------------  -----\n",
      " 0   1_MÉLENCHON  69670 non-null  int64\n",
      " 1   MACRON       69670 non-null  int64\n",
      "dtypes: int64(2)\n",
      "memory usage: 1.6 MB\n"
     ]
    }
   ],
   "source": [
    "df_12.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:22.578901Z",
     "iopub.status.busy": "2022-06-09T15:24:22.578419Z",
     "iopub.status.idle": "2022-06-09T15:24:22.582655Z",
     "shell.execute_reply": "2022-06-09T15:24:22.583151Z"
    }
   },
   "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": "2022-06-09T15:24:22.586237Z",
     "iopub.status.busy": "2022-06-09T15:24:22.585771Z",
     "iopub.status.idle": "2022-06-09T15:24:22.966503Z",
     "shell.execute_reply": "2022-06-09T15:24:22.966905Z"
    }
   },
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:22.975029Z",
     "iopub.status.busy": "2022-06-09T15:24:22.973571Z",
     "iopub.status.idle": "2022-06-09T15:24:23.725560Z",
     "shell.execute_reply": "2022-06-09T15:24:23.725871Z"
    }
   },
   "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 exposé au début de cet article.\n",
    "\n",
    "Coté esthétique, on montre aussi :\n",
    " - qu'un nuage de points est souvent trompeur, car il donne trop \"d'importance visuelle\" aux points qui sont en dehors du gros de la distribution. Ici, nous avons utilisé un histogramme qui donne une \"image\" qui semble mieux équilibrée par rapport à l'ensemble des votes (ça reste subjectif, \"dans l'œil de l'observateur\"),\n",
    " - que la forme de \"banane\" est liée au gauchissement de certaines distributions des préférences (par exemple le fait que la statistique de premier ordre de \"Mélenchon\" soit plus \"tassée\" vers $0$).\n",
    "\n",
    "## Modèle de prédiction du transfert des voix\n",
    "\n",
    "Maintenant que nous avons récolté les données pour chacun des 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 l'apprentissage automatique (machine learning en anglais) pour pouvoir inférer le report de voix entre les deux tours : Pour cela nous allons utiliser un travail précédemment effectué appliqué 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 de la Covid](https://laurentperrinet.github.io/sciblog/posts/2020-10-10-fitting-covid-data.html).\n",
    "\n",
    "### 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": "2022-06-09T15:24:23.734030Z",
     "iopub.status.busy": "2022-06-09T15:24:23.733460Z",
     "iopub.status.idle": "2022-06-09T15:24:23.735880Z",
     "shell.execute_reply": "2022-06-09T15:24:23.736370Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nuls</th>\n",
       "      <th>Blancs</th>\n",
       "      <th>Abstentions</th>\n",
       "      <th>ARTHAUD</th>\n",
       "      <th>ROUSSEL</th>\n",
       "      <th>MACRON</th>\n",
       "      <th>LASSALLE</th>\n",
       "      <th>LE PEN</th>\n",
       "      <th>ZEMMOUR</th>\n",
       "      <th>MÉLENCHON</th>\n",
       "      <th>HIDALGO</th>\n",
       "      <th>JADOT</th>\n",
       "      <th>PÉCRESSE</th>\n",
       "      <th>POUTOU</th>\n",
       "      <th>DUPONT-AIGNAN</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>108</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>150</td>\n",
       "      <td>18</td>\n",
       "      <td>149</td>\n",
       "      <td>43</td>\n",
       "      <td>66</td>\n",
       "      <td>5</td>\n",
       "      <td>30</td>\n",
       "      <td>26</td>\n",
       "      <td>3</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>38</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>50</td>\n",
       "      <td>10</td>\n",
       "      <td>23</td>\n",
       "      <td>14</td>\n",
       "      <td>41</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>18</td>\n",
       "      <td>266</td>\n",
       "      <td>4</td>\n",
       "      <td>30</td>\n",
       "      <td>159</td>\n",
       "      <td>24</td>\n",
       "      <td>237</td>\n",
       "      <td>69</td>\n",
       "      <td>216</td>\n",
       "      <td>15</td>\n",
       "      <td>25</td>\n",
       "      <td>40</td>\n",
       "      <td>8</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>15</td>\n",
       "      <td>265</td>\n",
       "      <td>6</td>\n",
       "      <td>13</td>\n",
       "      <td>201</td>\n",
       "      <td>19</td>\n",
       "      <td>210</td>\n",
       "      <td>68</td>\n",
       "      <td>194</td>\n",
       "      <td>19</td>\n",
       "      <td>46</td>\n",
       "      <td>42</td>\n",
       "      <td>4</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>246</td>\n",
       "      <td>8</td>\n",
       "      <td>18</td>\n",
       "      <td>229</td>\n",
       "      <td>28</td>\n",
       "      <td>227</td>\n",
       "      <td>74</td>\n",
       "      <td>227</td>\n",
       "      <td>16</td>\n",
       "      <td>65</td>\n",
       "      <td>35</td>\n",
       "      <td>3</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Nuls  Blancs  Abstentions  ARTHAUD  ROUSSEL  MACRON  LASSALLE  LE PEN  \\\n",
       "0     1      16          108        3        6     150        18     149   \n",
       "1     1       3           38        2        7      50        10      23   \n",
       "2     5      18          266        4       30     159        24     237   \n",
       "3     6      15          265        6       13     201        19     210   \n",
       "4     8      10          246        8       18     229        28     227   \n",
       "\n",
       "   ZEMMOUR  MÉLENCHON  HIDALGO  JADOT  PÉCRESSE  POUTOU  DUPONT-AIGNAN  \n",
       "0       43         66        5     30        26       3             21  \n",
       "1       14         41        3     10         8       3              0  \n",
       "2       69        216       15     25        40       8             13  \n",
       "3       68        194       19     46        42       4             20  \n",
       "4       74        227       16     65        35       3             19  "
      ]
     },
     "execution_count": 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": "2022-06-09T15:24:23.740186Z",
     "iopub.status.busy": "2022-06-09T15:24:23.739663Z",
     "iopub.status.idle": "2022-06-09T15:24:23.741958Z",
     "shell.execute_reply": "2022-06-09T15:24:23.742309Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "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": "2022-06-09T15:24:23.746097Z",
     "iopub.status.busy": "2022-06-09T15:24:23.745534Z",
     "iopub.status.idle": "2022-06-09T15:24:23.747788Z",
     "shell.execute_reply": "2022-06-09T15:24:23.748209Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((69670, 15), (69670, 5))"
      ]
     },
     "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": "2022-06-09T15:24:23.751821Z",
     "iopub.status.busy": "2022-06-09T15:24:23.751341Z",
     "iopub.status.idle": "2022-06-09T15:24:24.253490Z",
     "shell.execute_reply": "2022-06-09T15:24:24.253900Z"
    }
   },
   "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": "2022-06-09T15:24:24.257665Z",
     "iopub.status.busy": "2022-06-09T15:24:24.257051Z",
     "iopub.status.idle": "2022-06-09T15:24:24.259263Z",
     "shell.execute_reply": "2022-06-09T15:24:24.259593Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([69670, 15])"
      ]
     },
     "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 utilisées pour apprendre le modèle (base d'apprentissage), avec celles qui sont utilisées pour tester ce modèle (base de test) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.263741Z",
     "iopub.status.busy": "2022-06-09T15:24:24.263249Z",
     "iopub.status.idle": "2022-06-09T15:24:24.268391Z",
     "shell.execute_reply": "2022-06-09T15:24:24.268773Z"
    }
   },
   "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) * 0.9)\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])"
   ]
  },
  {
   "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": "2022-06-09T15:24:24.272332Z",
     "iopub.status.busy": "2022-06-09T15:24:24.271838Z",
     "iopub.status.idle": "2022-06-09T15:24:24.273456Z",
     "shell.execute_reply": "2022-06-09T15:24:24.273956Z"
    }
   },
   "outputs": [],
   "source": [
    "train_loader = DataLoader(train_set, batch_size=32, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.277015Z",
     "iopub.status.busy": "2022-06-09T15:24:24.276471Z",
     "iopub.status.idle": "2022-06-09T15:24:24.282108Z",
     "shell.execute_reply": "2022-06-09T15:24:24.282542Z"
    }
   },
   "outputs": [],
   "source": [
    "for n_1, n_2 in train_loader:\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Durant l'apprentissage, nous allons utiliser la méthode classique de « séparation par paquets ». Ceci consiste à séparer les données de façon aléatoire sous forme de différents « paquets » de bureaux de vote dont la taille est fixée ici à $32$. Nous vérifierons plus tard que si cette procédure permet d'accélérer l'apprentissage - la taille du paquet n'ayant qu'une influence sur la vitesse pour obtenir le résultat final (et non sur le résultat)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.286001Z",
     "iopub.status.busy": "2022-06-09T15:24:24.285428Z",
     "iopub.status.idle": "2022-06-09T15:24:24.287688Z",
     "shell.execute_reply": "2022-06-09T15:24:24.288086Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([32, 15]), torch.Size([32, 5]))"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_1.shape, n_2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans chaque paquet (de bureaux de votes tirés au hasard sur la population française), nous pouvons compter le nombre de votes pour les différentes alternatives :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.291825Z",
     "iopub.status.busy": "2022-06-09T15:24:24.291349Z",
     "iopub.status.idle": "2022-06-09T15:24:24.294953Z",
     "shell.execute_reply": "2022-06-09T15:24:24.295290Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([ 722.,   98., 1090.,  707.,  905.,  944.,  597., 1201.,  334.,  987.,\n",
       "          652.,  134., 1153.,   38., 1398.,  793., 1018.,  840.,  263.,   64.,\n",
       "         1067.,  572.,  355.,  912.,  735.,  733.,  748., 1073.,  335.,  536.,\n",
       "          629., 1030.]),\n",
       " tensor([ 723.,   98., 1092.,  707.,  905.,  945.,  597., 1201.,  334.,  989.,\n",
       "          653.,  134., 1153.,   38., 1396.,  793., 1018.,  840.,  263.,   64.,\n",
       "         1069.,  572.,  355.,  912.,  737.,  733.,  749., 1075.,  335.,  536.,\n",
       "          629., 1030.]))"
      ]
     },
     "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 alternatives, on peut calculer des fréquences d'occurrence, et que comme chaque individu peut faire un seul choix et un seul, la somme de ses fréquences d'occurrence pour chacun des paquets est égale à $1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.298958Z",
     "iopub.status.busy": "2022-06-09T15:24:24.298348Z",
     "iopub.status.idle": "2022-06-09T15:24:24.301244Z",
     "shell.execute_reply": "2022-06-09T15:24:24.301596Z"
    }
   },
   "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": "2022-06-09T15:24:24.305667Z",
     "iopub.status.busy": "2022-06-09T15:24:24.305060Z",
     "iopub.status.idle": "2022-06-09T15:24:24.308612Z",
     "shell.execute_reply": "2022-06-09T15:24:24.308967Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([6967, 15]), torch.Size([6967, 5]))"
      ]
     },
     "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 formaté les données, nous allons exprimer dans le langage de la librairie `torch` 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 matrice de poids `self.lin.weight`. Ces poids sont des valeurs réelles (sous format d'un `logit`) et sont utilisées  de telle sorte que la contrainte qui fait que la somme des éléments sur chaque ligne est bien égale à $1$ (grâce à l'utilisation de `torch.softmax(self.lin.weight, axis=1)` avant chaque codage) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.313732Z",
     "iopub.status.busy": "2022-06-09T15:24:24.313256Z",
     "iopub.status.idle": "2022-06-09T15:24:24.314802Z",
     "shell.execute_reply": "2022-06-09T15:24:24.315190Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch.utils.data import TensorDataset, DataLoader, random_split\n",
    "import torch.nn.functional as F\n",
    "\n",
    "torch.set_default_tensor_type(\"torch.FloatTensor\")\n",
    "\n",
    "class TransfertVoix(torch.nn.Module):\n",
    "    def __init__(self, N_1er, N_2eme):#, device=None):\n",
    "        super(TransfertVoix, self).__init__()\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",
    "        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": "2022-06-09T15:24:24.318741Z",
     "iopub.status.busy": "2022-06-09T15:24:24.318119Z",
     "iopub.status.idle": "2022-06-09T15:24:24.320481Z",
     "shell.execute_reply": "2022-06-09T15:24:24.320809Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15, 5)"
      ]
     },
     "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 initialement choisie de façon totalement aléatoire et donc déconnecté des données à la première époque de cet apprentissage :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.323943Z",
     "iopub.status.busy": "2022-06-09T15:24:24.323468Z",
     "iopub.status.idle": "2022-06-09T15:24:24.325258Z",
     "shell.execute_reply": "2022-06-09T15:24:24.325736Z"
    }
   },
   "outputs": [],
   "source": [
    "trans = TransfertVoix(N_1er, N_2eme)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.328892Z",
     "iopub.status.busy": "2022-06-09T15:24:24.328387Z",
     "iopub.status.idle": "2022-06-09T15:24:24.331442Z",
     "shell.execute_reply": "2022-06-09T15:24:24.331774Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[ 0.3532, -0.4249, -0.1104, -0.0098,  0.3663],\n",
      "        [ 0.1314,  0.1393,  0.2407, -0.2820, -0.2106],\n",
      "        [-0.1837, -0.2016, -0.3132,  0.4245,  0.1353],\n",
      "        [ 0.1423,  0.0523,  0.2604, -0.2651, -0.1407],\n",
      "        [-0.3224,  0.0649, -0.3304, -0.0631, -0.2614],\n",
      "        [-0.2406,  0.1892,  0.2505, -0.2691, -0.2399],\n",
      "        [-0.2697,  0.0210, -0.1019, -0.0457,  0.1510],\n",
      "        [-0.3081, -0.1536, -0.2883, -0.0966, -0.1921],\n",
      "        [-0.1968, -0.0381, -0.3438,  0.1664,  0.1303],\n",
      "        [ 0.4051, -0.3519, -0.3098, -0.3335,  0.4097],\n",
      "        [ 0.2001, -0.3427, -0.0740,  0.0525, -0.2990],\n",
      "        [ 0.2742, -0.4451,  0.1304, -0.4326, -0.1397],\n",
      "        [ 0.3331,  0.2803, -0.1192, -0.2880, -0.4419],\n",
      "        [-0.3071, -0.2627,  0.2995, -0.0703, -0.1361],\n",
      "        [-0.2800, -0.2266, -0.4155, -0.1032,  0.0963]], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "for p in trans.parameters():print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.335089Z",
     "iopub.status.busy": "2022-06-09T15:24:24.334446Z",
     "iopub.status.idle": "2022-06-09T15:24:24.337011Z",
     "shell.execute_reply": "2022-06-09T15:24:24.337399Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([15, 5])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans.lin.weight.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.340787Z",
     "iopub.status.busy": "2022-06-09T15:24:24.340320Z",
     "iopub.status.idle": "2022-06-09T15:24:24.343505Z",
     "shell.execute_reply": "2022-06-09T15:24:24.343855Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.2634, 0.1210, 0.1657, 0.1832, 0.2668],\n",
       "        [0.2225, 0.2242, 0.2482, 0.1471, 0.1580],\n",
       "        [0.1646, 0.1617, 0.1446, 0.3025, 0.2265],\n",
       "        [0.2243, 0.2050, 0.2524, 0.1492, 0.1690],\n",
       "        [0.1717, 0.2529, 0.1703, 0.2225, 0.1825],\n",
       "        [0.1628, 0.2502, 0.2660, 0.1582, 0.1629],\n",
       "        [0.1589, 0.2125, 0.1879, 0.1988, 0.2420],\n",
       "        [0.1803, 0.2105, 0.1839, 0.2228, 0.2025],\n",
       "        [0.1706, 0.2000, 0.1473, 0.2454, 0.2367],\n",
       "        [0.2906, 0.1363, 0.1422, 0.1389, 0.2920],\n",
       "        [0.2624, 0.1525, 0.1995, 0.2264, 0.1593],\n",
       "        [0.2851, 0.1389, 0.2469, 0.1406, 0.1885],\n",
       "        [0.2791, 0.2648, 0.1776, 0.1500, 0.1286],\n",
       "        [0.1579, 0.1651, 0.2896, 0.2001, 0.1873],\n",
       "        [0.1793, 0.1891, 0.1565, 0.2139, 0.2612]], 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 ligne de la matrice de transition et bien vérifiée :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.346998Z",
     "iopub.status.busy": "2022-06-09T15:24:24.346535Z",
     "iopub.status.idle": "2022-06-09T15:24:24.349775Z",
     "shell.execute_reply": "2022-06-09T15:24:24.350128Z"
    },
    "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, 1.0000, 1.0000, 1.0000],\n",
       "       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": "2022-06-09T15:24:24.353771Z",
     "iopub.status.busy": "2022-06-09T15:24:24.353238Z",
     "iopub.status.idle": "2022-06-09T15:24:24.355159Z",
     "shell.execute_reply": "2022-06-09T15:24:24.355638Z"
    }
   },
   "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 multipliée 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": "markdown",
   "metadata": {},
   "source": [
    " - entrée (et sa somme sur les différents choix au 1er tour):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.359246Z",
     "iopub.status.busy": "2022-06-09T15:24:24.358725Z",
     "iopub.status.idle": "2022-06-09T15:24:24.361588Z",
     "shell.execute_reply": "2022-06-09T15:24:24.362009Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([6967, 15]),\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": "markdown",
   "metadata": {},
   "source": [
    " - transition:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.365486Z",
     "iopub.status.busy": "2022-06-09T15:24:24.364904Z",
     "iopub.status.idle": "2022-06-09T15:24:24.367196Z",
     "shell.execute_reply": "2022-06-09T15:24:24.367549Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([15, 5])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans.lin.weight.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - sortie:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.370996Z",
     "iopub.status.busy": "2022-06-09T15:24:24.370499Z",
     "iopub.status.idle": "2022-06-09T15:24:24.375676Z",
     "shell.execute_reply": "2022-06-09T15:24:24.375297Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([6967, 5])"
      ]
     },
     "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": "2022-06-09T15:24:24.379177Z",
     "iopub.status.busy": "2022-06-09T15:24:24.378620Z",
     "iopub.status.idle": "2022-06-09T15:24:24.382294Z",
     "shell.execute_reply": "2022-06-09T15:24:24.382695Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.1973, 0.1938, 0.1855, 0.2101, 0.2133], 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": [
    "(Ce premier résultat est sûrement faux car les poids sont initialement fixés aléatoirement)."
   ]
  },
  {
   "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": "2022-06-09T15:24:24.386864Z",
     "iopub.status.busy": "2022-06-09T15:24:24.386241Z",
     "iopub.status.idle": "2022-06-09T15:24:24.389756Z",
     "shell.execute_reply": "2022-06-09T15:24:24.390110Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.0189, 0.0505, 0.2536, 0.3714, 0.3057]), 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": "2022-06-09T15:24:24.408422Z",
     "iopub.status.busy": "2022-06-09T15:24:24.407679Z",
     "iopub.status.idle": "2022-06-09T15:24:24.509456Z",
     "shell.execute_reply": "2022-06-09T15:24:24.509798Z"
    }
   },
   "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, 'r')\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": "2022-06-09T15:24:24.514453Z",
     "iopub.status.busy": "2022-06-09T15:24:24.513937Z",
     "iopub.status.idle": "2022-06-09T15:24:24.516756Z",
     "shell.execute_reply": "2022-06-09T15:24:24.517188Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Nuls            1.651714\n",
       " Blancs          4.582147\n",
       " Abstentions    28.010677\n",
       " MACRON         38.497926\n",
       " LE PEN         27.257536\n",
       " dtype: float64,\n",
       " tensor([ 1.7085,  4.6699, 27.4290, 38.3725, 27.8200]))"
      ]
     },
     "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": "2022-06-09T15:24:24.520807Z",
     "iopub.status.busy": "2022-06-09T15:24:24.520251Z",
     "iopub.status.idle": "2022-06-09T15:24:24.523099Z",
     "shell.execute_reply": "2022-06-09T15:24:24.523425Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.1197)"
      ]
     },
     "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. C'est donc un algorithme supervisé par les observations (sur les données de la base d'apprentissage) et que nous allons pouvoir tester sur la base de test.\n",
    "\n",
    "Nous allons utiliser les distributions du second tour 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) entre deux distributions $P$ et $Q$ de support non-nul $k \\in \\Omega$ est calculée comme\n",
    "\n",
    "$$\n",
    "KL(P, Q) = \\sum_{k \\in \\Omega} P_k \\cdot \\log \\frac {P_k}{Q_k}\n",
    "$$\n",
    "\n",
    "\n",
    "Cette divergence est l'équivalent d'une distance dans les espaces de probabilité. Mathématiquement, c'est une semi-norme, car elle obéit à deux propriétés fondamentales : elle est toujours positive et est égale à zéro quand elle est appliquée à distributions identiques.\n",
    "\n",
    "Pour généraliser cette méthode, nous allons aussi utiliser deux autres mesures et montrer ensuite que les résultats quantitatifs sont similaires :\n",
    "- L1: la somme des valeurs absolues des différences entre les valeurs prédites et observées,\n",
    "- BCE: la norme traditionnellement utilisée en régression multinomiale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.526770Z",
     "iopub.status.busy": "2022-06-09T15:24:24.526224Z",
     "iopub.status.idle": "2022-06-09T15:24:24.527995Z",
     "shell.execute_reply": "2022-06-09T15:24:24.528581Z"
    }
   },
   "outputs": [],
   "source": [
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.543437Z",
     "iopub.status.busy": "2022-06-09T15:24:24.542934Z",
     "iopub.status.idle": "2022-06-09T15:24:24.544872Z",
     "shell.execute_reply": "2022-06-09T15:24:24.545240Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch.nn.functional as F\n",
    "\n",
    "learning_rate = 10.0\n",
    "beta1, beta2 = 0.99, 0\n",
    "# beta1, beta2 = 0.9, 0.999 # décommenter pour utiliser Adam\n",
    "num_epochs = 2 ** 5 + 1\n",
    "num_epochs = 2 ** 10 + 1\n",
    "batch_size = 256\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",
    "        N_2eme = p.shape[1]\n",
    "        div = torch.absolute(p - p_pred)\n",
    "        loss_train = (div * weight[:, None]).sum() / N_2eme\n",
    "    else: # BCE\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",
    "    n_1, n_2 = dataset[train_set.indices]\n",
    "    sum_sum_2 = n_2.sum()\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 / sum_sum_2 # 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 / sum_2.sum() # normalise par rapport à la taille du dataset de test\n",
    "        loss_test = pdf_loss(p_2_pred, p_2, weight, loss_type=loss_type)\n",
    "        loss_test_l1 = pdf_loss(p_2_pred, p_2, weight, loss_type='l1')\n",
    "        if verbose: print(f'Erreur ~ {loss_test_l1.item()*100:.1f}%')\n",
    "\n",
    "    return trans, loss_train, loss_test, loss_test_l1, p_1.detach().numpy(), p_2.detach().numpy(), p_2_pred.detach().numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Résulats\n",
    "\n",
    "### Convergence de l'apprentissage suivant plusieurs fonctions de coût"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:24:24.551818Z",
     "iopub.status.busy": "2022-06-09T15:24:24.550806Z",
     "iopub.status.idle": "2022-06-09T15:44:11.805938Z",
     "shell.execute_reply": "2022-06-09T15:44:11.806279Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='l1'\n",
      "Iteration: 0 / 1025 - Loss: 6.40975e-02\n",
      "Iteration: 32 / 1025 - Loss: 1.63781e-02\n",
      "Iteration: 64 / 1025 - Loss: 1.61895e-02\n",
      "Iteration: 96 / 1025 - Loss: 1.61289e-02\n",
      "Iteration: 128 / 1025 - Loss: 1.60956e-02\n",
      "Iteration: 160 / 1025 - Loss: 1.60780e-02\n",
      "Iteration: 192 / 1025 - Loss: 1.60647e-02\n",
      "Iteration: 224 / 1025 - Loss: 1.60588e-02\n",
      "Iteration: 256 / 1025 - Loss: 1.60487e-02\n",
      "Iteration: 288 / 1025 - Loss: 1.60473e-02\n",
      "Iteration: 320 / 1025 - Loss: 1.60419e-02\n",
      "Iteration: 352 / 1025 - Loss: 1.60354e-02\n",
      "Iteration: 384 / 1025 - Loss: 1.60370e-02\n",
      "Iteration: 416 / 1025 - Loss: 1.60405e-02\n",
      "Iteration: 448 / 1025 - Loss: 1.60306e-02\n",
      "Iteration: 480 / 1025 - Loss: 1.60271e-02\n",
      "Iteration: 512 / 1025 - Loss: 1.60262e-02\n",
      "Iteration: 544 / 1025 - Loss: 1.60275e-02\n",
      "Iteration: 576 / 1025 - Loss: 1.60279e-02\n",
      "Iteration: 608 / 1025 - Loss: 1.60300e-02\n",
      "Iteration: 640 / 1025 - Loss: 1.60278e-02\n",
      "Iteration: 672 / 1025 - Loss: 1.60227e-02\n",
      "Iteration: 704 / 1025 - Loss: 1.60187e-02\n",
      "Iteration: 736 / 1025 - Loss: 1.60158e-02\n",
      "Iteration: 768 / 1025 - Loss: 1.60266e-02\n",
      "Iteration: 800 / 1025 - Loss: 1.60175e-02\n",
      "Iteration: 832 / 1025 - Loss: 1.60171e-02\n",
      "Iteration: 864 / 1025 - Loss: 1.60178e-02\n",
      "Iteration: 896 / 1025 - Loss: 1.60152e-02\n",
      "Iteration: 928 / 1025 - Loss: 1.60174e-02\n",
      "Iteration: 960 / 1025 - Loss: 1.60232e-02\n",
      "Iteration: 992 / 1025 - Loss: 1.60135e-02\n",
      "Iteration: 1024 / 1025 - Loss: 1.60157e-02\n",
      "Erreur ~ 1.6%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='kl'\n",
      "Iteration: 0 / 1025 - Loss: 7.55288e-02\n",
      "Iteration: 32 / 1025 - Loss: 1.11190e-02\n",
      "Iteration: 64 / 1025 - Loss: 1.10002e-02\n",
      "Iteration: 96 / 1025 - Loss: 1.09653e-02\n",
      "Iteration: 128 / 1025 - Loss: 1.09267e-02\n",
      "Iteration: 160 / 1025 - Loss: 1.09112e-02\n",
      "Iteration: 192 / 1025 - Loss: 1.09057e-02\n",
      "Iteration: 224 / 1025 - Loss: 1.08782e-02\n",
      "Iteration: 256 / 1025 - Loss: 1.08378e-02\n",
      "Iteration: 288 / 1025 - Loss: 1.08269e-02\n",
      "Iteration: 320 / 1025 - Loss: 1.08161e-02\n",
      "Iteration: 352 / 1025 - Loss: 1.08035e-02\n",
      "Iteration: 384 / 1025 - Loss: 1.08113e-02\n",
      "Iteration: 416 / 1025 - Loss: 1.08095e-02\n",
      "Iteration: 448 / 1025 - Loss: 1.08075e-02\n",
      "Iteration: 480 / 1025 - Loss: 1.08146e-02\n",
      "Iteration: 512 / 1025 - Loss: 1.08062e-02\n",
      "Iteration: 544 / 1025 - Loss: 1.08053e-02\n",
      "Iteration: 576 / 1025 - Loss: 1.08002e-02\n",
      "Iteration: 608 / 1025 - Loss: 1.07952e-02\n",
      "Iteration: 640 / 1025 - Loss: 1.08064e-02\n",
      "Iteration: 672 / 1025 - Loss: 1.07950e-02\n",
      "Iteration: 704 / 1025 - Loss: 1.07948e-02\n",
      "Iteration: 736 / 1025 - Loss: 1.08039e-02\n",
      "Iteration: 768 / 1025 - Loss: 1.07900e-02\n",
      "Iteration: 800 / 1025 - Loss: 1.07911e-02\n",
      "Iteration: 832 / 1025 - Loss: 1.07972e-02\n",
      "Iteration: 864 / 1025 - Loss: 1.07919e-02\n",
      "Iteration: 896 / 1025 - Loss: 1.08087e-02\n",
      "Iteration: 928 / 1025 - Loss: 1.07883e-02\n",
      "Iteration: 960 / 1025 - Loss: 1.08002e-02\n",
      "Iteration: 992 / 1025 - Loss: 1.07893e-02\n",
      "Iteration: 1024 / 1025 - Loss: 1.07961e-02\n",
      "Erreur ~ 1.7%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='bce'\n",
      "Iteration: 0 / 1025 - Loss: 8.66346e-02\n",
      "Iteration: 32 / 1025 - Loss: 1.44177e-02\n",
      "Iteration: 64 / 1025 - Loss: 1.39880e-02\n",
      "Iteration: 96 / 1025 - Loss: 1.36400e-02\n",
      "Iteration: 128 / 1025 - Loss: 1.35635e-02\n",
      "Iteration: 160 / 1025 - Loss: 1.35378e-02\n",
      "Iteration: 192 / 1025 - Loss: 1.35256e-02\n",
      "Iteration: 224 / 1025 - Loss: 1.35254e-02\n",
      "Iteration: 256 / 1025 - Loss: 1.35203e-02\n",
      "Iteration: 288 / 1025 - Loss: 1.35240e-02\n",
      "Iteration: 320 / 1025 - Loss: 1.35519e-02\n",
      "Iteration: 352 / 1025 - Loss: 1.34987e-02\n",
      "Iteration: 384 / 1025 - Loss: 1.35054e-02\n",
      "Iteration: 416 / 1025 - Loss: 1.34933e-02\n",
      "Iteration: 448 / 1025 - Loss: 1.35059e-02\n",
      "Iteration: 480 / 1025 - Loss: 1.34897e-02\n",
      "Iteration: 512 / 1025 - Loss: 1.34902e-02\n",
      "Iteration: 544 / 1025 - Loss: 1.34938e-02\n",
      "Iteration: 576 / 1025 - Loss: 1.34798e-02\n",
      "Iteration: 608 / 1025 - Loss: 1.34926e-02\n",
      "Iteration: 640 / 1025 - Loss: 1.34872e-02\n",
      "Iteration: 672 / 1025 - Loss: 1.35011e-02\n",
      "Iteration: 704 / 1025 - Loss: 1.34880e-02\n",
      "Iteration: 736 / 1025 - Loss: 1.34943e-02\n",
      "Iteration: 768 / 1025 - Loss: 1.34903e-02\n",
      "Iteration: 800 / 1025 - Loss: 1.34824e-02\n",
      "Iteration: 832 / 1025 - Loss: 1.34923e-02\n",
      "Iteration: 864 / 1025 - Loss: 1.34855e-02\n",
      "Iteration: 896 / 1025 - Loss: 1.34866e-02\n",
      "Iteration: 928 / 1025 - Loss: 1.34847e-02\n",
      "Iteration: 960 / 1025 - Loss: 1.34858e-02\n",
      "Iteration: 992 / 1025 - Loss: 1.35008e-02\n",
      "Iteration: 1024 / 1025 - Loss: 1.34896e-02\n",
      "Erreur ~ 1.7%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for loss_type in ['l1', 'kl', 'bce',]:\n",
    "    print(f'{loss_type=}')\n",
    "    trans, loss_train, loss_test, loss_test_l1, 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(\"Résultat \" + candidat)\n",
    "        axs[i_col].set_xlim(0, 1)\n",
    "        axs[i_col].set_ylim(0, 1)\n",
    "    axs[0].set_ylabel(\"Prédiction \")\n",
    "    plt.suptitle(\"Prédiction des résultats pour chaque choix au 2ème tour\", fontsize=16)\n",
    "    plt.subplots_adjust(left=0.1, bottom=0.1, right=0.95, top=0.9)\n",
    "    plt.savefig(datetime + '_prediction_transfert-des-voix_' + loss_type +'.png');\n",
    "    plt.show()\n"
   ]
  },
  {
   "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 bureaux de vote (tirés au hasard, environ $7000$).\n",
    "\n",
    "On remarque de suite une prédiction très correcte des données du second tour à partir des observations du premier. Ceci montre la validité de notre hypothèse de transition, et aussi de son homognénéité dans le teritoire. On note aussi que les trois méthodes donnent sensiblement des résultats similaires et nous allons utiliser `bce` dans la suite.\n",
    "\n",
    "Il faut noter que le nombre de paramètres libres de notre modèle est simplement celui de la matrice de transition stochastique soit $4 \\times 15 = 60$.\n",
    "\n",
    "Pour avoir une idée de l'erreur de prédiction, on peut estimer l'erreur absolue moyenne, c'est à dire la moyenne de l'écart observé sur la population:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:11.809776Z",
     "iopub.status.busy": "2022-06-09T15:44:11.809304Z",
     "iopub.status.idle": "2022-06-09T15:44:11.811104Z",
     "shell.execute_reply": "2022-06-09T15:44:11.811607Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Erreur ~ 1.7%\n"
     ]
    }
   ],
   "source": [
    "print(f'Erreur ~ {loss_test_l1.item()*100:.1f}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'erreur est relativement faible (inférieure à 2 points de pourcentage) mais il faut garder en tête qu'elle présente des variations important par bureau de vote.\n",
    "\n",
    "### analyse de le matrice de transition\n",
    "\n",
    "On peut maintenant récupérer du modèle la matrice de transition qui a été inférée grâce a notre apprentissage automatique :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:11.815646Z",
     "iopub.status.busy": "2022-06-09T15:44:11.814432Z",
     "iopub.status.idle": "2022-06-09T15:44:11.817903Z",
     "shell.execute_reply": "2022-06-09T15:44:11.818289Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.22462106e-01, 2.38107704e-02, 2.16653920e-03, 1.35150552e-01,\n",
       "        4.16409969e-01],\n",
       "       [1.25217410e-02, 6.02925777e-01, 1.24712114e-03, 1.87495118e-03,\n",
       "        3.81430387e-01],\n",
       "       [2.24835298e-06, 1.73289554e-05, 8.99260223e-01, 2.10442711e-02,\n",
       "        7.96758831e-02],\n",
       "       [2.90501952e-01, 1.25755202e-02, 1.87223486e-03, 2.31431494e-03,\n",
       "        6.92735970e-01],\n",
       "       [1.59886003e-01, 3.94331962e-01, 2.60606105e-03, 3.01951393e-02,\n",
       "        4.12980825e-01],\n",
       "       [2.01579169e-07, 1.28099327e-06, 3.69888876e-05, 9.99914289e-01,\n",
       "        4.72215652e-05],\n",
       "       [1.83704972e-01, 2.80349672e-01, 1.00350019e-03, 1.77587860e-03,\n",
       "        5.33165932e-01],\n",
       "       [6.18519664e-07, 1.03414561e-06, 1.90748451e-05, 1.76127705e-05,\n",
       "        9.99961615e-01],\n",
       "       [6.31992426e-03, 7.43023679e-02, 5.65578565e-02, 2.04505101e-01,\n",
       "        6.58314824e-01],\n",
       "       [1.83869135e-02, 7.29578361e-02, 2.77632922e-01, 6.03558481e-01,\n",
       "        2.74639111e-02],\n",
       "       [5.71057610e-02, 2.14592353e-01, 1.46875379e-03, 7.24952996e-01,\n",
       "        1.88017054e-03],\n",
       "       [8.52782905e-05, 1.16634439e-03, 1.20680554e-04, 9.98534441e-01,\n",
       "        9.32412731e-05],\n",
       "       [2.60630436e-02, 1.25730798e-01, 1.33752404e-03, 8.45501304e-01,\n",
       "        1.36736606e-03],\n",
       "       [1.71328634e-01, 5.20844698e-01, 4.50346153e-03, 1.16699608e-02,\n",
       "        2.91653246e-01],\n",
       "       [1.81171037e-02, 5.42829074e-02, 9.90897883e-04, 1.20818859e-03,\n",
       "        9.25400853e-01]], dtype=float32)"
      ]
     },
     "execution_count": 77,
     "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": 78,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:11.822209Z",
     "iopub.status.busy": "2022-06-09T15:44:11.821698Z",
     "iopub.status.idle": "2022-06-09T15:44:11.823877Z",
     "shell.execute_reply": "2022-06-09T15:44:11.824209Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.99999994, 0.99999994, 0.9999999 , 1.        , 0.9999999 ,\n",
       "        0.99999994, 1.        , 0.99999994, 1.        , 1.        ,\n",
       "        1.        , 0.99999994, 1.        , 1.        , 0.99999994],\n",
       "       dtype=float32),\n",
       " (15, 5))"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.sum(axis=1), M.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Une particularité de cette matrice (prédite sur l'ensemble des bureaux de votes) est que l'on peut maintenant s'en servir pour prédire la préférence au second tour en fonction de celle au premier.\n",
    "\n",
    "En effet, si la préférence pour le choix d'un individu se pose au premier tour *entièrement* sur le choix $i^\\ast$, on peut le formaliser comme $p_i = 0$ pour $i \\neq i^\\ast$ et $p_{i^\\ast}=1$ et on obtient la prédiction:\n",
    "\n",
    "$$\n",
    "\\hat{q}_j = M_{i^\\ast j}\n",
    "$$\n",
    "\n",
    "En language commun, la préférence d'une personne votant $i^\\ast$ au premier tour est la $i^\\ast$-ième ligne de la matrice de transition (de taille $15 \\times 5$ dans notre cas)."
   ]
  },
  {
   "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 visuellement ces préférences de report de voix en fonction de chacun des choix éfféctués au premier tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:11.828393Z",
     "iopub.status.busy": "2022-06-09T15:44:11.827864Z",
     "iopub.status.idle": "2022-06-09T15:44:11.830015Z",
     "shell.execute_reply": "2022-06-09T15:44:11.830346Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 42.2,   2.4,   0.2,  13.5,  41.6],\n",
       "       [  1.3,  60.3,   0.1,   0.2,  38.1],\n",
       "       [  0. ,   0. ,  89.9,   2.1,   8. ],\n",
       "       [ 29.1,   1.3,   0.2,   0.2,  69.3],\n",
       "       [ 16. ,  39.4,   0.3,   3. ,  41.3],\n",
       "       [  0. ,   0. ,   0. , 100. ,   0. ],\n",
       "       [ 18.4,  28. ,   0.1,   0.2,  53.3],\n",
       "       [  0. ,   0. ,   0. ,   0. , 100. ],\n",
       "       [  0.6,   7.4,   5.7,  20.5,  65.8],\n",
       "       [  1.8,   7.3,  27.8,  60.4,   2.7],\n",
       "       [  5.7,  21.5,   0.1,  72.5,   0.2],\n",
       "       [  0. ,   0.1,   0. ,  99.9,   0. ],\n",
       "       [  2.6,  12.6,   0.1,  84.6,   0.1],\n",
       "       [ 17.1,  52.1,   0.5,   1.2,  29.2],\n",
       "       [  1.8,   5.4,   0.1,   0.1,  92.5]], dtype=float32)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(precision=1)\n",
    "np.set_printoptions(suppress=True)\n",
    "M*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:11.838215Z",
     "iopub.status.busy": "2022-06-09T15:44:11.837163Z",
     "iopub.status.idle": "2022-06-09T15:44:12.494172Z",
     "shell.execute_reply": "2022-06-09T15:44:12.494508Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kkEMydOjQ/Pe//52iuNt/DyNGjMg3vvGNfPDBBx91FTTdlBw3tttuuw5lseKKK05ynieccEJ93L/+9a/1/osuumh+/OMfdzrN7rvvnnnnnTePP/547r333px//vlTdF3629/+NmeffXZuv/32jB49OmeddVaGDRuWf/3rX/VxXn755fz+97+f7Ly6sxNOOCGjRo3Ko48+mpVXXjlf+MIXOhyXP8z10VlnnZU//vGPufPOO/Pggw/m7rvvzgILLFD/DU3uvICars4Hkto2d//99+fxxx/P97///Wy11Vb1fd2k9l9/+9vfMnLkyBx11FEdttu+ffs2YQlbQ+N1y6yzzpqzzjqrQ//2T/v1+GGHHZYXX3wxDz30UO6777783//9X9566636/G655ZY88MADWXfddXPMMcdM9D2N85vUdcx+++1XP5b8/e9/z7777luf11prrdVhXl/84hdnwJpqrs7KqaqqbLXVVtliiy3y+OOP57HHHsvbb7+dQw89dLLzm9S20F33Ue3r8OGHH84NN9yQ3//+9znyyCOnePr23/aQIUPyk5/8JMlHv877+c9/Xr/v1Xg+t80220z0vcOHD88qq6ySq6++utO4Hnrooey777658MILM3r06IwcOTI77rhjnnnmmfo4vXv3zi9/+csul62r75jUecnUkDxpU1XV2CT7JPlDkr8nuaKqqoebG9XU6dOnT/bcc8+cfPLJEw372te+lquuuqre/fGPf3yicR5++OGsuuqq9az6448/Pl3j7e7efPPNzDPPPBP1f+aZZ7LWWmtl8ODBGTx4cP2C5NZbb826666bbbbZJssvv3z9CbIkufvuu/O5z30uAwcOzKqrrpq33nqrx5bX22+/ndtvvz3nnXdeLrvssnr/N998M5tuummWW265fPOb38z48eMzbty4fO1rX6tn4E8++eRcddVVueeee7Ljjjtm0KBBee+993LvvffWn2rbaKON8uKLLyZJ1l133Rx88MFZddVVs+yyy+a2227LmDFjcvjhh+fyyy/PoEGDcvnll+eCCy7IPvvsk6RWvl/4whcyYMCArL/++vnHP/6RpLYN7rfffvnc5z6XJZdcsr49vvjii1l77bUzaNCg9O/fP7fddtsMXqPTT1dl1a53795ZddVV88ILL3Qy9ZQbPnx4dtppp2y44YYZMWLER5rHoEGDcvjhh+f000+fqlhmRmussUa9DH71q1/l85//fDbccMMkyRxzzJHTTz+9fhN4Ul588cXMN998+djHPpYkmW+++bLwwgvnrbfeytixY/OpT30qSS3Rv9xyy02npekeNtlkk/zud79LUvt977DDDh2GX3311dlss82y/fbbd9i2fvKTn+TMM8/M3HPPnSSZe+65s8suu0w0/8Yyf+KJJ3LvvffmsMP+94KSww8/PPfcc0+efPLJJMn888+f9ddfPxdeeOG0XdCZ1K233pp+/frlW9/6VoebVC+++GIWXXTReveAAQPq/RdaaKH06lU7DV900UU7nB8MHz48J510Ul544YU8//zzM2gpmJQ+ffrkc5/7XJ544onJjnvAAQdMl4u2mdFjjz2Wo446KhdffHH9996VbbfdNpdfXntXTWf7ucUXXzz//e9/89JLL6Wqqlx//fX50pe+VB9+3HHH5fTTT88cc8yRJNlwww3zuc99LpdeeumHinmZZZbJHHPMkddee+1DTddqJnfcmFa+/OUv5+GHH86jjz7aof+TTz6Zv/3tbznmmGPqZb/EEktk0003new8jzvuuJxwwgmZb775kiSDBw/OLrvsUn+wI0kOPPBA21mbUkr233//fPrTn64nlCZ3zj2hH//4xznzzDPrSeRZZ5013//+9zP33HNP0XkBNV2dD0xovfXWy5577plzzjknybTbf/VEa6211iSPze+++25+8Ytf5Gc/+1n9mmTBBRfMtttuO9G4jefDXZnUdcyE530rrbTSh16e7qq9nG6++ebMNtts2XXXXZPUrv9PPvnk/PKXv8y77777kebdU/ZRCyywQM4555ycfvrpHR6GmxJrr712nnjiiRlynffkk0/m7bffzjHHHNPlfvC4447LD37wg6ywwgr1fkOHDs3aa69d7/7Od76Tk08+OWPHjv1Q3zFw4MB84hOfyA033PCR4u+K5EmDqqquq6pq2aqqlqqqqlucje2999659NJL88Ybb3zoac8666x8+9vfzsiRI3PPPfd0OBAwZd57770MGjQoyy+/fHbfffcOO6l2CyywQG644Ybcd999ufzyy7PffvvVh91///055ZRT8sgjj+Spp57KX/7yl4wZMybbbbddTj311IwaNSo33nhjZp999h5bXiNGjMjGG2+cZZddNp/61Kdy7733Jknuuuuu/OxnP8sjjzySJ598MldffXVGjhyZF154IQ899FAefPDB7Lrrrtlmm20yZMiQXHrppRk5cmT69OmTfffdN1dddVXuvffefP3rX+/wJMTYsWNz11135ZRTTsmRRx6ZWWedtcPTD9ttt12H+Pbdd9/ssssueeCBB7Ljjjt2KN8XX3wxt99+e37729/Wn4z51a9+lY022qheY2nQoEHTfyXOIF2VVbv2p6s23njjSc6nfbtq/xx+eMeXuVx++eXZfvvts8MOO0zVk9uDBw/O6NGjP/L0M6Nx48blpptuytChQ5PUkuif/exnO4yz1FJL5e23386bb745yXltuOGGee6557Lssstmr732qj+BN++882bo0KFZfPHFs8MOO+TSSy/N+PHj69OdfPLJ9bJdb731pvESzpzakyL//e9/88ADD2S11VbrMLz9xljjb/7NN9/MW2+9lSWXXHKy87/++uuzxRZbJEkeeeSRDBo0KL17964P7927dwYNGpSHH/7fMyUHH3xwvep4T9e+/rfccsv87ne/qz+xvvfee2e33XbLeuutlx//+Mf1Go7bbrttvcmHAw44oN78UJI899xzefHFF7Pqqqt2uJn8Uay33nr1bamzB2l6ug+zr3n33Xdz00031W+EPPnkkx2OQ40POmy77ba57777pijR0p198MEHGTZsWE466aQstthiSSa93rbeeuv604PXXnttNttss4nmuc022+TKK6/MX//61wwePLh+I+zNN9/MO++8M9H+bsiQIR32W1PivvvuyzLLLJMFFljgQ03XaiZ33Gh/6Kf9017DoCsHHnhgfdwdd9yx3r9Xr1456KCD6k+0tnv44YcnOpY0mtS5XGfnHhOW5RprrJFZZ5213kRHdzG5c9xJaTxvndw5d6M333wzb7/9dpZYYolOh0/peQFdnw90pr28puX+q6cZO3Zsfv/739ePzRNuP5dffnmeeOKJLLbYYvUHiSal8Xy4q/lN6jpm//33zxe+8IV86Utfysknn5zXX3+9Pq/bbrutw7y60039yWksp87273PPPXcWW2yxj3ze1JP2UUsuuWTGjRuXl19++UNN99vf/jYrrbTSDLnOu+yyy7L99ttnrbXWyqOPPpqXXnpponEefvjhDB7c5etFkiSLLbZY1lxzzVx88cUf+jsOPfTQDrXIpgXJk25u7rnnzs477/yRmmtYY4018pOf/CTHHXdcnn322cw+++zTIcLurb2a3ejRo3P99ddn5513nihL/MEHH2SPPfbISiutlK985SsdmnpYddVVs+iii6ZXr14ZNGhQnnnmmTz66KNZaKGFssoqqySplXGfPn16bHkNHz4822+/fZLahWL7jcNVV101Sy65ZHr37p0ddtght99+e5Zccsk89dRT2XfffXP99dd3ehL16KOP5qGHHsoGG2yQQYMG5Zhjjunw5O9WW22VJPnsZz/boVphV+64444MGzYsSbLTTjvl9ttvrw/bYost0qtXr6y44or1Hf4qq6yS888/Pz/60Y/y4IMPZq655vpoK6YFdVVW7TdTFlxwwSy00EL1p7O7MmEV6qOOOqo+7J577sl8882XxRZbLOuvv37uv//+vPrqq0lqT+ZNqLN+7T7sEx0zs/aLg09/+tN56aWXssEGG0zRdF2tv1JKPv7xj+fee+/NOeeck/nnnz/bbbddLrjggiTJueeem5tuuimrrrpqTjzxxHz961+vT9vYlE53uynyUQ0YMCDPPPNMhg8fnk022aTDsJdeeimPP/541lxzzSy77LKZZZZZ8tBDD03RfHfccccsscQS+fGPf5y99977Q8W05JJLZrXVVsuvfvWrDzVddzNmzJhcd9112WKLLTL33HNntdVWyx/+8IckyUYbbZSnnnoqe+yxR0aPHp2VV145r7zyShZddNE8+uij+elPf5pevXpl/fXXrzcRePnll9efhmzcT34Ujc127b///lO/sN3MlOxr2o9Pn//857PpppvWazpM2PzUWmutVZ+md+/eOfDAA/PTn/50hixHqzrssMPSr1+/Dg+VTGq9fepTn8o888yTyy67LCussEL9CexG2267ba688sppVpOi8Rh28sknp1+/fllttdWmqPmQVjep40YycbNdk7tuaGy2a8Kn4YcNG5Y777yz3lb6lJjUudyU+uEPfzjNb44029Ssl8bz1q7OuafEH/7whwwaNCh9+/bt0EQbkzap84HO9KTrjGmt/bplyJAhWWyxxbLbbrslmXj7mfChxq6st956WWSRRfL73/++w7Glq/l1dR2z66675u9//3u+8pWv5NZbb83qq6+e999/P8nEzXYttdRS03KVtKSuymlSJnVt+VFNj3m2gilZrvYHqd58880P9QqBqbnOaz/+9OrVK1tvvXWuvPLKSY7/n//8J4Pa3jt74okndhh2yCGH5IQTTujwoOWUfEd7DZbGe29TS/KkB/jOd76T8847r0Pb/3369Kn/AMePH99pu+XDhg3LNddck9lnnz2bbLJJbr755hkWc3e0xhpr5N///ndeeeWVDv1PPvnkLLjgghk1alTuueeeDmXR/kRdUrsY76zKWrueWF6vvvpqbr755uy+++7p27dvTjjhhFxxxRWpqmqig0kpJfPMM09GjRqVddddN2eddVan7WBWVe1ll+0nNg8++GD++Mc/1oe3l8nkymNKNJZv+wn02muvnT//+c9ZZJFF8rWvfS0XXXTRVH1Hq5hUWbXfTHnyySdz77335pprPvrrpoYPH57Ro0enb9++WWqppfLmm2/m17/+dZLajZnGZjheffXVepMQnbn//vs7VCXtztovDtpf0tbeNMaKK6440dOKTz31VD7+8Y9n7rnnnmidJrXq7O3NPvTu3TvrrrtujjzyyJx++un1skhqVdn333//3HDDDR3607mhQ4fme9/73kQ3DK+44oq89tprWWKJJdK3b9/6zbK55547H//4xzu8A2VCl156aZ566qnssssu9XaZV1xxxYwcObLDSer48eMzspM28X/wgx/kuOOO69E3AP7whz/k9ddfz0orrZS+ffvm9ttv73CTat55582wYcNy8cUXZ5VVVsmf//znJLX9/5e+9KWccMIJ+cEPflB/l8bw4cNzwQUXpG/fvhk6dGgeeOCBHtMMZytqPz7df//9+dGPfjTF0+20007585//XH+HR09z66235te//vWHbvpyu+22y957791lYuTTn/50Zpllltxwww1Zf/316/3nnnvuzDnnnBPt7+69997069cvSe0413iOPeE5wP7775+HH344v/71r7PbbrtN8btSWllXx41prU+fPjnggANy3HHH1fv169cvo0aN+khPrXZ27tFYlu2+8IUv5L333sudd9750QLvZtrPWyd1zt2Z9vOF9uRXew34/v37Z8yYMR/qvKAnm9z5wITay2tK9l901JjU+NnPfjbJd2IuvfTS+cc//jHJGvO33HJLnn322QwaNChHHHHEFMXQ1XXMwgsvnK9//esZMWJE+vTpM8UPNHVHnZVTZ/v3N998M//4xz+y9NJLd3ptOblr9sntoz7KPFvVU089ld69e2eBBRaYouVqf5Dqoosuyic/+clpfp03bty4DjUlH3zwwTz++OPZYIMN0rdv31x22WWd7gf79euX++67L0ntHs3IkSOz55575u233+4w3jLLLJNBgwZ1eOfdlH7HtK59InnSA8w777zZdtttc95559X79e3bt77TuuaaazqtUvrUU09lySWXzH777ZfNN988DzzwwAyLuTsaPXp0xo0bV28fs90bb7xRb/v84osvnuxFxnLLLZcXX3wxd999d5L/tbvZE8vrqquuyk477ZRnn302zzzzTJ577rksscQSue2223LXXXfl6aefzvjx43P55ZdnzTXXzL///e+MHz8+W2+9dY455pj6DnuuueaqvzRuueWWyyuvvJI77rgjSa1m0OSqezZOP6HPfe5z9baGL7300g5PWXbm2WefzYILLpg99tgju+++ez3GmV1XZdV4Y2m++ebLscce+5Gf1h0/fnyuuOKKPPjgg3nmmWfyzDPPZMSIEfWD6brrrptLLrmkfgJw4YUXdtlUywMPPJCjjz76Qz+NP7ObY445ctppp+Wkk07K2LFjs+OOO+b222/PjTfemKT2BNF+++2Xgw46KEkt2XfNNdfUf/9XX311Bg4cmN69e+fRRx/tcNN35MiRWXzxxfP222/n1ltvnag/k/b1r389RxxxxETtJw8fPjzXX399/Td/77331vc5hxxySPbee+/6BePbb789UUK2lJKjjz46d955Z0aPHp2ll146K6+8coeTzWOOOSaDBw/O0ksv3WHa5ZdfPiuuuGKuvfba6bHIM4Xhw4fn3HPPra//p59+OjfccEPefffd3HzzzfX2m9966608+eSTWWyxxXLffffVm/AaP358HnjggSy++OL1l2a+8MIL9fkdcsghU/3ieGa8WWaZJfvvv3+PbC7ttddey6677pqLLrroQ9ee3XLLLXPQQQdlo4026nKco446Kscdd9xEzUEdeOCB2W+//erNT9144425/fbb67V/11lnnVxyySVJaseyK664otNzgKFDh2bIkCHd4p1OXR03poevfe1rufHGG+sPiS211FIZMmRIjjjiiPp51zPPPFN/D8ukHHTQQTn44IPzn//8J0ntPOGCCy7IXnvtNdG4P/zhD3P88cdPwyWZ+VRVldNOOy0vvvhiNt5440leH3XlkEMOybe+9a16M0NVVdUTiB/mvKAnm9T5wIT+9Kc/5Zxzzskee+yRZPL7Lz66OeaYI7vttlu+/e1v1xPor7zyykRPqvfp0yennHJKLrroonqrBZ2Z1HXM9ddfX7+v9q9//Sv/+c9/ssgii0zjJZq5rb/++nn33Xfr1yPjxo3LAQcckK997WuZY445ssoqq+Qvf/lL/vWvfyWptSrx/vvv5zOf+UyX85zcPmqZZZbJP//5z/z9739PUrvfMjM2j/7KK6/km9/8ZvbZZ5+UUqbLumo0Jdd5vXv37lBTcvjw4fnRj35U3w/+85//zD//+c88++yzHaY76KCD8uMf/7heJkm6fOfNoYce2qFGypR+x4YbbpjXXnttmt0X7TNN5kLLO+CAAzo8/bXHHntk8803z8CBA7PxxhtnzjnnnGiaK664IhdffHFmmWWWfPrTn84PfvCDGRlyt9BeVTGpnYReeOGFE13s7bXXXtl6661z0UUXdVkWjWadddZcfvnl2XffffPee+9l9tlnz4033tgjy2v48OE5+OCDO/Tbeuutc+aZZ2aVVVbJPvvskyeeeCLrrbdettxyy/p7Ttoz7e036b/2ta/lm9/8Zmafffbccccdueqqq7LffvvljTfeyNixY/Od73xnkk/+rLfeejn22GMzaNCgiapD/uxnP8uuu+6aE044IfPPP3/OP//8SS7TrbfemhNOOCGzzDJLPv7xj3ebmiddldWEiZItttgiP/rRj3LbbbdNNtE0odtuuy2LLLJIFl544Xq/tddeO4888khefPHF7Lnnnhk9enQGDhyYUkqGDBnS4ftvu+22rLzyynn33XezwAIL5LTTTuvwZGtPsfLKK2fAgAEZPnx4dtppp4wYMSL77rtv9t5774wbNy477bRT9tlnnyS1ZkH22WefrLnmmimlZIEFFsi5556bpHZxse++++b1119Pnz59svTSS+ecc85JVVU5/vjj841vfCOzzz575pxzznpzXkmtNl77Da4k9Sfyb7rppg7vcrryyiuzxhprTP8V0iIWXXTRDu9MSmo3op599tmsvvrq9X5LLLFEPvGJT+Rvf/tbvvWtb+Xtt9/OKquskllmmSWzzDJLDjjggInmPfvss+eAAw7ICSeckPPOOy/nnXde9t1333qTAmussUaHBzAaHXrooVl55ZWn4ZK2rnfffbfDb3CvvfbK9ddfn7POOqveb84558yaa66Za6+9Nv/4xz+yzz771Gv77r777llllVVy/fXXZ4899qg35bDqqqtmn332yXHHHZctt9yyw3duvfXW2W677ert3g8YMKD+8uVtt902AwYMyAUXXFDfTpLUn8Jeb7316uccAwYM6DbHkw9rwnL77ne/m6TzfU3fvn2naJ7tzXm1+/rXvz7R9rnbbrt1uyaFpsRZZ52Vl19+Od/61rc69N9hhx0mu97mmmuuic4VJvS5z32u0/777rtvXnvttay00krp3bt3Pv3pT2fEiBH15qhOPfXUfOMb38hpp52Wqqqy8847d3gxaaPDDz88w4YNyx577DHZF923ss6OG+0uv/zyDs1ZnHHGGVl44YXz6KOPdthe2hOABx54YIff81133dVhfrPOOmv222+/fPvb3673O/fcc3PAAQdk6aWXzuyzz5755psvJ5xwwmTjHjp0aF544YV87nOfSyklc801Vy655JIstNBCE427ySabZP7555/sPLujAw88MEcffXTefffdrL766rnlllsy66yzdnnO3d6/szL+1re+lXfeeSerrbZaPvaxj+XjH/94Pv/5z9eP7x/mvKCnGTt2bGaZZZZJng8k/9vm3n333SyxxBL59a9/Xa/hPrn9F1Om8d5Lkmy88cY59thjc8wxx+SHP/xhVlxxxcw222yZc845O20Sb6GFFsoOO+yQn//85znssMM6nd+hhx7a5XXMH//4x3z729/ObLPNlqTW3OGnP/3pjB49uv7Ok3Y//OEPs80220yP1dDSSin5zW9+k7322itHH310xo8fn0022aT+3qwFF1wwp556ajbZZJOMHz8+H//4xzN8+PDJHosntY/62Mc+lksuuSS77rpr/vvf/2aWWWbJueeem0984hPTd2Gngfbf4AcffJA+ffpkp512qp/HTo91NaEPe5132WWX5brrruvQb8stt8xll13W4d1rK620Uk499dTsvPPOefPNN+vNrh955JETzbNfv34ZPHhw/aHiKf2O9vg333zzKY5/UkpPbmphapRSKuuu9ZRSenTzIa1KubQm5dKalEtrUi6tSbm0JuXSmpRLa1IurUm5tKZWK5dRo0Zljz32mCih2NO0WrlQo1xak3JpTW3l0unLZGbeR2kAAAAAYAY766yzssMOO/TIWoYAPYmaJx+RmietSQa3NSmX1qRcWpNyaU3KpTUpl9akXFqTcmlNyqU1KZfWpFxak3JpTcqlNSmX1jSpmieTfOfJbB+b7V/vj3l/wekT1sxtttlmSymdrlOaSLm0JuXSmpRLa1IurUm5tCbl0pqUS2tSLq1JubQm5dKalEtrUi6tSbm0JuXSmmabbbbxXQ2bZM2TUko1+pbR0yWomd3y6y0vU9iCZHBbk3JpTcqlNSmX1qRcWpNyaU3KpTUpl9akXFqTcmlNyqU1KZfWpFxak3JpTdPtnSfLr7d8jj3j2Hr3eZefl59d8LNJTvP8v57PZrtuNjVfS5ONGzcuK6+8cr785S8nSXbccccst9xy6d+/f77+9a/ngw8+mGiakSNHZo011ki/fv0yYMCAXH755fVhO+64YwYMGJAf/OAH9X7HHHNM/u///m+6L0t39/Wvfz0LLLBA+vfv3+nwESNGZMCAARk0aFCGDBmS22+/PUny6KOP5rOf/WwGDBiQO+64I0kyduzYfPGLX8y77747w+Lvrq6//vost9xyWXrppXPsscdONPz999/Pdtttl6WXXjqrrbZannnmmSTJX/7ylwwYMCBDhgzJ448/niR5/fXXs+GGG2b8+C6T5DR47rnnst5662XFFVdMv379cuqppyapvexxjTXWyEorrZTNNtssb775ZqfTd7VNHXzwwRkwYEB23nnner9LLrkkp5xyynRblu6kq/X6s5/9LMsvv3z69euXgw46qNNpu9qeHFumL/ux5upsmxk5cmRWX331+jF9Ui+vffPNN7Poootmn332SVIrr4033jj9+/fPGWecUR9vzz33zH333Tf9FqSHsL20psmVS5JcccUV9XOGYcOGJXGePL1N7vrljTfeyGabbZaBAwemX79+Of/885Mol+mtb9++WWmllerHmAmdcMIJGTRoUAYNGpT+/fund+/eefXVV/PKK69kzTXXTP/+/Tucg22++eb55z//OQOXoHtyfGk9XV1vTujWW2/NoEGD0q9fv6yzzjpJYnuZBjo7hmy33Xb1/VPfvn0zaNCgKZ42ca0/vc0Mx/2pSp7MOsusueG2G/LaG69Nq3iYCZx66qlZYYUV6t077rhjRo8enQcffDDvvfdezj333ImmmWOOOXLRRRfl4YcfzvXXX5/vfOc7ef311/PAAw9k9tlnzwMPPJC77747b7zxRl588cX87W9/yxZbbDEDl6p7+trXvpbrr7++y+Hrr79+Ro0alZEjR+aXv/xldt999yTJ2WefnVNPPTXXXXddTjzxxCTJmWeema9+9auZY445Zkjs3dW4ceOy99575/e//30eeeSRDB8+PI888kiHcc4777zMM888eeKJJ7L//vvn4IMPTpKcdNJJue6663LKKafkrLPOSlK7GfyDH/wgvXpN1e68x+jTp09OOumkPPLII7nzzjvz85//PI888kh23333HHvssXnwwQez5ZZb5oQTTuh0+s62qTfeeCP33XdfHnjggcw666z1feH555+fvffee0Ys1kyvs/V6yy23ZMSIERk1alQefvjhfO9735touq62J8eW6ct+rPk622YOOuigHHHEERk5cmSOOuqoLhOOSXLYYYdl7bXXrnf/4Q9/yJprrpkHHnggF198cZJaUnncuHEZPHjw9FmIHsL20pqmpFwef/zx/PSnP81f/vKXPPzww/WbJM6Tp6/JXb/8/Oc/z4orrphRo0bl1ltvzQEHHJAxY8YolxnglltuyciRI3PPPfdMNOzAAw/MyJEjM3LkyPz0pz/NOuusk3nnnTfDhw/PN7/5zdx11131bejaa6/NyiuvnIUXXngGL0H34vjSmrq63mz0+uuvZ6+99so111yThx9+OFdeeWWS2F6mgc6OIZdffnl9/7T11ltnq622muJpXetPfzPDcX+q9op9evfJtl/eNhdcecFEw75/7Pdz/Z/+t/CDvzTxhdfjTz+er3zrK9li9y0ydLeheeb5Z6YmHGaA559/Pr/73e/qN9mTZJNNNkkpJaWUrLrqqnn++ecnmm7ZZZfNMssskyRZeOGFs8ACC+SVV17JLLPMkvfeey/jx4/PBx98kN69e+fwww/PkUceOcOWqTtbe+21M++883Y5/OMf/3i9rcV33nmn/v8ss8ySd999N++++25mmWWWvP7667n22ms7ZNr5aO66664svfTSWXLJJTPrrLNm++23z4gRIzqMM2LEiOyyyy5Jkm222SY33XRTqqqaqFyefPLJPPfcc1l33XWbsCQzp4UWWqh+I3CuuebKCiuskBdeeCGPPfZY/UbiBhtskF//+tedTt/ZNtWrV6988MEHqaqqXjYnnnhi9t1338wyyyzTd4G6ic7W65lnnpnvf//7+djHPpYkWWCBBSaarqvtybFl+rIfa77OtplSSr3W3BtvvNHlRfa9996bl156KRtuuGG9X3u5tO/LklqC5eijj55OS9Bz2F5a05SUyy9+8YvsvffemWeeeZL87zjkPHn6mtz1Syklb731Vqqqyttvv5155503ffr0US4tZPjw4dlhhx2S/G97ef/999O7d++MHTs2p5xyyiQT/EwZx5fW1NX1ZqNf/epX2WqrrbLYYoslmfj4Ynv56CZ1DKmqKldccUV9/zQl07rWn/5mhuP+JF8YPyV23GLHDN1taHbffvfJjzyBy669LDtvtXM222CzjPlgjOqBM4HvfOc7Of744/PWW29NNOyDDz7IxRdf3GW1xHZ33XVXxowZk6WWWiq9evXK/PPPn8GDB2ennXbKE088kfHjx3vKcQb6zW9+k0MOOSQvv/xyfve73yVJ9t577+y88855//33c/bZZ+foo4/2FMo08sILL+Qzn/lMvXvRRRfN3/72ty7H6dOnTz7xiU/kP//5Tw455JDsvPPOmX322XPxxRfne9/7Xo455pgZGn938swzz+T+++/Paqutln79+mXEiBHZYostcuWVV+a5556b4vnMNddc2WSTTbLyyitn/fXXzyc+8Yn87W9/y2GHHTYdo+/+Hnvssdx222059NBDM9tss+XEE0/MKqus0mGcrranFVZYwbFlOrIfa02nnHJKNtpoo3zve9/L+PHj89e//nWiccaPH58DDjggl1xySW688cZ6/w022CAXX3xxVl999Rx44IG55pprMnjwYE85TgO2l9Y0JeXy2GOPJUk+//nPZ9y4cfnRj36UjTfe2Hlyk+2zzz4ZOnRoFl544bz11lu5/PLL06tXL+UynZVSsuGGG6aUkm984xvZc889Ox3v3XffzfXXX5/TTz89STJs2LAMGzYs55xzTo477ricccYZ2WmnndQGmgYcX1pf4/Vmo8ceeywffPBB1l133bz11lv59re/nZ133tn2Mp3ddtttWXDBBesPdk8J1/rN1wrH/alOnnx8zo9niw23yMVXX1x/OnRKDVpxUM6+5Oz869//ygZrbZC+i/ad2nCYjn77299mgQUWyGc/+9nceuutEw3fa6+9svbaa2ettdbqch4vvvhidtppp1x44YX1H3RjO4GbbbZZzj777Pz4xz/OqFGjssEGG2SPPfaY1otCgy233DJbbrll/vznP+ewww7LjTfemMUWW6xexk888USef/75rLDCCtlpp50yZsyYHH300Vl22WWbG3gPNGjQoNx5551Jkj//+c9ZaKGFUlVVtttuu8wyyyw56aSTsuCCCzY5ypnD22+/na233jqnnHJK5p577vzyl7/Mfvvtl6OPPjpDhw7NrLPO+qHmd9BBB9WfCNp9991z1FFH5dxzz80f//jHDBgwID/84Q+nx2J0a2PHjs2rr76aO++8M3fffXe23XbbPPXUU/UacpPj2NKa7MemnzPPPDMnn3xytt5661xxxRXZbbfdOiRIkuSMM87IJptskkUXXbRD/z59+uRXv/pVktrDMBtttFFGjBiR7373u/nHP/6RnXfeOUOHDp1hy0KN7aW5xo4dm8cffzy33nprnn/++ay99tp58MEHnSc32R/+8IcMGjQoN998c5588slssMEGWWuttZTLdHb77bdnkUUWycsvv5wNNtggyy+/fIfmH9tde+21+fznP19/ivgTn/hE/QG91157Lccee2x+85vfZI899shrr72WAw44IGusscYMXRYcX2aECa83G40dOzb33ntvbrrpprz33ntZY401svrqq2fZZZe1vUxHjbXiPgzX+s3VCsf9aZKO2XmbnXPVdVflvf++V+/Xp3efVONr1f7Hjx+fD8ZO/BLxzb64Wc748Rn52Kwfyze+/43ced+d0yIcppO//OUvueaaa9K3b99sv/32ufnmm/PVr341SXLkkUfmlVdeyf/7f/+vy+nffPPNbLrppvnxj3+c1VdffaLhI0aMyGc/+9m8/fbbefLJJ3PFFVfkqquu8oK/GWTttdfOU089lX//+98d+h966KE55phjctppp2X33XfP8ccfr+mbqbDIIot0qNXw/PPPZ5FFFulynLFjx+aNN97Ipz71qfrwqqpyzDHH5LDDDsuRRx6Z448/PnvssUdOO+20GbMQM7kPPvggW2+9dXbcccd6e6fLL798/vjHP+bee+/NDjvskKWWWuojzfv+++9PVVVZbrnlcuWVV+aKK67Ik08+WX8RI1Nu0UUXzVZbbVVvErJXr14T7Z+mZHtybJn27Mda04UXXljfp33lK1/p9IXxd9xxR04//fT07ds33/ve93LRRRfl+9//fodxzjjjjOy88865884784lPfCKXX355TjrppBmyDN2R7aU1TUm5LLroohk6dGhmmWWWLLHEEll22WUnOp47T57xzj///Pr5wdJLL50lllgio0eP7jCOcpn22rePBRZYIFtuuWWnx5gkueyyy7q8OXn00Ufn0EMPzfDhw7PmmmvmwgsvzI9+9KPpFXK35/jSujq73my06KKLZqONNsqcc86Z+eabL2uvvXZGjRrVYRzby7Q1duzYXH311dluu+0+8jxc6zdHKxz3p0ny5JNzfzJfWvdL+fV1/2sjfpFPL5KHH3s4SXLzX2/uNHny3D+fy2cW/kx23nrnfOHzX8ijTz06LcJhOvnpT3+a559/Ps8880wuu+yyfOELX8gll1ySc889N3/4wx8yfPjwLqtHjRkzJltuuWV23nnnbLPNNhMN/+CDD+ptOb733nv1J4vHjRuXMWPGTNfl6smeeOKJetvm9913X95///0OJ1N/+tOfsvDCC2eZZZbJu+++m169eqVXr15uOk6FVVZZJY8//niefvrpjBkzJpdddtlET/MOHTo0F154YZLkqquuyhe+8IUOT9tfdNFF2WSTTTLvvPMqlw+pqqrstttuWWGFFfLd73633v/ll19OUkv2H3PMMfnmN7/5kebf/o6ADz74IOPGjUsSZfMRbbHFFrnllluS1Kq2jxkzJvPNN1+HcSa3PTm2TB/2Y61p4YUXzp/+9Kckyc0339xpkwSXXnpp/vGPf+SZZ57JiSeemJ133jnHHntsffhrr72W3/72t9l5553r5VJKyXvvvTfRvJgytpfWNCXlssUWW9SfaPz3v/+dxx57LEsuuWR9uPPk5lhsscVy0003JUleeumlPProo8plOnvnnXfqzXa/8847+eMf/5j+/ftPNN4bb7yRP/3pT9l8880nGvb444/n+eefz7rrruv4Mo04vrSmrq43G22++ea5/fbbM3bs2Lz77rv1Zofb2V6mvRtvvDHLL7/8RLWvPwzX+s3REsf9qqq6/CSpRt8yusvPHLPNUf//9l/fXs32sdmqvXfZu949cIWB1XJLLlftvv3u9XFvHH5jtUzfZarRt4yuvrvHd6ulF1+6Wn6p5as1V1mzunPEnZP8vlb61FZdz3XLLbdUm266aVVVVdW7d+9qySWXrAYOHFgNHDiwOvLII6uqqqq777672m233aqqqqqLL7646tOnT32cgQMHVvfff399fieffHJ1/vnnV1VVVePHj6+23377qn///tVBBx30oeLq6eUyoe2337769Kc/XfXp06daZJFFqnPPPbc688wzqzPPPLOqqqo69thjqxVXXLEaOHBgtfrqq1e33XZbfdrx48dXX/ziF6v//Oc/VVVV1SOPPFKtvPLK1UorrVTdfvvtHyoO5dLR7373u2qZZZapllxyyeqYY46pqqqqDjvssGrEiBFVVVXVe++9V22zzTbVUkstVa2yyirVk08+WZ/2nXfeqdZdd91qzJgxVVVV1Z///Oeqf//+1eDBg6vRo0d/qDh6YrncdtttVZJqpZVWqu+Lfve731WnnHJKtcwyy1TLLLNMdfDBB1fjx4+vqqqqXnjhhepLX/pSffrOtql2v/nNb6ojjjii3n3AAQdU/fv3r4YNG/ahYuyJ5dLZen3//ferHXfcserXr1+18sorVzfddFNVVROXSWfbU7tpdWypqp5ZLpNiP9ZcnW0zt912WzV48OBqwIAB1aqrrlrdc889VVV1PB9rdP7551d77713h37f+c53qltuuaWqqloZbrDBBtWKK65YnXbaaR8qvp5aLl2xvbSmyZXL+PHjq/33379aYYUVqv79+1fDhw+vT+s8efqZ3PXLCy+8UG2wwQZV//79q379+lUXX3xxfVrlMn08+eST1YABA6oBAwZUK664Yn17aSyXqqodV7bbbrtO5/GVr3yleuyxx6qqqqqXXnqpWmONNaoVV1yxuuqqqz5ULMqlI8eX1tPV9eaE28vxxx9frbDCClW/fv2qk08+ucM8bC8fXVfX67vsskuH9V9VzbnWr6qeWS6T0mLH/U7zI6Vqe+q8M6WUavQto7sc3pMtv97ymdS6ozlKKcqlBSmX1qRcWpNyaU3KpTUpl9akXFqTcmlNyqU1KZfWpFxak3JpTcqlNSmX1tRWLp2+YHXav4IeAAAAAABgJiZ5AgAAAAAA0KDPpAbO1me28cuvt7wESydmm222Di/aojUol9akXFqTcmlNyqU1KZfWpFxak3JpTcqlNSmX1qRcWpNyaU3KpTUpl9akXFrTbLPNNr6rYZN958mrR706XYKa2c17+LzaqGtB2g5sTcqlNSmX1qRcWpNyaU3KpTUpl9akXFqTcmlNyqU1KZfWpFxak3JpTcqlNU23d57Md8R8WfuMtbPWz9fKumeum7/9429Jkn+89o987vTPTc2smYk899xzWW+99bLiiiumX79+OfXUU7sc9+67706fPn1y1VVXJUkeffTRfPazn82AAQNyxx13JEnGjh2bL37xi3n33XdnSPzdweuvv55tttkmyy+/fFZYYYXccccdefXVV7PBBhtkmWWWyQYbbJDXXnttoumeffbZDB48OIMGDUq/fv1y1llnJUnef//9bLzxxunfv3/OOOOM+vh77rln7rvvvhm2XN3V9ddfn+WWWy5LL710jj322ImGv//++9luu+2y9NJLZ7XVVsszzzyTJPnLX/6SAQMGZMiQIXn88ceT1Mp+ww03zPjxXSbJmUJf//rXs8ACC6R///6dDh8xYkQGDBiQQYMGZciQIbn99tuT2I9NC//973+z6qqrZuDAgenXr1+OOOKIJMnNN9+cwYMHp3///tlll10yduzYLufx5ptvZtFFF80+++yTxH5serMfa56uzrtGjhyZ1Vdfvb6Puuuuuzqd/sILL8wyyyyTZZZZJhdeeGES28v0ZntpTY8++mgGDRpU/8w999w55ZRTOh3XNcyMMyXl4pxs+ujq+HLllVemX79+6dWrV+65554up+/bt29WWmmlerm0O/jggzNgwIDsvPPO9X6XXHJJl9sbU25yx5c///nPGTx4cIf9V2JbmRY6u3Y88MADs/zyy2fAgAHZcsst8/rrr3c6bWf3bxLbyrTS2b5oSsumq3sCymb66ur4MaFmnY9NVfJk9llmz5/3+nNu2/u2HPbFw3L0DUdPq7iYifTp0ycnnXRSHnnkkdx55535+c9/nkceeWSi8caNG5eDDz44G264Yb3f2WefnVNPPTXXXXddTjzxxCTJmWeema9+9auZY445ZtgyzOy+/e1vZ+ONN87o0aMzatSorLDCCjn22GOz/vrr5/HHH8/666/f6cnUQgstlDvuuOP/t3fnYVGVDR/Hv8Om4o6PKIJKigvbiKip5UuagUVqobiiUOGSafa4l4alYpplormW5p5LVIIbmUsupSLK4pYCSYKamgIqg8DA/f5BnocJRlEYPer9uS6uC84593jO/LyXsxMXF8fhw4eZOXMmFy9e5KeffqJDhw4kJCSwevVqAOLj48nPz8fT0/Nhb94TJT8/n+HDh7N9+3ZOnTrFunXritWXZcuWUbNmTZKSkhg1ahQTJkwAYPbs2Wzbto2wsDDlRFdoaCgTJ07EzEw+YbGs3njjDaKioozO79y5M/Hx8cTFxfHNN98waNAgQLZj5aFChQrs3r1b+X6joqL47bffCAoKYv369Zw4cYKGDRsqB3pLEhISgpeXl/K3bMdMR7Zjj5axcdf48eP56KOPiIuLY+rUqYwfP75Y2evXrzNlyhQOHz5MdHQ0U6ZMIT09XdYXE5L1Rb2aNWtGXFwccXFxHD16FGtra/z8/IotJ/dhHq7S5CLHZKZhrH9xc3Pjhx9+MBhnGbNnzx7i4uKUkyyZmZkcO3aMhIQErKysOH78ONnZ2Sxfvpzhw4ebepOeaKXpXxo0aMCKFSvo37+/wXRZV8qupH1Hb29vTpw4QUJCAk2bNmXGjBklli3p+I2sK+Xr321RabMpKVeZzcPx78z+7VGOx8pt1H0z5yY1KtUoNv18+nl8l/rScVFHg7tTDpw7QLdvuhG0Poi289oyJHyIctvSsQvH6PJ1F/5vwf/x0pKXuJlzk9NXTvPSkpfwWuhFhwUdSL6WXF6rLpWRnZ2dsmNdtWpVnJ2duXDhQrHlvvzyS3r27Imtra0yzdLSEp1Oh06nw9LSkoyMDDZv3mxwNle6u8zMTPbt20dwcDAAVlZW1KhRg4iICIKCggAICgpi06ZNxcpaWVlRoUIFoPCqxztXMd7JJS8vT6mXISEhTJsmT5CWVXR0NE5OTjRq1AgrKyv69u1LRESEwTJFs/P392fXrl0IIYrVl+TkZFJTU+nYseMj2JInj5eXFzY2NkbnV6lSRXk2aVZWlvK7bMfKTqPRUKVKFQDy8vLIy8vD3NwcKysrmjZtChQOeL///vsSyx89epTLly8bDKRkO2Y6sh17tIyNuzQaDTdu3AAKxwb16tUrVvann37C29sbGxsbatasibe3N1FRUbK+mJCsL4+HXbt20bhxYxo2bFhsntyHeXSM5SLHZKZhrH9xdnamWbNmD/SZZmZmSt9yJ5fPP/+cd999F0tLy/Jc/adOafoXR0dHtFptsRPusq6UXUn7jj4+PlhYFL5aul27dqSlpRUrZ+z4jawrplWabKDkXGU26vAox2N3fWH8vWTnZeO10IscfQ5/3fyLiDcjii3zn8r/4YegH6hoWZHka8kM/m4wu9/eDUDCpQR+G/EbdlXteHnpyxw+fxhPe0+CNwazrPcyPO09uXH7BpUsKrHiyAqGthtKrxa9yNXnki/yy7LqkomkpKQQGxtL27ZtDaZfuHCBH3/8kT179nDkyBFl+vDhwwkMDCQnJ4clS5Ywbdo0eTXdfTp37hy1a9fmzTffJD4+nlatWjF37lwuX76MnZ0dAHXr1uXy5csllk9NTeXVV18lKSmJzz77jHr16mFra8vq1atp164d48aNIzIyEk9PzxIPxEj358KFC9SvX1/528HBgcOHDxtdxsLCgurVq3Pt2jU++OADAgMDqVSpEqtXr2bs2LGEhoY+1PV/2v3444988MEHXLlyha1btwKyHSsv+fn5tGrViqSkJIYPH86zzz6LXq8nJiaG1q1bEx4eTmpqarFyBQUFjBkzhjVr1rBz505lure3t2zHTES2Y+pRdNwVFhZGly5dGDt2LAUFBfz222/Fli8puwsXLtCrVy9ZX0xE1pfHw/r16+nXr1+x6XIf5tEylgvIMZmpGduvvxuNRoOPjw8ajYahQ4cyZMgQqlatiq+vLy1btqRz585Ur16dw4cPExISYsK1fzqUpn8xRtYV0/vmm2/o06dPsenGjt/IulJ+SmqLijKWjTEyG9O7V2aPejxWppMndx7bBRB9Ppph3w/jtxGGO2r6Aj3jt47n+KXjmJuZG9wx4mnviX11ewDc7dw5n3GeahWrUadKHTztC694qFaxGgBt6rdh9t7ZXLxxka4uXWlcq3FZVl0ygVu3btGzZ0/CwsKoVq2awbz//ve/fPrpp8X+Azdo0IBffvkFgKSkJNLS0nB2dmbgwIHk5uYybdo05apjqWR6vZ5jx47x5Zdf0rZtW957771ij+jSaDTKFVn/Vr9+fRISErh48SKvv/46/v7+1KlTh2+//RYovAq8S5cuREREMHr0aM6fP09gYCDdu3c3+bZJhjw8PDh06BBQ+PxaOzs7hBD06dMHS0tLZs+eTZ06dR7xWj7Z/Pz88PPzY9++fYSEhLBz507ZjpUTc3Nz4uLiyMjIwM/Pj5MnT7J+/XpGjRpFTk4OPj4+mJubFyu3cOFCfH19cXBwMJhuYWEh2zEVku1Y+fn3uOvDDz9kzpw59OzZk40bNxIcHGxwQvFuZH1RJ1lfHo7c3FwiIyNLfISH3Id5dO6WC8gxmSndbb/+bg4cOIC9vT1XrlzB29ub5s2b4+Xlxfjx45VHSQ4aNIipU6eydOlSduzYgVar5cMPPzTVpkhGyLpiWtOnT8fCwoKAgIBi84wdv5k2bZqsK+XEWFsEd8/mbmQ2pnW3zODRj8fK7VTMsw2e5bruOn9n/W0wfeFvC6lduTb739nP7qG7yc3PVeZVsKig/G6uMUdfYPxFsP5af74N+JaKlhXps7oP+/7YV16rLpWDvLw8evbsSUBAAD169Cg2PyYmhr59++Lo6Eh4eDjvvPNOscdITZo0idDQUObNm8egQYOYNWsWU6ZMeUhb8PhycHDAwcFBuSrI39+fY8eOUadOHS5dugTApUuXDG5tK0m9evVwc3Nj//79BtMXLlxIYGAghw4donr16mzYsIHZs2ebZmOeAvb29gZXz6elpWFvb290Gb1eT2ZmJrVq1VLmCyEIDQ0lJCSEKVOmMGvWLAYPHsy8efMezkZIeHl58ccff/D334Z9nmzHyq5GjRp06tSJqKgo2rdvz/79+4mOjsbLy6vEgc/BgweZP38+jo6OjB07llWrVvH+++8bLCPbsfIl27FHr6Rx18qVK5Xfe/XqVeIL40uTnawv5UvWF/Xbvn07np6eJZ6Ikvswj87dcilKjsnK17326+/mTttma2uLn59fsX4oNjYWIQTNmjXju+++Y+PGjSQnJ5OYmFhu6/80KU3/UhqyrpSvFStWsGXLFtauXVviBazGjt8UJetK2Rhri+6VTWnIbEzjXv3Hox6PldvJk7NXz5Iv8rGxNnw23I2cG9SpWgczMzM2xG8gv+Duj9tyquXE5VuXOXahsPG4mXMTfb6elOspONZ0ZGi7obzS/BVO/nWyvFZdKiMhBMHBwTg7OzN69OgSlzl37hwpKSmkpKTg7+/PwoULef3115X5e/fupV69ejRp0gSdToeZmRlmZmbodLqHtBWPr7p161K/fn3OnDkDFD4b2MXFhe7duysvV165ciWvvfZasbJpaWlkZ2cDkJ6ezoEDBwyeZ5uens6WLVsIDAxUctFoNEoZ6f61adOGxMREzp07R25uLuvXry92NW/R7MLDw3nxxRcNOvdVq1bh6+uLjY2NrC8PUVJS0v/ezXXsGDk5OQYHt2Q79uCuXr1KRkYGANnZ2fz88880b96cK1euAIXvZPr00095++23i5Vdu3Yt58+fJyUlhc8//5zAwECDu+9kO1b+ZDv2aBkbd9WrV4+9e/cCsHv3bpo0aVKsbJcuXdixYwfp6emkp6ezY8cOunTposyX9aX8yfqifuvWrTP6aCi5D/Po3C0XOSYzjdLs1xuTlZXFzZs3ld937NiBm5ubwTJ33qWVl5dHfn7hcSGZy4MrTf9yL7KulK+oqChmzZpFZGSk0ZdVGzt+U5SsKw/OWFtUmmxKQ2ZT/krTfzzq8Vi5vPMECjvahX4LMTczfKRG8LPBBK0PYkPcBjo36Uxlq8p3/UwrCyuW9V7GhK0TuJ13m4qWFfkx6Ec2ndjEhvgNWJpbYlvFltFe99eZS6bz66+/snr1atzd3fHw8ADgk08+4fz58wAlHuwq6s7VdBs2bABgyJAhBAQEoNfrWbRokUnX/Unx5ZdfEhAQQG5uLo0aNWL58uUUFBTQu3dvli1bRsOGDdm4cSNQeMZ28eLFLF26lNOnTzNmzBg0Gg1CCMaOHYu7u7vyuVOnTmXSpEmYmZnRpUsXFixYgLu7+z0zlYyzsLBg/vz5dOnShfz8fN566y1cXV2ZPHkyrVu3pnv37gQHBzNw4ECcnJywsbFh/fr1SnmdTseKFSvYsWMHAKNHj8bX1xcrKyvlkSvSg+nXrx+//PILf//9Nw4ODkyZMoW8vDygsB37/vvvWbVqFZaWllSqVIkNGzYoB7dkO1Y2ly5dIigoiPz8fKXt6tq1K+PGjWPLli0UFBQwbNgwXnzxRcCwHbsX2Y6VP9mOPVrGxl1ff/017733Hnq9nooVK/LVV18BhvXFxsaGkJAQ2rRpA8DkyZMNXoop60v5k/VF3bKysvj5559ZsmSJMm3x4sWA3Id5lO6VixyTmYax/iUnJ4d3332Xq1ev8uqrr+Lh4cFPP/3ExYsXGTRoENu2bePy5cv4+fkBhXfQ9e/fn5dffln57E2bNtG6dWvlXVoeHh64u7uj1Wpp0aLFQ9/WJ0Fp+pcjR47g5+dHeno6mzdv5qOPPuLkycILkWVdKZuS9h1nzJhBTk4O3t7eQOGLyRcvXmxQV6Dk4zd3yLpSNsbaIicnp1JlU1KuwcHBgMzGVIxlpqbxmObOFRslztRoxPWp18vlH3rS2Ey24W7fnfRo3DkJIKmLzEWdZC7qJHNRJ5mLOslc1Enmok4yF3WSuaiTzEWdZC7qJHNRJ5mLOslc1OmfXEp8nlv5vn5ekiRJkiRJkiRJkiRJkiRJkiTpMSdPnkiSJEmSJEmSJEmSJEmSJEmSJBVx13eeWFKhwGayjTzBUoKKFSoavMhRUoeKFWUuaiRzUSeZizrJXNRJ5qJOMhd1krmok8xFnWQu6iRzUSeZizrJXNRJ5qJOMhd1qlixYoGxefd858l8jptkpR53I3CXz6hTIfnsQHWSuaiTzEWdZC7qJHNRJ5mLOslc1Enmok4yF3WSuaiTzEWdZC7qJHNRJ5mLOpn0nSfx7GIE7vzFHwCc5QiLGF7q8ofYRAZXHvjfT+N3TrJP+TuBPexg6QN/nvRgoqKiaNasGU5OTsycObPY/C+++AIXFxe0Wi2dO3fmzz//BODMmTO0atUKrVbLwYMHAdDr9bz00kvodLqHug1Ponvlsm/fPjw9PbGwsCA8PFyZLnMpH3PmzMHV1RU3Nzf69evH7du32b17N56enri5uREUFIRery+x7IQJE3Bzc8PNzY0NGzYo0wMCAtBqtUycOFGZFhoayqZNm0y9OU882Y6p071yWbx4Me7u7nh4eNChQwdOnToFwK+//opWq6V169YkJiYCkJGRgY+PDwUFRi8qkUrpXrnk5OTQp08fnJycaNu2LSkpKYDMxdRkv69Osr6ok6Ojo9J/tG7dutj8zz77DA8PDzw8PHBzc8Pc3Jzr169z9epVOnTogJubm8H467XXXuPixYsPcQseX6mpqXTq1AkXFxdcXV2ZO3cuAH369FG+c0dHRzw8PEosX9IYG+Q42ZRk/6JOsn9RJ1lf1OleuaxYsYLatWsr/dDSpYXHlmUupvVY1BchhNEfQMzn+F1/POkiGuMpXuFtMZ/jYiTfCFe87lnuzo8TrcU41pd6+X//DGCa8KLvA5d/0J/Cr04SQgi9Xi8aNWokkpOTRU5OjtBqteLkyZMGy+zevVtkZWUJIYRYuHCh6N27txBCiFGjRon9+/eL1NRU0aNHDyGEEPPmzRPLly9/oHWRufxPaXI5d+6ciI+PFwMHDhTfffedMl3mUnZpaWnC0dFR6HQ6IYQQvXr1EsuWLRMODg7izJkzQgghQkJCxNKlS4uV3bJli3jppZdEXl6euHXrlmjdurXIzMwU8fHxIjg4WAghxEsvvSQyMjLExYsXRdeuXR9oHZ/GXIyR7Zg6lSaXzMxM5feIiAjRpUsXIYQQfn5+IjU1Vezfv1+MHj1aCCHEmDFjxJ49ex5oXWQu/1OaXBYsWCCGDh0qhBBi3bp1Sn2RuZiO7PfVSdYX9WrYsKG4evVqqZaNjIwUnTp1EkIIMXfuXLF69WqRlZUlXnjhBWX+Rx999EDr8TTmcvHiRXH06FEhhBA3btwQTZo0KVYvRo8eLaZMmVKsbElj7OXLl8txsgnJ/kWdZP+iTrK+qFNpclm+fLkYPnx4sbIyF9NRYX0p8fzIXd95ci856EgmlpEsYwnv8uo/d5zc5haLeIerpNKENvThQ0Cwlsmcp/CK0Pb4UZO6nOckK3kfSyowhjX8RTI/8Bk56KhMTQYSSnVqE8abOOJOIkfQcZMApuCIlq0sII8ckonFh0HkcZvznKQ3k7jGBdYymVukUwUbBjANG+xYzSQqUoXznOQGf/M6o2mJD5lc5RvGcpssCsinDx/iRKuyfEVPhejoaJycnGjUqBEAffv2JSIiAhcXF2WZTp06Kb+3a9eONWvWAGBpaYlOp0On02FpaUlGRgabN28mKirq4W7EE6g0uTg6OgJgZmZ4E5rMpXzo9Xqys7OV77Ny5cpYWVnRtGlTALy9vZkxYwbBwcEG5U6dOoWXlxcWFhZYWFig1WqJiorC3d2d7OxsCgoKyMvLw9zcnMmTJzNlypRHsXlPFNmOqVNpcqlWrZrye1ZWlvL82H/nkpycTGpqKh07dnyo2/AkKk0uERERfPzxxwD4+/szYsQIhBAyFxOS/b46yfryZFi3bh39+vUD/ldfcnJyMDc3R6/XExYWxubNmx/xWj4+7OzssLOzA6Bq1ao4Oztz4cIFpV4IIdi4cSO7d+8usfy/x9j16tXD0tJSjpNNRPYv6iT7F3WS9UWdSpOLMTIX03lc6kuZTp4ksBsXnqcOjlSmOuc5CcCfnOBDNmFDPRbwNvHspBb2ZHCFSfwIgI4bWFONvazDj7E0xJV88viOGQxhHlWx4ShRbGYeA5gGQAH5jGMdJ9nHdhbxLkt5leHKyRIofAzYHd8xg2fpTjte4yA/Ev7PZwPc4CqjWMVlzrGEd2mJDzFsw5nneZkhFJBPLrfL8vU8NS5cuED9+vWVvx0cHDh8+LDR5ZctW8Yrr7wCwPDhwwkMDCQnJ4clS5Ywbdo0Jk6cWKxSSPfvfnMpSuZSdvb29owdO5YGDRpQqVIlfHx86N27N+PHjycmJobWrVsTHh5OampqsbItWrRgypQpjBkzBp1Ox549e3BxcaF3797Url0bT09PBg4cSFJSEgUFBXh6ej6CLXyyyHZMnUqby4IFC/jiiy/Izc1VDrR88MEHBAYGUqlSJVavXs3YsWMJDQ19aOv+JCtNLkWXsbCwoHr16ly7dk3mYkKy31cnWV/US6PR4OPjg0ajYejQoQwZMqTE5XQ6HVFRUcyfPx+A/v37079/f7766is+/fRTFi5cyMCBA7G2tn6Yq//ESElJITY2lrZt2yrT9u/fT506dWjSpEmx5UsaY/v4+ADIcbKJyP5FnWT/ok6yvqhTaXP5/vvv2bdvH02bNmXOnDnUr19f5mJCj0t9KdPJkxi205EAAFrxCjFsx40XaIgb/6Fw41vjSzKxNKMt10hjI5/ghhfNea7Y510mhUskMZ/CgWsB+VSntjK/BS8BUB8XrnHv58meI57BzAHgWbqyiS+UeVpexAwz7GjMTa4B0BBX1jCZfPS04EUcaP4gX4t0F2vWrCEmJoa9e/cC0KBBA3755RcAkpKSSEtLw9nZmYEDB5Kbm8u0adOUq/Slh0fmUnbp6elERERw7tw5atSoQa9evVi7di3r169n1KhR5OTk4OPjg7m5ebGyPj4+HDlyhOeee47atWvTvn17ZbmwsDBluW7durFkyRKmT59OfHw83t7eDB48+GFt4lNLtmPqM3z4cIYPH863335LaGgoK1euxMPDg0OHDgGFz0m1s7NDCEGfPn2wtLRk9uzZ1KlT5xGv+dNH5qJOsh1TJ1lfTOvAgQPY29tz5coVvL29ad68OV5eXsWW27x5M88//zw2NjYAVK9ena1btwKF472ZM2fy448/MnjwYNLT0xkzZgzt27d/qNvyuLp16xY9e/YkLCzM4E7Sonf6/FtJY+w1a9YwYMAAOU5WIdm/qJPsX9RJ1pdHq1u3bvTr148KFSqwZMkSgoKC2L17t8xFpR5mLg98OiaLTM4Szbd8zGS6sJPlxPITINBg+HJ6DWBNdT7ge5rQhgNs5Fs+KvaZAkFdGvMB4XxAOJP4kRF8pcy3wOqflTangPwHXXWDz7rz7wI40Zr/soIa2LKaDzlMZJn+jaeFvb29wdXzaWlp2NvbF1tu586dTJ8+ncjISCpUqFBs/qRJkwgNDWXevHkMGjSIWbNmydusy6C0udyLzOXB7Ny5k2eeeYbatWtjaWlJjx49+O2332jfvj379+8nOjoaLy8vo435pEmTiIuL4+eff0YIUWy5iIgIWrVqxa1bt0hOTmbjxo2Eh4fLF5Y9INmOqdP9tmN9+/Yt9lJYIQShoaGEhIQwZcoUZs2axeDBg5k3b56pVvuJV5pcii6j1+vJzMykVq1aynyZS/mT/b46yfqiXndysLW1xc/Pj+jo6BKXW79+vdED+dOmTWPSpEmsW7eODh06sHLlSuUROdLd5eXl0bNnTwICAujRo4cyXa/X88MPP9CnT58SyxkbYxclx8nlS/Yv6iT7F3WS9UWdSpNLrVq1lH38QYMGcfTo0WKfI3MpX49LfXngkyex7OBZujKNHUzlJ0L/eTRXMkf5kxP8TRoFFHCUKBrhyS3SKaCAlnjTlXdJ5TQAFalMDlkA1OEZbpHOH8QBkE8el0i663pUoDK3KXkQ9AweHKXwWWdH2Epj7n7L7nUuUo1aPI8/z9FDWUfp7tq0aUNiYiLnzp0jNzeX9evX0717d4NlYmNjGTp0KJGRkdja2hb7jL1791KvXj2aNGmCTqfDzMwMMzMzOcAtg9Lkci8ylwfXoEEDDh06hE6nQwjBrl27cHZ25sqVKwDk5OTw6aef8vbbbxcrm5+fz7VrhXfEJSQkkJCQoDyOAAp3NsPCwhg/fjzZ2dnKOx7y8/PJzc19CFv35JHtmDqVJpfExETl961btxZ7xMeqVavw9fXFxsZG5lJOSpNL9+7dWblyJQDh4eG8+OKLSlsFMhdTkP2+Osn6ok5ZWVncvHlT+X3Hjh24ubkVWy4zM5O9e/fy2muvFZuXmJhIWloaHTt2VHLRaDRkZ2ebfP0fd0IIgoODcXZ2ZvTo0Qbzdu7cSfPmzXFwcCixrLEx9h1ynFz+ZP+iTrJ/USdZX9SpNLlcunRJ+T0yMtKgbwGZiyk8NvXF2JvkC180j5jP8RJ/mtBGvMMig2n+vC/q8IxojKdw5f+ELY7ieXqJecSL9wkXDjgLe5oJe5qJYSwU8zkugvlC2OIo7GkmvuCIeJ/vRGM8hT1NRV0ai358JOZzXDjRWoxjvZjPcTGTfcKGemI+x8WnHBANcBX2NBNv8pkYwDThRV8xn+NiKj+Jpjwr6tFENKWtmMoOMZ/joi3dRTCzlfW2opKYz3ExgFBhh5NwoLlojKf4mO1Gt7/wq5Pu2Lp1q2jSpIlo1KiRCA0NFUIIERISIiIiIoQQQnTu3FnY2tqKFi1aiBYtWohu3bopZQsKCsRLL70krl27JoQQ4tSpU6Jly5bC3d1dHDhw4L7WQ+Zi6F65REdHC3t7e2FtbS1sbGyEi4uLUlbmUnaTJ08WzZo1E66urmLAgAHi9u3bYuzYsaJ58+aiadOmYs6cOcqyR44cEcHBwUIIIbKzs4Wzs7NwdnYWbdu2FbGxsQafO2fOHLF8+XIhRGFOffv2FW5ubmL8+PH3tX5Pay7GyHZMne6Vy8iRI4WLi4to0aKF6Nixozhx4oRSNisrS3Ts2FHk5uYKIYTYt2+fcHNzE56enuL333+/r/WQuRi6Vy7Z2dnC399fNG7cWLRp00YkJycrZWUupiP7fXWS9UV9kpOThVarFVqtVri4uCi5LFq0SCxatEhZbvny5aJPnz4lfkavXr3E2bNnhRBCXL58WbRv3164uLiI8PDw+1qXpzGX/fv3C0C4u7sr46qtW7cKIYQICgoyyEAIIS5cuCBeeeUV5e+Sxth3yHGyacj+RZ1k/6JOsr6o071yef/994WLi4vQarWiY8eO4vTp00pZmYvpqKy+lHh+RFM4v2QajUbM53j5nal5gozAnbt9d9KjodFoZC4qJHNRJ5mLOslc1Enmok4yF3WSuaiTzEWdZC7qJHNRJ5mLOslc1Enmok4yF3X6JxdNSfPK/xX0kiRJkiRJkiRJkiRJkiRJkiRJjzGLu800M7cqGJHvLk+wlKBixYoGz4qU1EHmok4yF3WSuaiTzEWdZC7qJHNRJ5mLOslc1Enmok4yF3WSuaiTzEWdZC7qJHNRp4oVKxYYm3fPx3b5TN1ikpV63O2Y3FXeZqVC8vY3dZK5qJPMRZ1kLuokc1EnmYs6yVzUSeaiTjIXdZK5qJPMRZ1kLuokc1EnmYs6meyxXTsmd+V4+OfK3wX5+eyZ2Z9ja6YYLBf7bSiHvxpTrHzKgR84MO9tDi58l0OLR3ExbhcAR755nwNzh/LbghEcWjyKG5f+UMrk3c7i+Pez2R82mP1zBnH8+9nk3c4CIDv9Mjsmd+X8oc3K8qe3LOJC7M6ybKb0j7feegtbW1vc3NyUaSEhIWi1Wjw8PPDx8eHixYslljU3N8fDwwMPDw+6d++uTA8ICECr1TJx4kRlWmhoKJs2bTLZdjxNoqKiaNasGU5OTsycObPY/C+++AIXFxe0Wi2dO3fmzz//BODMmTO0atUKrVbLwYMHAdDr9bz00kvodLqHug1PmtTUVDp16oSLiwuurq7MnTu32DK///477du3p0KFCnz++f/a2KtXr9KhQwfc3NwM6shrr71mtO5JpSfrizrdvn2bZ599lhYtWuDq6spHH31UbJmcnBz69OmDk5MTbdu2JSUlBYBff/0VrVZL69atSUxMBCAjIwMfHx8KCoxeWPLUKal/v379Ot7e3jRp0gRvb2/S09MBEEIwcuRInJyc0Gq1HDt2rMTPPHr0KO7u7jg5OTFy5EhlB2HChAlotVoCAwOVZdesWUNYWJjpNvApItsxdbpXLrINMx1j4y5jbdy/yX0Y08nIyMDf35/mzZvj7OzMwYMHS50LwI0bN3BwcGDEiBFAYT16+eWXcXNzY+HChcpyQ4YMMdpXSYbOnDmj/H/38PCgWrVqhIWFMW7cOJo3b45Wq8XPz4+MjIwSyzs6OuLu7o6HhwetW7dWpsu+v+zmzp2Lm5sbrq6uyvcWHx9P+/btcXd3p1u3bty4caPUZUHmUh7mzJmDq6srbm5u9OvXj9u3byvzRo4cSZUqVYyWTUhIoH379ri6uuLu7s7t27dlO2ZiJe3zFLV27Vq0Wi3u7u4899xzxMfHA/I4jKnda5y8b98+PD09sbCwIDw8XJn+MPdfynTyxNyqIreu/El+Xg4A15JjqVitlsEyedm3uHExCf3tLHTX/1Kmpx7ZxrXkWNoN+YL273xJ6zemU/TEm7v/WJ4bPp/6z/py9qdvlOknN82lUs26/N9/v+b/Ri2lUs26nIqYp8y3qlyDPw9FUqDPK8umSSV44403iIqKMpg2btw4EhISiIuLo2vXrkydOrXEspUqVSIuLo64uDgiIyOBws6iUqVKJCQkcOTIETIzM7l06RKHDx/m9ddfN/XmPPHy8/MZPnw427dv59SpU6xbt45Tp04ZLNOyZUtiYmJISEjA39+f8ePHA7BkyRLmzp3Ltm3blIP3ixYtYsCAAVhbWz/0bXmSWFhYMHv2bE6dOsWhQ4dYsGBBsVxsbGyYN28eY8eONZi+bt063n77baKjo5VB7ebNm2nZsiX16tV7WJvwRJL1Rb0qVKjA7t27iY+PJy4ujqioKA4dOmSwzLJly6hZsyZJSUmMGjWKCRMmADB79my2bdtGWFgYixcvBgoPbk2cOBEzM/lU0jtK6t9nzpxJ586dSUxMpHPnzspAdvv27SQmJpKYmMhXX33FsGHDSvzMYcOG8fXXXyvLRkVFkZmZybFjx0hISMDKyorjx4+TnZ3N8uXLGT58uMm380kn2zF1Kk0usg0zHWPjLmNt3L/JfRjTee+993j55Zf5/fffiY+Px9nZudS5QOFFfF5eXsrfP/30Ex06dCAhIYHVq1cDhQeX8/Pz8fT0NPn2PAmaNWum/H8/evQo1tbW+Pn54e3tzYkTJ0hISKBp06bMmDHD6Gfs2bOHuLg4YmJiAGTfXw5OnDjB119/TXR0NPHx8WzZsoWkpCQGDRrEzJkzOX78OH5+fnz22WelLitzKbsLFy4wb948YmJiOHHiBPn5+axfvx6AmJiYu5781ev1DBgwgMWLF3Py5El++eUXLC0tZTtmYiXt8xT1zDPPsHfvXo4fP05ISAhDhgwB5HEYUyrNOLlBgwasWLGC/v37G0x/mPsvZR51/6dJa66ePQLAX8f3Utf9BYP5V07/Ru1mz1LX3Yu/ju9Tpp/b9x3O3YZjUbFwgywqWmPfsnOxz69Rvzk5N68BoLt2kRsXk2ncsa8yv3HHvmReSEJ3/RIAlpWrUatRC+UuFqn8eHl5YWNjYzCtWrVqyu9ZWVn39dw+S0tLsrOzKSgoIC8vD3NzcyZPnsyUKVPuXVi6p+joaJycnGjUqBFWVlb07duXiIgIg2U6deqkNCrt2rUjLS0NKMxGp9Oh0+mwtLQkIyODzZs3G1yVIj0YOzs7ZeBTtWpVnJ2duXDhgsEytra2tGnTBktLS4Ppd3LJycnB3NwcvV5PWFiYcvBLenCyvqiXRqNRrtrKy8sjLy+vWF8TERFBUFAQAP7+/uzatQshRLFskpOTSU1NpWPHjg97M1StpP696HcaFBSkXGUVERFBYGAgGo2Gdu3akZGRwaVLlwzKXrp0iRs3btCuXTs0Gg2BgYFs2rQJMzMz8vLyEEIomXz++ee8++67xdo76f7JdkydSpOLbMNMx9i4y1gbVxpyH6bsMjMz2bdvH8HBwQBYWVlRo0aNUudy9OhRLl++jI+PjzLtTn25089A4QmWadOmmXZjnlC7du2icePGNGzYEB8fHywsCl+XW7TvKA3Z95fd6dOnadu2LdbW1lhYWPDCCy/www8/cPbsWeUEore3N99//32py8pcyoderyc7Oxu9Xo9Op6NevXrk5+czbtw4Zs2aZbTcjh070Gq1tGjRAoBatWphbm4u2zETK2mfp6jnnnuOmjVrAiWPk+VxmPJXmnGyo6MjWq222IVDD3P/pcwnT+6cFMnPy+XW5RSqOzQ1mH8pYR927l7UdX+Bv47vBUB/W4c+R4e1Td17fv7ficewbd4OgFtXU6lm9wwaM3NlvsbMnGp2z3DrynllmmMHf1J+/RFRkF/WzZNKYdKkSdSvX5+1a9cavfPk9u3btG7dmnbt2imDYGdnZ2rXro2npyfdunUjKSmJgoICeUa9nFy4cIH69esrfzs4OBQ7SF/UsmXLeOWVVwAYPnw4n3zyCUFBQUycOJFp06bJqxxNICUlhdjYWNq2bVuq5fv3709ERATe3t5MnDiRhQsXMnDgQHlVcDmQ9UXd8vPz8fDwwNbWFm9v72J1pmh+FhYWVK9enWvXrvHBBx8QGBjIjBkzGDFiBJMmTSI0NPRRbMJj5/Lly9jZ2QFQt25dLl++DJSurly4cAEHB4diy1StWhVfX19atmyJnZ0d1atXl1dqlyPZjqlTaeuMbMNMr+i4y1gb929yH8Y0zp07R+3atXnzzTdp2bIlgwYNIisrq1S5FBQUMGbMGINH20LhweOUlBTatWvHyJEjiYyMxNPTU14V/IDWr19Pv379ik3/5ptvlL7j3zQaDT4+PrRq1YqvvvoKQPb95cDNzY39+/dz7do1dDod27ZtIzU1FVdXV+Ug43fffUdqamqpy8pcys7e3p6xY8fSoEED5Tv08fFh/vz5dO/eXWnLSnL27Fk0Gg1dunTB09NTOdEi2zH1KDpOlsdhTOd+91+Kepj7LxZl/YCqdZ/hdsYV/jq+l/80aW0wL+dWOrrrF6nR0BWNRoPG3IKbl1OoVN32np97PPxzCvL15Odm0/6defdcvihrm7pUd2jKpYS991VOejDTp09n+vTpzJgxg/nz55d41dWff/6Jvb09f/zxBy+++CLu7u40btzY4Hma3bp1Y8mSJUyfPp34+Hi8vb0ZPHjwQ9ySp9eaNWuIiYlh797COtOgQQN++eUXAJKSkkhLS8PZ2ZmBAweSm5vLtGnTaNq06V0+UbqXW7du0bNnT8LCwgzu4Lqb6tWrs3XrVgDS09OZOXMmP/74I4MHDyY9PZ0xY8bQvn17U662hKwvj4K5uTlxcXFkZGTg5+fHiRMnjD6rtigPDw/lEV/79u3Dzs4OIQR9+vTB0tKS2bNnU6dOHVOv/mNPo9Hc152ldzN+/HjlKq1BgwYxdepUli5dqlyB9+GHH5bLvyPdnWzHHg+yDSs/dxt33a2Nk/swpqHX6zl27Bhffvklbdu25b333iv2iC5juSxcuBBfX1+Dk/RQeOLx22+/BQrvVO3SpQsRERGMHj2a8+fPExgYaPDeGsm43NxcIiMjiz2ea/r06VhYWBAQEFBiuQMHDmBvb8+VK1fw9vamefPmeHl5yb6/jJydnZkwYQI+Pj5UrlwZDw8PzM3N+eabbxg5ciTTpk2je/fuWFlZlbosyDFZWaWnpxMREcG5c+eoUaMGvXr1YtWqVXz33XfKmMoYvV7PgQMHOHLkCNbW1nTu3JlWrVrRuXNn2Y6pwJ49e1i2bBkHDhwA5HEYtXqY+y/lcjqmdrO2nP3pG+pqDR/ZdfnEAfTZt9g/J5h9X7xFdsZl/jq+D4uK1phbVTJ4B8q/ufuP5f9GLaWeR2d+37oEgCq163Pj0jlEkRckioICblw6R5Xa9Q3KN/LqzbkD4UgPT0BAQIm3ikLhWXmARo0a0bFjR2JjYw3mR0RE0KpVK27dukVycjIbN24kPDxcvqS0DOzt7Q2uPklLS1NyKGrnzp1Mnz6dyMhIKlSoUGz+nasc582bx6BBg5g1a5Z8LEEZ5eXl0bNnTwICAujRo8cDfca0adOYNGkS69ato0OHDqxcuZKPP/64fFf0KSLry+OhRo0adOrUqdizaovmp9fryczMpFat/72DTQhBaGgoISEhTJkyhVmzZjF48GDmzbu/izOeJnXq1FEex3Xp0iVsbQsvfClNXbG3tzd4pEdJy8TGxiKEoFmzZnz33Xds3LiR5ORk5aXY0v2T7Zg6lbbOyDbMdEoadxlr4/5N7sOYhoODAw4ODsqdpP7+/hw7dqxUuRw8eJD58+fj6OjI2LFjWbVqFe+//77BMgsXLiQwMJBDhw5RvXp1NmzYwOzZs02/YU+I7du34+npaXBydsWKFWzZsoW1a9caPdl4p77Y2tri5+dHdHS0wXzZ9z+44OBgjh49yr59+6hZsyZNmzalefPm7Nixg6NHj9KvXz8aN25c6rJFyVwezM6dO3nmmWeoXbs2lpaW9OjRg48++oikpCScnJxwdHREp9Ph5ORUrKyDgwNeXl785z//wdraGl9f32IvhJft2KORkJDAoEGDiIiIMBiL3SGPw5Sv0u6/3Iup91/K5eSJvac3jTr1o2odR4Ppl47vxXPgFLxGf4PX6G9o93aY8t6TZ7x6cXrLIvS3CweW+pzsYu8p0Wg0OHUeQGbaGbKupmJdqx7V7Brxx94NyjJ/7N1AtXqNsa5leBtb5dr1qVK7AVfPGHbYUvkq2qFGRETQvHnzYsukp6eTk5MDwN9//82vv/6Ki4uLMj8vL095XmB2drYyGMvPzyc3N9fEW/DkatOmDYmJiZw7d47c3FzWr19f7CqF2NhYhg4dSmRkZIk7J3v37qVevXo0adIEnU6HmZkZZmZmcoewDIQQBAcH4+zszOjRox/oMxITE0lLS6Njx45KLhqNhuzs7HJe26eHrC/qdfXqVTIyMgDIzs7m559/LtbXdO/enZUrVwIQHh7Oiy++aLBjv2rVKnx9fbGxsZHZlFLR73TlypW89tpryvRVq1YhhFB25v79WAI7OzuqVavGoUOHEEKwatUqpfwdd57fnJeXR35+4WNWZSZlI9sxdSpNLrINMx1j4y5jbVxRch/GdOrWrUv9+vU5c+YMUPh+DRcXl1LlsnbtWs6fP09KSgqff/45gYGBBnetpKens2XLFgIDA+U4+QGtW7fO4JFdUVFRzJo1i8jISKOPqcnKyuLmzZvK7zt27Ch2l7Ds+x/clStXADh//jw//PAD/fv3V6YVFBQQGhrK22+/XeqyRclcHkyDBg04dOgQOp0OIQS7du1i9OjR/PXXX6SkpJCSkoK1tTVJSUnFynbp0oXjx4+j0+nQ6/Xs3bvXoH+R7dijcf78eXr06MHq1atLvGNBHocpf6UZJ9/Lw9h/KfNjuwAqVv8PDdsZblx2+mVuZ1yhev3/HeCwrlkXi4qVyUg9Q/02vuTnZHNoySg05uaYmVnQ8Hm/Yp9tblmBhs+9TsqvP+D6+nu4vv4ev29dzP45g4DCF8q7vjayxPVq9EJvDi56rzw2UQL69evHL7/8wt9//42DgwNTpkxh27ZtnDlzBjMzMxo2bMjixYsBiImJYfHixSxdupTTp08zdOhQzMzMKCgo4P333zfoGBYsWEBQUBDW1tZotVp0Oh3u7u74+vpSo0aNR7S1jz8LCwvmz59Ply5dyM/P56233sLV1ZXJkyfTunVrunfvzrhx47h16xa9evUCCgcAkZGRwP+uctywofBk5ZAhQwgICECv17No0aJHtl2Pu19//ZXVq1fj7u6Oh4cHAJ988gnnzxe+t+ntt9/mr7/+onXr1ty4cQMzMzPCwsI4deqU8piJSZMmMX36dKCwXr7++uvMnDnT6DuHpHuT9UW9Ll26RFBQEPn5+RQUFNC7d2+6du1qkE1wcDADBw7EyckJGxsb1q9fr5TX6XSsWLGCHTt2ADB69Gh8fX2xsrJSbot/2pXUv7///vv07t2bZcuW0bBhQzZu3AiAr68v27Ztw8nJCWtra5YvX658joeHB3FxcUDh1XJvvPEG2dnZvPLKKwbPR9+0aROtW7dWnt/s4eGBu7u7wYszpfsn2zF1Kk0usg0zHWPjLmNtnNyHeXi+/PJLAgICyM3NpVGjRixfvlzp5++Wy71MnTqVSZMmYWZmRpcuXViwYAHu7u5GDyxLhrKysvj5559ZsmSJMm3EiBHk5OTg7e0NFL5IefHixVy8eJFBgwaxbds2Ll++jJ9f4fEcvV5P//79efnll5XPkH1/2fTs2ZNr165haWnJggULqFGjBnPnzmXBggUA9OjRgzfffBPAIBdjZe+QuTy4tm3b4u/vj6enJxYWFrRs2ZIhQ4YYXT4yMpKYmBimTp1KzZo1GT16NG3atEGj0eDr68urr76qLCvbMdMoaZ8nLy8PKDwOM3XqVK5du8Y777wDFI7hYmJilPLyOEz5K804+ciRI/j5+ZGens7mzZv56KOPOHnyJPDw9l80QgjjMzUa4TN1S7n9Y0+SHZO7crfvTno0NBqNzEWFZC7qJHNRJ5mLOslc1Enmok4yF3WSuaiTzEWdZC7qJHNRJ5mLOslc1Enmok7/5FLicynL/xX0kiRJkiRJkiRJkiRJkiRJkiRJjzF58kSSJEmSJEmSJEmSJEmSJEmSJKmIu77zxFKjKdgxuas8wVKCihUqGLzIUVKHihUrylxUSOaiTjIXdZK5qJPMRZ1kLuokc1EnmYs6yVzUSeaiTjIXdZK5qJPMRZ1kLupUsWLFAmPz7vnOk7VFXoon/U/AqVPyGXUqJJ8dqE4yF3WSuaiTzEWdZC7qJHNRJ5mLOslc1Enmok4yF3WSuaiTzEWdZC7qJHNRJ5O98+St06eLTfv+yhVGnD3LB8nJyk9Wfr7BMldzc3nj9Gk+SE5mXFISyy5dokAIg+l3fvZnZADwXmIiYampymccvnGDxRculGX1pQeUn59Py5Yt6dq1KwDz58/HyckJjUbD33//bbTc+fPn8fHxwdnZGRcXF1JSUgAICAhAq9UyceJEZdnQ0FA2bdpkys14Yty+fZtnn32WFi1a4OrqykcffQTArl278PT0xMPDgw4dOpCUlFSs7LVr1+jUqRNVqlRhxIgRyvScnBxefvll3NzcWLhwoTJ9yJAhHDt2zPQb9YSbM2cOrq6uuLm50a9fP27fvm0wPycnhz59+uDk5ETbtm2VuvLrr7+i1Wpp3bo1iYmJAGRkZODj40NBgdGT5NK/ZGRk4O/vT/PmzXF2dubgwYPEx8fTvn173N3d6datGzdu3ChWzlhdA9mOlZcH6V/+/PNPpa1zdXVl8eLFgGzHTC0qKopmzZrh5OTEzJkzi82X7ZhpOTo64u7ujoeHB61btwYgJCQErVaLh4cHPj4+XLx4sVg5WV/K7q233sLW1hY3Nzdl2vXr1/H29qZJkyZ4e3uTnp4OgBCCkSNH4uTkhFarNfpdHj16FHd3d5ycnBg5cqSyQz1hwgS0Wi2BgYHKsmvWrCEsLMx0G/gEKqnf//jjj7G3t8fDwwMPDw+2bdtWYlljYzbZ75tGamoqnTp1wsXFBVdXV+bOnVtsmc8++0zJzc3NDXNzc65fv87Vq1fp0KEDbm5uBjm89tprJbaH0v25V7//xRdf4OLiglarpXPnzvz5558AnDlzhlatWqHVajl48CAAer2el156CZ1O91C34Ukkx2PqdK9c9u3bh6enJxYWFoSHhyvTZX0pO2P9SGn29+/WB8kxWdnNnTsXNzc3XF1dle9t3LhxNG/eHK1Wi5+fHxn/nAP4t5L2feDh5WKSR3K9YmPDjMaNlZ/K5ubFlqljZcWMxo2Z2bgxF3JyOHrzpsH0Oz//V6OGUubc7duk5eSYYpWl+zB37lycnZ2Vv59//nl27txJw4YN71ouMDCQcePGcfr0aaKjo7G1tSUhIYFKlSqRkJDAkSNHyMzM5NKlSxw+fJjXX3/dxFvyZKhQoQK7d+8mPj6euLg4oqKiOHToEMOGDWPt2rXExcXRv39/QkNDi5WtWLEi06ZN4/PPPzeY/tNPP9GhQwcSEhJYvXo1UNjZ5Ofn4+np+VC260l14cIF5s2bR0xMDCdOnCA/P5/169cbLLNs2TJq1qxJUlISo0aNYsKECQDMnj2bbdu2ERYWphzwCg0NZeLEiZiZyScsltZ7773Hyy+/zO+//058fDzOzs4MGjSImTNncvz4cfz8/Pjss8+KlTNW12Q7Vn4epH+xs7Pj4MGDxMXFcfjwYWbOnMnFixdlO2ZC+fn5DB8+nO3bt3Pq1CnWrVvHqVOnDJaR7Zjp7dmzh7i4OGJiYoDCnY+EhATi4uLo2rUrU6dOLVZG1peye+ONN4iKijKYNnPmTDp37kxiYiKdO3dWDpRs376dxMREEhMT+eqrrxg2bFiJnzls2DC+/vprZdmoqCgyMzM5duwYCQkJWFlZcfz4cbKzs1m+fDnDhw83+XY+SUrq9wFGjRpFXFwccXFx+Pr6FitnbMwm+33TsbCwYPbs2Zw6dYpDhw6xYMGCYv3LuHHjlNxmzJjBCy+8gI2NDevWrePtt98mOjpaOWiyefNmWrZsSb169R7B1jw5StPvt2zZkpiYGBISEvD392f8+PEALFmyhLlz57Jt2zZln3PRokUMGDAAa2vrh74tTxI5HlOn0uTSoEEDVqxYQf/+/Q2my/pSdsb6kdLs7xsrK8dkZXfixAm+/vproqOjiY+PZ8uWLSQlJeHt7c2JEydISEigadOmzJgxw+hn/Hvf52Hm8shbRXONhqaVKvFXbu49l/WtVYuIq1cfwlpJxqSlpbF161YGDRqkTGvZsiWOjo53LXfq1Cn0ej3e3t4AVKlSBWtraywtLcnOzqagoIC8vDzMzc2ZPHkyU6ZMMeVmPFE0Gg1VqlQBIC8vj7y8PDQaDRqNRjmbnpmZWeJOQ+XKlenQoQMVK1Y0mG5paYlOpyMvL0+5+jEkJIRp06aZeGueDnq9nuzsbPR6PTqdrlg2ERERBAUFAeDv78+uXbsQQii56HQ6LC0tSU5OJjU1lY4dOz6CrXg8ZWZmsm/fPoKDgwGwsrKiRo0anD17Fi8vLwC8vb35/vvvi5U1VtdkO1Y+HrR/sbKyokKFCkDh1XV3rpaT7ZjpREdH4+TkRKNGjbCysqJv375EREQYLCPbsYevWrVqyu9ZWVklPktZ1pey8/LywsbGxmBa0f/vQUFBylXvERERBAYGotFoaNeuHRkZGVy6dMmg7KVLl7hx4wbt2rVDo9EQGBjIpk2bMDMzU/K4U18+//xz3n33XSwtLR/Ktj4JjPX7pVXSmE32+6ZjZ2ennLCtWrUqzs7OXLjL0ybWrVtHv379gP+1Yzk5OZibm6PX6wkLC1MO4ksPrjT9fqdOnZSDu+3atSMtLQ2gWL+fkZHB5s2bDa4Slh6MHI+pU2lycXR0RKvVFjtRJetL2RnrR0qzv2+srByTld3p06dp27Yt1tbWWFhY8MILL/DDDz/g4+ODhUXh69iL9h2l8TBzMcnJk+3XryuP3Qr957ZAY3IKCjiZlUX9f3bkLufmGjy26/esLGXZdtWqkXL7dqlOtEim8d///pdZs2bd99UIZ8+epUaNGvTo0YOWLVsybtw48vPzcXZ2pnbt2nh6etKtWzeSkpIoKCiQVznep/z8fDw8PLC1tcXb25u2bduydOlSfH19cXBwYPXq1bz//vul/jxvb29SUlJo164dI0eOJDIyEk9PT3nVVjmwt7dn7NixNGjQADs7O6pXr46Pj4/BMhcuXKB+/fpA4dUP1atX59q1a3zwwQcEBgYyY8YMRowYwaRJk0q8o0gy7ty5c9SuXZs333yTli1bMmjQILKysnB1dVUGtd999x2pRR4TWVRJdU22Y+XjQfsXKLzFWqvVUr9+fSZMmEC9evVkO2ZCRdsoAAcHh2IHt2Q7ZloajQYfHx9atWrFV199pUyfNGkS9evXZ+3atSXeeQKyvpjC5cuXsbOzA6Bu3bpcvnwZKH1dcXBwKLZM1apV8fX1pWXLlsp4Qd7ZcP+M9ftQ+GhIrVbLW2+9pTxqrShjYzbZ7z8cKSkpxMbG0rZt2xLn63Q6oqKi6NmzJwD9+/cnIiICb29vJk6cyMKFCxk4cKC8WrsclKYtK2rZsmW88sorAAwfPpxPPvmEoKAgJk6cyLRp0+TdDeVEjsfU6X7rS1GyvpSvov1Iaff3Syorx2Rl5+bmxv79+7l27Ro6nY5t27YVy+Cbb75R+o5/K2nf52HmYvLHdn1o5IrROydJpqSk4FGlCh5VqwLFH9vVvHJlg5V9tVYtIu/yXg3JdLZs2YKtrS2tWrW677J6vZ79+/fz+eefc+TIEf744w9WrFgBQFhYGHFxcYwZM0a5ynH69On07t2br7/+upy34slkbm5OXFwcaWlpREdHc+LECebMmcO2bdtIS0vjzTffZPTo0aX+PAsLC7799ltiY2Pp1asXYWFhjBkzhtGjR+Pv709kZKQJt+bJlp6eTkREBOfOnePixYtkZWWxZs2aUpX18PDg0KFD7Nmzhz/++AM7OzuEEPTp04cBAwYoB2sk4/R6PceOHWPYsGHExsZSuXJlZs6cyTfffMPChQtp1aoVN2/exMrKqsTyJdU1kO1YWZWlfwGoX78+CQkJJCUlsXLlSi5fvizbMZWS7Vj5OHDgAMeOHWP79u0sWLCAffv2ATB9+nRSU1MJCAhg/vz5JZaV9cW07tz9Wx7Gjx9PXFwcs2fPJiQkhKlTp7J06VJ69+4tD3KVkrF+f9iwYSQnJxMXF4ednR1jxowpVvZuYzbZ75vWrVu36NmzJ2FhYQZ31RW1efNmnn/+eeVOsOrVq7N161ZiYmLw9PRk8+bN+Pv7M3jwYPz9/ZX3B0imtWbNGmJiYhg3bhxQ+HiiX375hYMHD2JtbU1aWhrOzs4MHDiQPn36cPbs2Ue8xk8nOR5TJ1lfys+/+5HS7u+XVBbkmKysnJ2dmTBhAj4+Prz88st4eHhgXuQVH9OnT8fCwoKAgIASyxvb93lYuTyy05d3TpJ80qgRPW1tS12uQ40a/K7TcT0vz4RrJ5Xk119/JTIyEkdHR/r27cvu3bsZMGBAqco6ODjg4eFBo0aNsLCw4PXXXy/20syIiAhatWrFrVu3SE5OZuPGjYSHh8sXY92HGjVq0KlTJ7Zv3058fLxypVafPn347bffHugzFy5cSGBgIIcOHaJ69eps2LCB2bNnl+dqP1V27tzJM888Q+3atbG0tKRHjx7FsrG3t1fOwuv1ejIzM6lVq5YyXwhBaGgoISEhTJkyhVmzZjF48GDmzZv3ULflceTg4ICDg4NSN/z9/Tl27BjNmzdnx44dHD16lH79+tG4ceO7fs6duvbv597LduzBlKV/KapevXrKVS1FyXasfBVto6DwkWv29vZGl5HtWPm7833b2tri5+dHdHS0wfyAgIASH0dQlKwv5adOnTrK47guXbqE7T/7NqWtK0UfUVDSMrGxsQghaNasGd999x0bN24kOTlZecmvZJyxfr9OnTqYm5tjZmbG4MGDi9UhKN2YTfb75S8vL4+ePXsSEBBAjx49jC63fv165ZFd/zZt2jQmTZrEunXr6NChAytXruTjjz820Ro/+UrTlkFhnZk+fTqRkZHKIyKLunN3w7x58xg0aBCzZs2Sj7srAzkeU6fS1pd7kfXlwZXUj5R2f/9efZAckz244OBgjh49yr59+6hZsyZNmzYFYMWKFWzZsoW1a9cavQDpXvs+ps7lsbv3y0Kj4RUbG7Zfu/aoV+WpM2PGDNLS0khJSWH9+vW8+OKLpb5ivk2bNmRkZHD1n3fW7N69GxcXF2V+Xl6e8kza7OxspcLk5+eTKx/TdldXr14lIyMDgOzsbH7++WecnZ3JzMxUrky4M+1+paens2XLFgIDA9HpdJiZmaHRaMjOzi7PTXiqNGjQgEOHDqHT6RBCsGvXrmLZdO/enZUrVwIQHh7Oiy++aNCJrFq1Cl9fX2xsbJRczMzM5I56KdStW5f69etz5swZAHbt2oWLiwtXrlwBoKCggNDQUN5+++1iZUuqa82bN1fmy3bswZWlf0lLS1PapPT0dA4cOECzZs2U+bIdK39t2rQhMTGRc+fOkZuby/r16+nevbvBMrIdM52srCxu3ryp/L5jxw7c3NwMdg4iIiIM2qc7ZH0xjaL/31euXMlrr72mTF+1ahVCCOVk1J3He91hZ2dHtWrVOHToEEIIVq1apZS/486dDXl5eeTn5wPI+lJKxvr9ou+e+fHHH3FzcytW9l5jNtnvlz8hBMHBwTg7O9/1rvnMzEz27t1brK4AJCYmkpaWRseOHWU7Vk5K0+/HxsYydOhQIiMjlRPIRe3du5d69erRpEkT2e+XEzkeU6fS5HIvsr48OGP9SGn290vTB8kx2YO7k8H58+f54Ycf6N+/P1FRUcyaNYvIyEijj9k0tu9TlMlzEUIY/QHEWhcXoz8aEDUtLJSfgDp1RI///EfUtLAQDSpUUH7CnJwMyoU5OQmHChWKfV6Yk5Ow1GgMyg6sU0esdXER/7G0FIubNhVrXVzEiubNRQ0LC/F/1avfdf1M+VP41T299uzZI1599VUhhBBz584V9vb2wtzcXNjZ2Yng4GAhhBBHjhxRfhdCiB07dgh3d3fh5uYmgoKCRE5OjjJvzpw5Yvny5UIIIQoKCkTfvn2Fm5ubGD9+/H2t19OYS3x8vPDw8BDu7u7C1dVVTJkyRQghxA8//CDc3NyEVqsVL7zwgkhOThZCCBERESFCQkKU8g0bNhQ1a9YUlStXFvb29uLkyZPKvP/+979iz549QgghsrOzhbe3t3BxcRHz5s27r3V8GnO5m8mTJ4tmzZoJV1dXMWDAAHH79m0REhIiIiIihBCF37W/v79o3LixaNOmjZKdEEJkZWWJjh07itzcXCGEEPv27RNubm7C09NT/P777/e1Hk9rLrGxsaJVq1bC3d1dvPbaa+L69esiLCxMNGnSRDRp0kRMmDBBFBQUCCGEuHDhgnjllVeEEMbr2h2yHSsf99u/3OlbtFqtcHd3F0uWLDH4PNmOmcbWrVtFkyZNRKNGjURoaKgQQsh27CFJTk4WWq1WaLVa4eLionz/PXr0EK6ursLd3V107dpVpKWlCSFkfSlvffv2FXXr1hUWFhbC3t5eLF26VPz999/ixRdfFE5OTqJz587i2rVrQojCvuCdd94RjRo1Em5ubuLIkSPK57Ro0UL5/ciRI8LV1VU0atRIDB8+XOmDhBDixx9/FB999JHy95gxY4Sbm5vo37//fa/7k5zL3ZTU7w8YMEC4ubkJd3d30a1bN3Hx4kUhhGG/L0TJY7Y7ZL9f/vbv3y8A4e7uLlq0aCFatGghtm7dKhYtWiQWLVqkLLd8+XLRp0+fEj+jV69e4uzZs0IIIS5fvizat28vXFxcRHh4+H2ti8zF0L36/c6dOwtbW1slt27duillCwoKxEsvvaS0jadOnRItW7YU7u7u4sCBA/e1HjIXQ3I8pk73yiU6OlrY29sLa2trYWNjI1xcXJSysr6UjbF+pDT7+8bK3lFeY7KnMRchhOjQoYNwdnYWWq1W7Ny5UwghROPGjYWDg4PyfQ8dOlQIYZiLsX2fO8o5lxLPj2gK55dMo9GItUXuDpD+J+DUKe723UmPhkajkbmokMxFnWQu6iRzUSeZizrJXNRJ5qJOMhd1krmok8xFnWQu6iRzUSeZizrJXNTpn1xKfG7YY/fYLkmSJEmSJEmSJEmSJEmSJEmSJFOSJ08kSZIkSZIkSZIkSZIkSZIkSZKKsLjbTEuN5nLAqVN1HtbKPE4qVqxYoNFo5MknlZG5qJPMRZ1kLuokc1EnmYs6yVzUSeaiTjIXdZK5qJPMRZ1kLuokc1EnmYs6yVzUqWLFipeNzbvrO08kSZIkSZIkSZIkSZIkSZIkSZKeNvJMlyRJkiRJkiRJkiRJkiRJkiRJUhHy5IkkSZIkSZIkSZIkSZIkSZIkSVIR8uSJJEmSJEmSJEmSJEmSJEmSJElSEfLkiSRJkiRJkiRJkiRJkiRJkiRJUhHy5IkkSZIkSZIkSZIkSZIkSZIkSVIR/w/Kdx2DVXa+fQAAAABJRU5ErkJggg==\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 = ['thistle', 'violet', 'darkviolet', 'steelblue', 'brown' ]\n",
    "n_rows = len(rows)\n",
    "\n",
    "index = np.arange(len(columns)) + 0.3\n",
    "bar_width = 0.4\n",
    "\n",
    "# Initialize the vertical-offset for the stacked bar chart.\n",
    "y_offset = np.zeros(len(columns))\n",
    "\n",
    "# Plot bars and create text labels for the table\n",
    "cell_text = []\n",
    "for row in range(n_rows):\n",
    "    ax.bar(index, M.T[row]*100, bar_width, bottom=y_offset, color=colors[row], linewidth=1)\n",
    "    y_offset = y_offset + M.T[row]*100\n",
    "    cell_text.append([f'{x*100:1.1f}%' for x in M.T[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=0.1, bottom=0.1, right=0.95, top=0.9)\n",
    "\n",
    "plt.ylabel(\"Pourcentage de report des voix\")\n",
    "plt.yticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.xticks([])\n",
    "plt.suptitle(\"Report des voix par résultat du 1er tour\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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 premier tour se sont abstenus au second (avec une légère différence dans la proportion de \"Mélenchon\" qui se sont abstenus). Remarquez aussi que les électeurs de \"Macron\" ou \"Le Pen\" au premier tour ont massivement voté pour la même personne au deuxième tour (\"vote d'adhésion\"). Environ un quart des électeurs de \"Le Pen\" au second tour s'était abstenu au premier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On observe aussi quelques points intéressants dans les votes nuls qui proviennent majoritairement de votant \"nul\" au premier tour ($40 \\%$) et ensuite par des électeurs ayant voté pour des candidats marginaux au premier tour (\"Arthaud\", \"Lassalle\", \"Roussel\", \"Poutou\"). On observe à peu près la même structure pour le votant \"blanc\". 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 ces observations par rapport aux particularités du vote \"militant\" lié à ces candidats.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut aussi se restreindre aux votes exprimés :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:12.499098Z",
     "iopub.status.busy": "2022-06-09T15:44:12.498624Z",
     "iopub.status.idle": "2022-06-09T15:44:12.500847Z",
     "shell.execute_reply": "2022-06-09T15:44:12.501176Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.3,   6.8, 100. ,   0.3,   0. ,  23.7,  95.6,  99.7, 100. ,\n",
       "         99.8,   3.8,   0.1],\n",
       "       [ 99.7,  93.2,   0. ,  99.7, 100. ,  76.3,   4.4,   0.3,   0. ,\n",
       "          0.2,  96.2,  99.9]], dtype=float32)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shift = 3\n",
    "MT = M[shift:, shift:].T\n",
    "MT /= MT.sum(axis=0)\n",
    "MT*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:12.514123Z",
     "iopub.status.busy": "2022-06-09T15:44:12.507431Z",
     "iopub.status.idle": "2022-06-09T15:44:12.828750Z",
     "shell.execute_reply": "2022-06-09T15:44:12.829142Z"
    },
    "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[shift:]\n",
    "rows = df_2.columns[shift:]\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=0.05, bottom=0.15, right=0.97, top=.9)\n",
    "\n",
    "plt.ylabel(\"Pourcentage de report des voix\")\n",
    "plt.yticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.xticks([])\n",
    "plt.suptitle(\"Report des voix exprimées connaissant le choix exprimé au 1er tour\", fontsize=16)\n",
    "plt.savefig(datetime + '_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\", \"Hidalgo\" ou \"Pécresse\" au premier tour, alors on va certainement voter \"Macron\" au deuxième tour. Ces électeurs se montrent particulièrement consensuel et suivent le « pacte républicain » mise en place pour faire un \"barrage\" au Front National (en suivant le terme consacré). 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.\n",
    "\n",
    "Connaissant les couleurs politiques d'autres candidats du premier tour, on peut être surpris que les électeurs de \"Arthaud\", \"Roussel\", \"Lassalle\" ou \"Poutou\" 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 parce qu'il y a moins de données disponibles.** "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ces résultats permettent de placer les tendances pour chaque profil de choix du 1er tour en fonction des choix faits au second, un premier axe horizontal donnant la part des voix *exprimées* pour Macron, le deuxieme la part des voix exprimées. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:12.832727Z",
     "iopub.status.busy": "2022-06-09T15:44:12.832247Z",
     "iopub.status.idle": "2022-06-09T15:44:12.836708Z",
     "shell.execute_reply": "2022-06-09T15:44:12.837044Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Nuls               247151\n",
       "Blancs             543609\n",
       "Abstentions      12824156\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             1627852\n",
       "PÉCRESSE          1679001\n",
       "POUTOU             268904\n",
       "DUPONT-AIGNAN      725176\n",
       "dtype: int64"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_1 = df_1.sum()\n",
    "n_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:12.866108Z",
     "iopub.status.busy": "2022-06-09T15:44:12.864444Z",
     "iopub.status.idle": "2022-06-09T15:44:13.370370Z",
     "shell.execute_reply": "2022-06-09T15:44:13.370716Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 Nuls\n",
      "1 Blancs\n",
      "2 Abstentions\n",
      "3 ARTHAUD\n",
      "4 ROUSSEL\n",
      "5 MACRON\n",
      "6 LASSALLE\n",
      "7 LE PEN\n",
      "8 ZEMMOUR\n",
      "9 MÉLENCHON\n",
      "10 HIDALGO\n",
      "11 JADOT\n",
      "12 PÉCRESSE\n",
      "13 POUTOU\n",
      "14 DUPONT-AIGNAN\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
    "\n",
    "p_nonexpr = M[:, :shift].sum(axis=1) / M.sum(axis=1)  * 100\n",
    "p_macron = M[:, -2] / M[:, -2:].sum(axis=1) * 100\n",
    "ax.scatter(p_macron, p_nonexpr, s=np.sqrt(n_1), c=np.arange(15), alpha=.5)\n",
    "\n",
    "for i_column, column in enumerate(df_1.columns):\n",
    "    print(i_column, column)\n",
    "    textshift = -15 if ( (i_column ==5) or (i_column == 7)) else 6 \n",
    "    ax.annotate(column,\n",
    "            xy=(p_macron[i_column], p_nonexpr[i_column]), xycoords='data',\n",
    "            xytext=(p_macron[i_column]+textshift, \n",
    "                    p_nonexpr[i_column]+5), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"->\",\n",
    "                            connectionstyle=\"arc3\"),\n",
    "            )\n",
    "\n",
    "# Adjust layout to make room for the table:\n",
    "plt.subplots_adjust(left=0.1, bottom=0.1, right=0.95, top=0.9)\n",
    "# ax.set_xlim(0, 100)\n",
    "# ax.set_ylim(0, 100)\n",
    "plt.xlabel(\"Pourcentage de voix pour Macron\")\n",
    "plt.ylabel(\"Pourcentage de voix non exprimées\")\n",
    "plt.yticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.xticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.suptitle(\"Tendances électorales présidentielle 2022\");\n",
    "plt.savefig(datetime + '_transfert-des-voix_tendances.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Celà montre un paysage en trois groupes distincts dans cette présidentielle: les \"abstentionnistes\", les \"extrèmes\", les \"républicains\". Notons que ce résultat est nettement lié à la coalition lancée pour faire barrage à l'extrème droite et que les reports seront largement variables dans d'autres élections, comme des legislatives."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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": "markdown",
   "metadata": {},
   "source": [
    "Muni de ces outils, on peut aussi faire certaines estimations (encore à prendre avec des pincettes) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:13.375131Z",
     "iopub.status.busy": "2022-06-09T15:44:13.374563Z",
     "iopub.status.idle": "2022-06-09T15:44:13.377168Z",
     "shell.execute_reply": "2022-06-09T15:44:13.377491Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Total des voix au 1er tour= 48747860, dont Macron = 9783058 (soit une pourcentage de 20.07%), \n",
      "-> nombre de reports de Macron du 1er vers Le Pen au 2eme = 462 personnes.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(f\"\"\"\n",
    "Total des voix au 1er tour= {x_1.sum():.0f}, dont Macron = {x_1[:, 5].sum():.0f} (soit une pourcentage de {x_1[:, 5].sum()/x_1.sum()*100:.2f}%), \n",
    "-> nombre de reports de Macron du 1er vers Le Pen au 2eme = {x_1[:, 5].sum()*MT[1, 2]:.0f} personnes.\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "À noter qu'on pourrait aussi utiliser une procédure similaire pour prédire pour un électeur du second tour la distribution des préférences au premier tour. En effet, si la préférence pour le choix d'un individu se pose au second tour *entièrement* sur le choix $j^\\ast$, on peut le formaliser comme $q_j = 0$ pour $j \\neq j^\\ast$ et $q_{j^\\ast}=1$ et on obtient la prédiction:\n",
    "\n",
    "$$\n",
    "\\hat{q}_j = M^{+}_{j^\\ast i}\n",
    "$$\n",
    "\n",
    "où $M^{+}$ est la pseudo-inverse de la matrice de transition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Influence des parametres\n",
    "\n",
    "Finalement, et pour clore l'exercise, nous validons 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": 86,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:44:13.382250Z",
     "iopub.status.busy": "2022-06-09T15:44:13.381354Z",
     "iopub.status.idle": "2022-06-09T15:50:05.537703Z",
     "shell.execute_reply": "2022-06-09T15:50:05.538084Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAIN: Loss avec do_optim=True = 1.50e-02 / Loss avec alternative choice do_optim=False = 1.50e-02 \n",
      "TEST: Loss avec do_optim=True = 1.50e-02 / Loss avec alternative choice do_optim=False = 1.50e-02 \n"
     ]
    }
   ],
   "source": [
    "trans, loss_train_alt, loss_test_alt, loss_test_l1_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": 87,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:50:05.541773Z",
     "iopub.status.busy": "2022-06-09T15:50:05.541204Z",
     "iopub.status.idle": "2022-06-09T15:50:05.543458Z",
     "shell.execute_reply": "2022-06-09T15:50:05.543847Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "do_optim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T15:50:05.549571Z",
     "iopub.status.busy": "2022-06-09T15:50:05.548978Z",
     "iopub.status.idle": "2022-06-09T16:31:55.691782Z",
     "shell.execute_reply": "2022-06-09T16:31:55.692144Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour learning_rate= 1.00e+00, loss_train=1.51e-02 / loss_test=1.51e-02; le temps de calcul est 352.325 s\n",
      "Pour learning_rate= 2.15e+00, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 367.290 s\n",
      "Pour learning_rate= 4.64e+00, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 373.419 s\n",
      "Pour learning_rate= 1.00e+01, loss_train=1.50e-02 / loss_test=1.51e-02; le temps de calcul est 362.251 s\n",
      "Pour learning_rate= 2.15e+01, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 352.767 s\n",
      "Pour learning_rate= 4.64e+01, loss_train=1.59e-02 / loss_test=1.65e-02; le temps de calcul est 351.497 s\n",
      "Pour learning_rate= 1.00e+02, loss_train=1.60e-02 / loss_test=1.57e-02; le temps de calcul est 350.160 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, loss_test_l1, p_1, p_2, p_2_pred = fit_data(df_1, df_2, learning_rate=learning_rate_, num_epochs=num_epochs, 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": 89,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T16:31:55.698396Z",
     "iopub.status.busy": "2022-06-09T16:31:55.697583Z",
     "iopub.status.idle": "2022-06-09T17:13:41.143462Z",
     "shell.execute_reply": "2022-06-09T17:13:41.143795Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  32  128  288  512  800 1152]\n",
      "Pour batch_size= 32, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 758.352 s\n",
      "Pour batch_size= 128, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 383.000 s\n",
      "Pour batch_size= 288, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 335.277 s\n",
      "Pour batch_size= 512, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 307.871 s\n",
      "Pour batch_size= 800, loss_train=1.57e-02 / loss_test=1.57e-02; le temps de calcul est 365.565 s\n",
      "Pour batch_size= 1152, loss_train=1.58e-02 / loss_test=1.58e-02; le temps de calcul est 355.077 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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SpKKxec9hrip9hcMjLoWKIVmXo15QlnUBkiRJUnddNraKVLGRNONDWZeiXmIgkSRJUvF4dQ3RcoRw/Ei/YZctSZIkFYWUEt++9978m9rF2RajXmMgkSRJUlHY1thEzZ5nOFI5Gqprsy5HvcRAIkmSpKLwzJZ9XBmv0DLhKidE7EcMJJIkSSoK69ato7ZkF0NnXpt1KepFBhJJkiQVhebNSwEodUB7v2IgkSRJUlFYUvYKrSUVMP7yrEtRL/Kxv5IkSSoKNw7eCEMWQlll1qWoF9lCIkmSpD6v6egR0vZVPu63HzKQSJIkqc/72vf+nWhrNpD0QwYSSZIk9XkV25fn/2OSgaS/MZBIkiSpT9t3uJlpR9fQOGgSDBubdTnqZQYSSZIk9Wmr6vdxZckrNI+/MutSdB4YSCRJktSnrX9lLWNiP8NnOSFif2QgkSRJUp924+ANAFROe13Gleh8MJBIkiSpT5vVvBYqhsKYOVmXovPAQCJJkqQ+a9/hZo5ueJLchIVQ6pze/ZGBRJIkSX3Wr9ZspHzXC+wbuSDrUnSeGEgkSZLUZ+15+WnKIkfN7OuyLkXniYFEkiRJfVbZtvyEiKWTr8q4Ep0vBhJJkiT1SUeb26g9vJrdg6fC4IuyLkfniYFEkiRJfdKarftYEK9wbNyirEvReeSjCiRJktQnza3cyeA4ROUl12ddis6jARlIIuIO4K3AcOCbKaVHs61IkiRJXQ1+dSUAQ6Y7IWJ/1q0uWxHxrYjYGRFrzrDNpohYHRGrImJ5h+U1EfGvEfFiRKyNiNf8iTpdHRFxS0S8FBHrIuKzZztOSun+lNJdwN3A+15rPZIkSTp/1tb9lNbKahg5K+tSdB51dwzJt4FburHdTSml+Smljh39/gb4UUrpEuAKYG3XnSJiTEQM67JsZnfqiIhS4CvArcAc4M6ImFNYNy8iHuzyGtNh988V9pUkSVIfsqOxidKtdWwfOg9KHPbcn3XrXzel9Biwt6cHj4hq4Abgm4XjNKeU9p9i0xuB+yOisrDfXcCXu1nHYmBdSmlDSqkZ+B5we2H71Smlt3V57Yy8vwAeSSmt7Ol1SZIk6fxas34zs0u2Ujrl6qxL0XnWm3EzAY9GxIqI+ERh2TRgF/APEfFMRHwjIqpO2jGl+4AfA9+PiA8CHwN+o5vnnQjUd3jfUFh2Jp8GbgbeExF3n2qDiHh7RNzT2NjYzTIkSZLUW/a89AQAoy51QsT+rjcDyXUppYXku059MiJuID9ofiHw1ZTSAuAwcMoxHimlLwJNwFeBd6SUDvVibV3P9aWU0pUppbtTSl87zTYPpJQ+UV1dfb7KkCRJ0mmUbl1GGyVUOCFiv9drgSSltLXwdSfwA/JdqRqAhpTS0sJm/0o+oJwkIq4H5hb2/XwPTr0VqO3wflJhmSRJkopQLpeoPbyanYNnQuXQrMvRedYrgSQiqo4PSi90yXozsCaltAOoj4iLC5u+EXjhFPsvAO4hP/bjo8DIiPhCN0+/DJgVEdMiogJ4P/DDc7ogSZIkZaaEHIvLNzLyUucfGQi6+9jf7wJPARdHRENEfLyw/OGImACMBR6PiGeBOuChlNKPCrt/GvhORDwHzAf+9BSnGAK8N6W0PqWUAz4MbO5OHSmlVuBT5MegrAXuTSk9383rlyRJUl+z8wWi+RAVUx3QPhB0a2LElNKdp1l+W4e3V5xmm1XAolOt67DNE13etwBf70EdDwMPn+kckiRJKg6//OmDvB6gdnHGlehC8KHOkiRJ6lNaNj/N/tIRUDMl61J0ARhIJEmS1GccaGphVvNadtdcARFZl6MLwEAiSZKkPmPty+uZGq9SMnlJ1qXoAjGQSJIkqc/YvfbXAIyZc0PGlehCMZBIkiSpz5hwaDUtlDN06pVZl6ILpFtP2ZIkSZIuhAXxMkyaD+WDsi5FF4gtJJIkSeoTUusx2LoSah0/MpAYSCRJktQn/Pqxn0HbMfZcdMrp7dRPGUgkSZLUJxzZ8DQA1bOvzbgSXUgGEkmSJPUJw3atYGfpGMpqJmZdii4gA4kkSZIyd6yllZlNz7OrZn7WpegCM5BIkiQpc6+88iJjYx9RuzjrUnSBGUgkSZKUuVH7ngVg3GVOiDjQGEgkSZKUuXEHnoPyIYyYvjDrUnSBGUgkSZKUuaYNT5EmLITS8qxL0QVmIJEkSVKmdu/bR+nONazi4qxLUQYMJJIkScrUpueeoDzaqJrxuqxLUQYMJJIkScrUkfVPAlB7+Y0ZV6IsGEgkSZKUqaqdK6gvmcTgmjFZl6IMGEgkSZKUmba2HNOOPs+umsuzLkUZKcu6AEmSJA1cac96RsRBjjr/yIBlC4kkSZIyU7ZtGQAT570+20KUGQOJJEmSMrN19S9pLR8Go3zk70BlIJEkSVJmmjcu5YXSi6HE29KByn95SZIkZeJw416mtG3m0OiFWZeiDBlIJEmSlInNzz1GSSSGzLgm61KUIQOJJEmSMnF4/ZO0pWDy5T5hayAzkEiSJCkTVa+uYGPpFEaMGJl1KcqQgUSSJEkXXq6NS3MvMc75RwY8A4kkSZIuvF0vEscOMnTmtVlXoowZSCRJknTBrV/5cwAOjl6QcSXKmoFEkiRJF9yhdU+yJw2ncvTMrEtRxgwkkiRJuuBG73+W9YMuo6K8NOtSlDEDiSRJki6olgM7mdC2lQOjnBBRBhJJkiRdYFtXPwbA4OlXZ1yJ+gIDiSRJki6shqW0UsqUeT5hS1CWdQGSJEkaWKYeeZ40cT4TR4/IuhT1AbaQSJIk6cJpa4GtK4naJURE1tWoDzCQSJIk6YI5uOkZaD3KczE761LURwzIQBIRd0TE1yPi+xHx5qzrkSRJGih2PP8rAJrHLcq4EvUV3QokEfGtiNgZEWvOsM2miFgdEasiYvnZlr8Wp6sjIm6JiJciYl1EfPZsx0kp3Z9Sugu4G3jfudQkSZKk7sttWcrWNJJLLrk061LUR3S3heTbwC3d2O6mlNL8lFLXyHu65QBExJiIGNZl2amm7TypjogoBb4C3ArMAe6MiDmFdfMi4sEurzEddv9cYV9JkiRdACP3Pcu6iksZWumzlZTXrU9CSumxiJh6Huu4Ebg7Im5LKR2LiLuAd5EPGWerYzGwLqW0ASAivgfcDryQUloNvK3rySI/gurPgUdSSit7/WokSZJ0ktTYwKi2nRwY8/6sS1Ef0ptjSBLwaESsiIhPdGP5iQ1Sug/4MfD9iPgg8DHgN7p53olAfYf3DYVlZ/Jp4GbgPRFx96k2iIi3R8Q9jY2N3SxDkiRJZ9K8aSkAIy+9PuNK1Jf0ZlvZdSmlrYUuUT+JiBdTSo+dYXknKaUvFlo3vgrMSCkd6sXaup7rS8CXzrLNA8ADixYtuut81SFJkjSQVG5fDmWDuebam7IuRX1Ir7WQpJS2Fr7uBH5AvivVaZd3FRHXA3ML23y+B6feCtR2eD+psEySJEl9SMvmpaQJ86G0POtS1If0SiCJiKrjg9Ijogp4M7DmdMtPsf8C4B7yYz8+CoyMiC908/TLgFkRMS0iKoD3Az8812uSJElSL2o5Ctuf5ZH9k7OuRH1Mdx/7+13gKeDiiGiIiI8Xlj8cEROAscDjEfEsUAc8lFL60RmWdzUEeG9KaX1KKQd8GNjcnTpSSq3Ap8iPQVkL3JtSer4n3wRJkiSdX8fqV1JOK03OP6IuuvuUrTtPs/y2Dm+vOMX6DadafortnujyvgX4eg/qeBh4+GznkSRJUjZ2vvAYtcCISxzQrs4G5EztkiRJurDaNi9lY24sl82annUp6mMMJJIkSTq/UmLE3lW8WH4po4dVZl2N+hgDiSRJks6vfRsZ3raP8XNvzLoS9UEGEkmSJJ1f9csAmP+6N2dciPoiA4kkSZLOqwOvPEFb+VBaR16cdSnqgwwkkiRJOq+ObniSp45No9VbT52CnwpJkiSdP8cOMvrIeuqr5jGovDTratQHGUgkSZJ03rTVr6CEHC0TnBBRp2YgkSRJ0nmz98XHyKVg5MXXZF2K+igDiSRJks6bls1P83KaxGXTJ2ddivqosqwLkCRJUj+VyzH+4BrKL7mNUSOHZF2N+igDiSRJks6P3S8TTY2MvvR6iMi6GvVRdtmSJEnSedG08UkANlfNzbgS9WUGEkmSJJ0XjS8/wd40lM1pfNalqA8zkEiSJOm8KN+2nJW5WVwx+aKsS1EfZiCRJElS7zuylxFHN7Fx8FyqB5dnXY36MAOJJEmSel2qrwOgefxVGVeivs5AIkmSpF53dMNTtFLCRbOXZF2K+jgf+ytJkqReN+TVFaTxl/OeJbOzLkV9nC0kkiRJ6l1trbB1BVG7hIoybzd1Zn5CJEmS1LteXQMtR/jJoalZV6IiYCCRJElSr2rZshSAl8svybgSFQPHkEiSJKlXHXz5CZrTRUyfYSDR2dlCIkmSpF5Vvm0ZK3KzmD/FCRF1dgYSSZIk9Z6DOxjWtI1XKi5jfPXgrKtRETCQSJIkqfcUJkQcOvN1GReiYmEgkSRJUu+pXwqllfzWb9yRdSUqEgYSSZIk9Zpc/VLShAVQVpl1KSoSBhJJkiT1jtZj5Lau4p+3jqWlLZd1NSoSBhJJkiT1ju3PUpZa2DT4MspLvc1U9/hJkSRJUq/IbXkagNIpSzKuRMXEiRElSZLUK46sf5I9uTHMmj4j61JURGwhkSRJ0rlLidKty1iZZrFgck3W1aiIGEgkSZJ07vZvYfCx3QyZcQ3TRw3NuhoVEbtsSZIk6dwVJkR8y1veASWRcTEqJraQSJIk6Zy1bn6atrIqjo28OOtSVGQMJJIkSTpnxzY+zdPHpvLEhv1Zl6IiYyCRJEnSuTl2iMH71rIizeKKSTVZV6MiYyCRJEnSudm2kpLURkPVPEYOrcy6GhWZATmoPSLuAN4KDAe+mVJ6NNuKJEmSilhhQHvJ5MUZF6Ji1K0Wkoj4VkTsjIg1Z9hmU0SsjohVEbG8y7rSiHgmIh48l2JPV0dE3BIRL0XEuoj47NmOk1K6P6V0F3A38L5zqUmSJGmga9r4FK/kJnLJ1NqsS1ER6m6XrW8Dt3Rju5tSSvNTSou6LP8dYO3pdoqIMRExrMuymd2pIyJKga8AtwJzgDsjYk5h3byIeLDLa0yH3T9X2FeSJEmvRS5H5Y4VDJ99LW+ZOy7ralSEuhVIUkqPAXtfywkiYhL57lHfOMNmNwL3R0RlYZ+7gC93s47FwLqU0oaUUjPwPeD2wvarU0pv6/LaGXl/ATySUlr5Wq5LkiRJwJ51xNF9jJ1zA+OrB2ddjYpQbw5qT8CjEbEiIj7RYflfA38A5E67Y0r3AT8Gvh8RHwQ+BvxGN887Eajv8L6hsOxMPg3cDLwnIu4+1QYR8faIuKexsbGbZUiSJA1ADfnxI2tKnH9Er01vBpLrUkoLyXed+mRE3BARbwN2ppRWnG3nlNIXgSbgq8A7UkqHerG2ruf6UkrpypTS3Smlr51mmwdSSp+orq4+X2VIkiQVvdyWpexPVfz7liFZl6Ii1WuBJKW0tfB1J/AD8l2prgXeERGbyHelekNE/POp9o+I64G5hX0/34NTbwU6jqCaVFgmSZKk86x541OszM1i/pQRWZeiItUrgSQiqo4PSo+IKuDNwJqU0n9JKU1KKU0F3g/8PKX0oVPsvwC4h/zYj48CIyPiC908/TJgVkRMi4iKwnl+eM4XJUmSpDM7uo9B+19hRW42C2prsq5GRaq7j/39LvAUcHFENETExwvLH46ICcBY4PGIeBaoAx5KKf2oB3UMAd6bUlqfUsoBHwY2d6eOlFIr8CnyY1DWAvemlJ7vwbklSZL0WjTke+Wvr7yUSRc5oF2vTbcmRkwp3Xma5bd1eHvFWY7xS+CXp1n3RJf3LcDXe1DHw8DDZzq/JEmSeln9UtooobT2KiIi62pUpHpzULskSZIGkvqllIyby5+8b0nWlaiIGUgkSZLUc7k22LqCqF1CzZCKrKtRETOQSJIkqed2vgDNh7jv1fGklLKuRkXMQCJJkqSeq18KwAP7Jjl+ROekW4PaJUmSpI5S/VJ2U8O4yc7QrnNjC4kkSZJ6rHVzHSvaZrHACRF1jgwkkiRJ6plDOylv3MSK3CzmOyGizpGBRJIkST1TXwfArpormD12WMbFqNg5hkSSJEk9U78USiv46898BEoc0K5zYwuJJEmSeiQ1LIPxV0D5oKxLUT9gIJEkSVL3tTaTtq7gO9vGsap+f9bVqB8wkEiSJKn7djxHSVszv26awYQaW0h07gwkkiRJ6r7CgPbtw+YxZpiBROfOQCJJkqTuq1/KdkYzafL0rCtRP2EgkSRJUvekRNuWp6lrm8WCyTVZV6N+wkAiSZKk7mlsoPTQDsqnXM01M0ZlXY36CechkSRJUvc05MeP3HbbO2DC8IyLUX9hC4kkSZK6p76OXNlgWkbNyboS9SMGEkmSJHVLql/K8pZp/MmP1mVdivoRA4kkSZLOrvkI7FhNXdssLp9UnXU16kcMJJIkSTq7bc8QuVZW5mYxv7Ym62rUjxhIJEmSdHb1SwFYX3Ep00ZVZVyM+hOfsiVJkqSzq6+jvmQiUydNJiKyrkb9iC0kkiRJOrOUoKGOiqlX89uvn5F1NepnbCGRJEnSme3dAEf2MPayGxg7fWTW1aifsYVEkiRJZ1YYP7K8bVbGhag/MpBIkiTpzOqXcqSkij/81bGsK1E/ZCCRJEnSGaX6OlalWVwxZUTWpagfMpBIkiTp9JoaYedanm6eyQLnH9F5YCCRJEnS6TUsJ0isSLNYMPmirKtRP2QgkSRJ0unV15GjhLUls7h43LCsq1E/5GN/JUmSdHoNdcSYS/m3995Ceal/y1bv81MlSZKkU8u15btsTV7CtFFVWVejfspAIkmSpFPb9SIcO8C/7ZrI1v1Hs65G/ZSBRJIkSadWXwfAl16+iMi4FPVfBhJJkiSdWn0dB0traBo6mfHVg7KuRv2UgUSSJEmnVr+UZ5nN/MkXEWEbic4PA4kkSZJOdng37F3Pr5tmOP+IzisDiSRJkk7WsAyATYMvY74ztOs8ch4SSZIknax+KZSU8fd/+FukMseP6PwZkIEkIu4A3goMB76ZUno024okSZL6mPo6GH8FlA/2CVs6r7rVZSsivhUROyNizRm22RQRqyNiVUQsLywbFBF1EfFsRDwfEX98LsWero6IuCUiXoqIdRHx2bMdJ6V0f0rpLuBu4H3nUpMkSVK/09ZC2rqSH+yexHfrtmRdjfq57o4h+TZwSze2uymlND+ltKjw/hjwhpTSFcB84JaIuLrrThExJiKGdVk2szt1REQp8BXgVmAOcGdEzCmsmxcRD3Z5jemw++cK+0qSJOm4HauJ1qP89OAUSktsH9H51a1AklJ6DNjb04OnvEOFt+WFVzrFpjcC90dEJUBE3AV8uZt1LAbWpZQ2pJSage8Btxe2X51SeluX187I+wvgkZTSyp5elyRJUr9WmBBxRW4WCxzQrvOsN5+ylYBHI2JFRHzi+MKIKI2IVcBO4CcppaUn7ZjSfcCPge9HxAeBjwG/0c3zTgTqO7xvKCw7k08DNwPviYi7T7VBRLw9Iu5pbGzsZhmSJEn9RP1S9peP4XDlWGaMHpp1NernejOQXJdSWki+69QnI+IGgJRSW0ppPjAJWBwRc0+1c0rpi0AT8FXgHR1aVnpdSulLKaUrU0p3p5S+dpptHkgpfaK6uvp8lSFJktQ3NSzjubiYy2urKbHLls6zXgskKaWtha87gR+Q70rVcf1+4BecZixKRFwPzC3s+/kenHorUNvh/aTCMkmSJPVU41ZorOfw6IXcMnd81tVoAOiVQBIRVccHpUdEFfBmYE1EjI6ImsLywcCbgBdPsf8C4B7yYz8+CoyMiC908/TLgFkRMS0iKoD3Az88x0uSJEkamBry40duve12fvPqKRkXo4Ggu4/9/S7wFHBxRDRExMcLyx+OiAnAWODxiHgWqAMeSin9CBgP/CIiniMfHH6SUnrwFKcYArw3pbQ+pZQDPgxs7k4dKaVW4FPkx6CsBe5NKT3fk2+CJEmSCurrSGWDaRszL+tKNEBESqd66JWOW7RoUVq+fHnWZUiSJF0YX38jr+w5xqcH/Sk/+swNWVejfiIiVnSYGqST3hzULkmSpGLWchS2P8tTzTOZPXbY2beXeoGBRJIkSXnbVkGuhceapjPf+Ud0gRhIJEmSlFefny5uZW4WCybXZFuLBgwDiSRJkvIalrG3chKHSmuYM2F41tVogCjLugBJkiT1ASlB/VLSpOv5/8+aQ2VZadYVaYAwkEiSJAn2bYTDuxh56fV8aJHzj+jCscuWJEmSoH4ZAKuYTVNLW8bFaCAxkEiSJAnql9JcWsW7/nUfOw8cy7oaDSB22ZIkSRLU17Fx0KXUMIjaEYOzrkYDiC0kkiRJA92xg7DzeZ5umcmC2hoiIuuKNIAYSCRJkga6rSsg5fjZoSlOiKgLzkAiSZI00NXXkQhW5WayYPJFWVejAcYxJJIkSQNd/VLS6Ev4p3e8mVljh2ZdjQYYW0gkSZIGslwO6pdRMnkJV9TWMKTCv1frwjKQSJIkDWS7X4ZjjTy8r5ZV9fuzrkYDkIFEkiRpIKtfCsD/XFvDC9sOZFyMBiIDiSRJ0kBWX8exiho2pnE+YUuZMJBIkiQNZA11bBp0GUMqypjtgHZlwEAiSZI0UB3ZC7tfZmnbTOZNrKas1FtDXXh+6iRJkgaqhmUAPN3s/CPKjs91kyRJGqjql0KU8pXf/zjNJYOyrkYDlIFEkiRpoKqvg3HziIoqKrOuRQOWXbYkSZIGorZW2LqC5blZ/MlDL2RdjQYwW0gkSZIGolfXQMsRHtxXy87hR7OuRgOYLSSSJEkDUX0dAD85MIUFtQ5oV3YMJJIkSQNRQx1Ng8ewlVHMn1yTdTUawAwkkiRJA1H9UjYPnktZSQlzJ1RnXY0GMAOJJEnSQHNwB+zfwr6RC7hl7jgGV5RmXZEGMAe1S5IkDTSF8SNX33ArV9cuzLgYDXS2kEiSJA009UtJpZWkcfOyrkQykEiSJA049XXsHj6H+X/6GDsam7KuRgOcgUSSJGkgaT0G21fxQtklAIwd7hztypaBRJIkaSDZ/iy0NfOrw9O4oraGiMi6Ig1wBhJJkqSBpH4pAA/um8SC2ppsa5EwkEiSJA0s9UtpGjqZnanGCRHVJ/jYX0mSpIEiJaivo2XCtfz23Bm2kKhPMJBIkiQNFPu3wKFXGTbzGv5w8SVZVyMBdtmSJEkaOAoTIr5QdilNLW0ZFyPlGUgkSZIGivql5MqrePu9e7l3eX3W1UiAgUSSJGngaKhjb8082ihlQe1FWVcjAQM0kETEHRHx9Yj4fkS8Oet6JEmSzrtjh2DHGtaWXUJlWQmXjB+WdUUS0M1AEhHfioidEbHmDNtsiojVEbEqIpYXltVGxC8i4oWIeD4ifudcij1dHRFxS0S8FBHrIuKzZztOSun+lNJdwN3A+86lJkmSpKKwbSWkNn51dDpzJ1ZTXjog/y6tPqi7n8RvA7d0Y7ubUkrzU0qLCu9bgd9LKc0BrgY+GRFzuu4UEWMiYliXZTO7U0dElAJfAW4F5gB3Hj9HRMyLiAe7vMZ02P1zhX0lSZL6t8KEiPfvnsB8H/erPqRbj/1NKT0WEVN7evCU0nZge+G/D0bEWmAi8EKXTW8E7o6I21JKxyLiLuBd5EPG2epYDKxLKW0AiIjvAbcDL6SUVgNv61pXRATw58AjKaWVPb0uSZKkolO/jDTqYr72tjdSM6Qi62qkdr05D0kCHo2IBPx9SumejisLQWIBsPSkHVO6LyKmAd+PiPuAjwFv6uZ5JwIdHxPRACw5yz6fBm4GqiNiZkrpa103iIi3A2+fOfNUDTWSJElFJJeDhjrikrexaOqIrKuROunNzoPXpZQWkm/V+GRE3HB8RUQMBf4N+ExK6cCpdk4pfRFoAr4KvCOldKgXa+t6ri+llK5MKd19qjBS2OaBlNInqqurz1cZkiRJF8aedXB0H6u4mMde3pV1NVInvRZIUkpbC193Aj8g35WKiCgnH0a+k1L699PtHxHXA3ML+36+B6feCtR2eD+psEySJEnQPn7kf79Uwz89vTnjYqTOeiWQRETV8UHpEVEFvBlYUxir8U1gbUrpr86w/wLgHvJjPz4KjIyIL3Tz9MuAWRExLSIqgPcDP3ztVyNJktTPNNSRG1TDY3trWDC5JutqpE66+9jf7wJPARdHRENEfLyw/OGImACMBR6PiGeBOuChlNKPgGuB3wTeUHgc8KqIuO0UpxgCvDeltD6llAM+DJwU309VR0qpFfgU8GNgLXBvSun5Hn0XJEmS+rP6OvaNuIJEiU/YUp/T3ads3Xma5R3DxRWnWP84EN04/hNd3rcAX+9BHQ8DD5/tPJIkSQPO0X2w60VenHwTJQGXT6rJuiKpE2fEkSRJ6s8aVgBQ1zKD2WOHMbSyNx+yKp07P5GSJEn9Wf1SiBI+85H38+EW5x9R32MgkSRJ6s/ql8LYuUTlMEZWZl2MdDK7bEmSJPVXuTbYuoL6ofP4/fue5UBTS9YVSScxkEiSJPVXO1+A5kM83TyDR9bsoKrCzjHqewwkkiRJ/VVhQsQfHZjM5ZOqKS0568NPpQvOQCJJktRf1deRqsbyq51DnBBRfZaBRJIkqb+qX8r+kfNpzcH82ouyrkY6JQOJJElSf3RoJ+zbxJ4R85k2qsoZ2tVnObJJkiSpP6qvA2DmwjfyizuWZFyMdHq2kEiSJPVH9UuhtII0/vKsK5HOyEAiSZLUHzUso3nMPBb9+eM8+vyOrKuRTstAIkmS1N+0NsPWlWwdejl7DjczaphTtKvvMpBIkiT1Nzueg7ZjrGI25aXBnPHDs65IOi0DiSRJUn9TmBDxx42TmTOhmkHlpRkXJJ2egUSSJKm/qa8jVdfy2I4yFvi4X/VxPvZXkiSpP0kJ6pfSWnsNH5g1mRsvHp11RdIZGUgkSZL6k8YGOLid8ilX87klc7KuRjoru2xJkiT1J4XxIzuq53GstS3jYqSzM5BIkiT1Jw3LoHwIH3noCJ/8zjNZVyOdlYFEkiSpP6lfSuv4Bby0u4nLJ1VnXY10VgYSSZKk/qL5COxYzfZhl5MSzPcJWyoCBhJJkqT+YtszkGtlVZoNwBUGEhUBn7IlSZLUXxQGtP/04GRmjC6jenB5xgVJZ2cgkSRJ6i/q62DkLD5880L2H2nJuhqpWwwkkiRJ/UFK0FAHs2/hyikjsq5G6jbHkEiSJPUHezfAkT1sH345P1v7Ki1tuawrkrrFQCJJktQfFMaP/PuuiXzqX54hMi5H6i67bEmSJPUH9Uuhspqf7qph3qQyykr9u7OKg59USZKk/qC+jtzEK3l++yEW+LhfFREDiSRJUrFraoSda3m1+gqa23IsmFyTdUVStxlIJEmSil3DciDxXFwMwPzai7KtR+oBx5BIkiQVu/o6iBJuftNt/GRJCeOqB2VdkdRtBhJJkqRi11AHY+ZQOriaWYOzLkbqGbtsSZIkFbNcGzQsp2nclfzXH6zmxR0Hsq5I6hEDiSRJUjHb9SIcO8C6ysv4l6VbOHC0NeuKpB4xkEiSJBWzwoSITzfPoLQkmDexOuOCpJ5xDIkkSVIxq18GQ0bxy11DuWRcC4MrSrOuSOoRW0gkSZKKWf1SUu1inm1oZL4TIqoIGUgkSZKK1eHdsHc9h8ZcSfWQchZMdv4RFZ8B2WUrIu4A3goMB76ZUno024okSZJeg/o6AIbNvIbH33gNKaWMC5J6rlstJBHxrYjYGRFrzrDNpohYHRGrImJ5T/btrtMdKyJuiYiXImJdRHz2bMdJKd2fUroLuBt437nWJUmSlImGOigpgwkLAIiIjAuSeq67Xba+DdzSje1uSinNTykt6sm+ETEmIoZ1WTazO3VERCnwFeBWYA5wZ0TMKaybFxEPdnmN6bD75wr7SpIkFZ/6Ohh/Bf/hn1bz5Z+9knU10mvSrUCSUnoM2PtaTtDNfW8E7o+ISoCIuAv4cjePtRhYl1LakFJqBr4H3F7YfnVK6W1dXjsj7y+AR1JKK1/LdUmSJGWqrQW2rqRlwlX8+pVdtLTlsq5Iek16c1B7Ah6NiBUR8Yke7ZjSfcCPge9HxAeBjwG/0c3dJwL1Hd43FJadyaeBm4H3RMTdp9ogIt4eEfc0NjZ2swxJkqQLaMdqaD3KxsGXkUs4oF1FqzcDyXUppYXku059MiJu6MnOKaUvAk3AV4F3pJQO9WJtXc/1pZTSlSmlu1NKXzvNNg+klD5RXe3kQpIkqQ8qDGhf2pLv5X6Fj/xVkeq1QJJS2lr4uhP4AfmuVN0WEdcDcwv7fr4Hu24Faju8n1RYJkmS1H/VL4Xhk3h8ZwVTRw5hRFVF1hVJr0mvBJKIqDo+KD0iqoA3A91+qlZELADuIT/246PAyIj4Qjd3XwbMiohpEVEBvB/4YU/qlyRJKjr1dVB7FZeOH84dC87WW13qu7r72N/vAk8BF0dEQ0R8vLD84YiYAIwFHo+IZ4E64KGU0o/OtG8XQ4D3ppTWp5RywIeBzd2pI6XUCnyK/BiUtcC9KaXne/JNkCRJKiqNW+FAA9Qu4TM3z+YzN8/OuiLpNevWxIgppTtPs/y2Dm+v6Mm+XbZ5osv7FuDrPajjYeDhs51HkiSpX2jIjx85PHYhlW05ykp7c1iwdGH56ZUkSSo29XVQNpgvrRnMoj/5KW05Z2hX8TKQSJIkFZv6pTBhASu3HmL6qCpKS5yhXcXLQCJJklRMWo7C9udom3QVzzU0Ov+Iip6BRJIkqZhsWwW5FhqGzuNYa475zj+iImcgkSRJKib1SwFY2jIDgAWTazIsRjp33XrKliRJkvqIhmUwYjqXXzyTz1LNxJrBWVcknRMDiSRJUrFIKd9CMvNmLhk3nEvGDc+6Iumc2WVLkiSpWOzbCId30TR+EY+9vIvDx1qzrkg6ZwYSSZKkYlGfnxBxNbP58LfqeLZ+f7b1SL3AQCJJklQs6uugYhhPHhxNBMybVJ11RdI5M5BIkiQVi/o6mLSIlfUHmT1mGMMGlWddkXTODCSSJEnFoOkA7HyeVLuYVfX7nX9E/YaBRJIkqRhsXQEpx47hl9N4tIX5zj+ifsLH/kqSJBWDhmVAMPqSa3nw0yWMrx6UdUVSrzCQSJIkFYP6pTDmUsqqLmJuVdbFSL3HLluSJEl9XS4H9cugdjFf+9V6nli3O+uKpF5jIJEkSerrdr8MxxppGb+I//Xjlwwk6lcMJJIkSX1d/VIAXiy/lNZc8glb6lcMJJIkSX1dfR0MHsHSxosAfMKW+hUDiSRJUl9XvxRqF/NMfSMTawYzZphP2FL/4VO2JEnqz47shb0bYO9GGDoaJl0FFT6iqagc2Qt7XoH5d7Jt9VFbR9TvGEgkSSp2TQdg73rYsz4fPvasL7xfB0f3dd62pAwmLIAp18CUa6F2CQyuyaRsdVPDsvzX2iX84PpraWppy7YeqZcZSCRJKgbNRwotHYXg0R461sPhnZ23HT4JRk6HOXfAyBkwciZcNA0aG2DzE7D5SXjq7+CJvwECxs3Nh5PjIaVqVBZXqNOpXwpRChMWAjCovDTjgqTeZSCRJKmvaD0G+zblWzY6Bo496+Hgts7bDh0LI2bA7LfkQ8eIGfmvF02DiiGnPv6YS2DWzfn/bjkKDcvz4WTzE7Di/8DSr+XXjbr4RDiZcg1UTzxvl6xuqK+DcfP4xtIdvLDtAH/53iuIiKyrknqNgUSSpAuprQX2b+ncrer4fzc2QMqd2HbIyHzQmH7jicAxcgaMmA6Vw86tjvLBMO36/AugtRm2rzrRgrLm32DFP+TX1Uzp0IJyTf783hBfGG2tsHUFLPhNfrr2VY40txlG1O8YSCRJ6m25tny42LOuy5iO9bB/M+RaT2xbWZ3vXlW7BK74QIfWjukw+KILV3NZBdQuzr+u+8/5a3h1zYkWlFd+DM/+S37boePywWTqtfmgMupiKPHBnefFq2ug5Qi5SYtZ/XQj775yUtYVSb3OQCJJ0muRy8HB7R0Gk3foXrVvI7Q1n9i2vCofMMbNg8vuKASOmfnwMWRk32xtKCmF8VfkX1f/NqSUny180+OFkPIkPP/v+W0HjzjRejLlGhg7D0q9xegV9XUAbBg8h8PNG1ngE7bUD/nTQpKk00kJDu8qBI11Jz/JqvXoiW1LK/NdmUbNgotvOdHFasQMGDaub4aOnoiA0RfnX1d9PP+92bfpRDjZ/AS8+GB+24phMHnJiXEoExbmW2DUcw11MGw8y/bmH9U8v/YCtppJF4iBRJKkI3s7t3K0j+3YAM0HT2xXUg4XTc0HjWk35ls9Rs7Mh47hEwdWt6UIGDEt/1rwwfyyA9s6BJQn4Wf/Pb+8bFB+/pPj41AmXXX6gffqrDAh4qCKUpZMG8HUkX7f1P9ESinrGvq0RYsWpeXLl2ddhiTpXHWcq6Nr+Og4V0eUQM3kE0Gj45iO6sl2ReqJw3tgS4cWlB2r84P2S8o7z4UyeQkMqs662r7nwHb4q0vgLX8Kr/tk1tVI5yQiVqSUFp1qnT9VJUn9R/PhLoPIN5zoanV4V+dtq2vzXawue2fnMR01U+xe1FuqRsKlb8+/AJoa82Mi2udC+Qo88df5EDh2Lky9Lh9SJr/OuVAg310LaJt4FZFLlJQUebc/6TQMJJKk4tLSlB+70OmRuRtOM1fHuHzIuPjWzq0dI6blH3urC2tQNcx6U/4F+ckety6HTU/kQ8ryb8HTf5dfN/qSznOhDJ+QXd1Zqa+D0krqjk7krj9+lO/81hKuqK3Juiqp1xlIJEl9T1sL7Nt86idYNdYDHbobDxmVDxrTX5/vVnW8tWPEdKgcmtUVqDsqhsC0G/IvyM+Fsu2ZEy0oz92XDymQH7vTcTb5i6YW/4MCzqa+DiYsYOW2oxw61srUkVVZVySdFwYSSVI2cm35cNHewtFhgsB9myG1ndh2UHU+aEy+GkZ+8MSYjhEzYHBNZpegXlZWkR9PMnkJXP+7+UkBO86F8tIjsOo7+W2HTejwqOFr80//6k8BpaUpP1Hlkrt5Zst+po+uonpIedZVSeeFgUSSdP7kcvluVJ0GkRfCx75NnefqqBiab9UYfwVc9q7CrOSFgeVDRvSvm011T2kZTJiff73uP+U/T7tfOtGCsulxWPOv+W2HjMyPPTneijJuXn4ulWK1/VloayZNuopVdfu4cfaYrCuSzhsDiSTp3KQEh3Z26Fa17sSA8r0bOs/VUTaoMFfHbLj4tg5PsJoBQ8caOnRmJSUw5tL866rfKsyFsvHUc6FUDofaJSdmkx8/v7geVlAY0L5t2OXsPvQ8850QUf2YgUSS1D1H9nbuVtXxSVZd5+oYMS0fNGbclA8gx59gNWzCwJqrQ+dXRP7zNWI6LPhQflnjVtjy1IkZ5X/6k/zyssFQ22EulImL+vZcKPVL4aKplFWP49NvOMa1M0ZmXZF03jgPyVk4D4mkAaWpsfNTqzrOTt60/8R2UVqYq6NDt6rjYzqqa52rQ33HoV35gNJxLhRSPjhPXHhiDErtEhg0POtq81KCv7w4P/nmu7+edTVSr3AeEknSCe1zdaw7OXwc2d1hw8iHi5HTYe67O4ePmsnF1f1FA9fQ0TDnHfkXwNH9nedCefLL8Pj/zs+FMu7yEy0ok1+Xn0clC/u3wKFXoXYxqxsamTa6iqGV3rKp//LTLUn9UUtTvm99e7eqdYUxHevh4PbO2w4bnw8Zl7y185iOi6ZB+aBs6pfOl8E1MPvN+RfkA3rDshPjUJZ/E57+Sn7d6Es7P8lr+PgLU2N9fvxI84SrePfXnuQj10zlv9526YU5t5SBARlIIuIO4K3AcOCbKaVHs61Ikl6DTnN1rOs8pqPrXB1VowtjOt5QGNPRYa6OCuc20ABWUZWfw2b66/PvW491mQvl+/mQAvn/XzpO1lgz5fw8iKF+KVQM5YW2STS3bmW+kyGqnzvnQBIR3wLeBuxMKc09zTabgINAG9B6uv5j53K+iLgF+BugFPhGSunPT3eMlNL9wP0RcRHwvwADiaS+KdeW777R/tSqDuFj/5Yuc3XU5IPG5Kth5IcKrR2F8DGoOrNLkIpKWWX+/6HJV8P1v1eYC2V14THDT8CLD8Ez/5zfdvjEzi0oo2b3TkCpXwoTF7KqIf+wiAU+YUv9XG+0kHwb+FvgH8+y3U0ppd2nWhERY4CjKaWDHZbNTCmt6875IqIU+ArwJqABWBYRP0wpvRAR84A/63KMj6WUdgKfK+wnqa9KCVIuf2Oecvkb8Fxb4WvX94WvKZ287Pj+J22bO/1xOi3Pnfk4nZb3Qp1tzYUgshFyLSe+HxVD8wFjwgKY954Ts5KPLMzVIal3lZbl/3+bsABe98n8/8+7XjzRgrLxMVh9X37bIaNgyutgynX5kDL2sp7PhXLsELz6PFz/uzxTv5+xwysZXz24969L6kPOOZCklB6LiKnneJgbgbsj4raU0rGIuAt4F3BrN8+3GFiXUtoAEBHfA24HXkgprSbfotIu8v4CeCSltPIca9dA1+mGueuNZerGjW7HG96z3eh2vRk+y430Scc7n3V22bbjzfm5bJtyWf8LvwaRvwmJ0g5fSzq/j5LCf5ecetuSsvzM05e89cSYjhEzYOgY5+qQslRSAmPn5F+L78r//Ny7ocNcKI/D2gfy21ZW51tajregTJgPpWeZbX3byvzPvtolrFqxnwW1F533S5KydqHGkCTg0YhIwN+nlO7ptDKl+yJiGvD9iLgP+Bj51o7umgjUd3jfACw5w/afBm4GqgstMV/rukFEvB14+8yZM3tQRh91xhvmU9ywdudGtyd/Me7ODWmP/7J9pjpf4zW91hv9/nrDfPxm+XQ3zKfatqQs393hlOu6HvdMx+nutl2Xl5zhOK/lmkrzN/+nO85J2x5fZmCQBoyIwpisGbDwN/PL9tcXHjVcaEV55cf55eVDYFKHuVAmLYLyLq0f9UvzXyct4m/eH5T680QDwIUKJNellLYWumb9JCJeTCk91nGDlNIXCy0bXwVmpJQOna9iUkpfAr50lm0eAB5YtGjRXeerjrPaugIe+J1z+yt1rg0oxrlmunvDfLobxtPdvHb3hvn4su7cMJ9p257+ZbzL8k7bnOX4p7qRP+0Nub/gJOm8qanNvy5/b/79oV2wpcNs8r/8MyBBaQVMvPLEOJTaJfknbI26GAZfxPzaTK9CumAuSCBJKW0tfN0ZET8g38WqUyCJiOuBucAPgM8Dn+rBKbYCHf+3nVRYVtzKBsHwSWfu1hHdvGE+/lfb7twwn/GvyKe58e31v2B7wyxJ6ieGjoY5t+dfUJgLZWk+nGx6Ap74G/j1X+Z//xEw/wP88qWdNLW0ccvcC/SoYSlD5z2QREQVUJJSOlj47zcD/73LNguAe8iP9dgIfCcivpBS+lw3T7MMmFXo9rUVeD/wgd66hsyMvQw+8L2sq5AkSb1pcA3Mfkv+BfmB7MfnQtn2DCz4EN/8yUb2HGo2kGhAKDnXA0TEd4GngIsjoiEiPl5Y/nBETADGAo9HxLNAHfBQSulHXQ4zBHhvSml9SikHfBjY3N3zpZRaybeo/BhYC9ybUnr+XK9NkiTpvKscCjNugjf8EXzoX8lNWsKq+v3M93G/GiB64ylbd55m+W0d3l5xlmM80eV9C/D1Hp7vYeDhMxYrSZLUx23YfYiDTa1OiKgBY0DO1F5MHnxuG4+s2UFJBCUBJREE8Kfvmseg8lIeeHYbT6zbTUTkx3YXtvnvt89t33/Vlv2UlOT3iwgGlZfwmZtnA/Dw6u28tOPgieOXBFUVpXzk2mkA/GjNDhr2HSE6nL96cDl3LJgIwM/Wvsqug8fydUX++COqynnDJWMBeOzlXRxoamk/PgQjh1Zw1dT8fAlPb9hDU0tb+/4lEYyoquDS8cMBWFW/n7ZcrnD+/DWMqKqgdsQQAF7acRCg/dojguGDyhk9rJKUEg37jrYf93gNQyrLGFpZRi6XaDyary1KaF9fXlpCeWkJKSVac6l9eTiuRZJ0ATyzZT8ACwwkGiAMJH3c7oPHeHH7gfzTcFMiV/iaCg/OWr/rEL94aSe5BKmwPEF7IFm2cS//uqLhxH5AVUVpeyB5aPV2Hnpue6dzjh1e2R5Ivr9sC794aVen9dNHV7UHkr//1QbqNu3ttP7ySdXtgeTPH3mRF7Yf6LT+ddNH8t1PXA3AH/7bc2zec6TT+psvHcM3/sNVAPzW/1nO7kPHOq2/ff4E/ub9CwC44ytPcLSlrdP6DyyZzJ++cx4pwfVf/MVJ39NP3DCd/3rbpRxqbmXB//jJSev/882z+Z2bZ7HjQBOv+7Ofd1oXAX9026X81vXTWb/rELf9za87BZYI+PzbL+M9V05izdZGPvIPdcCJMFcS8Me3z+VNc8aycss+fvf7qyiJyD9UrLD+f9w+lyXTR/L0hj184aEXiML+dFg/d2I1v35lF1/5xbr8+kKggvz6qaOq+MVLO/nO05vbw+Tx7f7b2y9jzPBB/Gztqzzw7LZCGDx+DfC5t81h+KByfvrCq/zy5Z3tQfD49X321kuoLCvlpy+8yrLNezuH5Qh+9035z9bPX3yVF7YdaA+TJQGVZSXtn61fvrSTTbsPdwrLVZWlvHPBJAAef2U3Ow40dTg2DBtU1v7ZenrDHvYfaekQOKF6cDmLCmF35ZZ9HG1uywflwvewekg5l4zLh90Xth2gpS3Xvj/k9z8edjfsOkQu0en8VZVljBpaCcCOxqZCCD/xh4JB5aVUVZaRUuLQsdb2IHx8m9KS/Ot8SIUfChFBSomWtkSi8DMhQSJRUVpCWWkJrW05Dje3QWH58Z8fwwaVU1FWQlNLG41HW9r3O/5zZWRVBYPKSzl0rJU9h461Lz/+M2nSRYMZVF7KvsPNvHqwqf3n1vGfV7PGDqWyrJSdB5rYuv8oic4/t66YVENFWQn1e49Qv+9Iob4T9V8zYxSlJcG6nQep33s0X3vuxHME3zQn/9lY3dBI/b4j7edOQHlJcOu8fF/8pRv20LDvaPvPRBIMqijlHVdMAOAXL+5sr4/Cz92Of4h58Llt7Ghs6vT9GT2sknctzH92v1e3hV0Hj3WqvfaiIbz7yvz6b/x6A3sPN3daP2vMMN5TWP9Xj77EoWNt5ArfuJQSl0+qad//v/3weY615qDDv+/VM0bwzgWTaMslfv++Z098b4Fcyv9cvX3+RJpbc/zpw2sZPqiMoYPKGDaonGGDypgzfjjTRw+lLZfYfegYwwaVMbi81D/EZOTFHQcZVlnGjNFDsy5FuiAMJH3cR66d1n4DdyqfuXl2e7g4lT++fS5/XAgnp/KVDyzkb+9MJwWe4/7ug1fSksvlnzJcuHHp+Ovpqx9ayLHWXP6XXi5/nPKyE1t87UNX0tTa1uH4iSEVJz52X/3g8fXHb4ryv/iP+9sPLKC5Ndd+Y5FLibHDB7Wv/+v3z6ctlzqtnzKyqn39/3zP5e2/mI9f2/Eb0sqyEj7/9jmdbppyKbFoan4SqqGVZfzem2a333DlCncPCwp9eqsHl/ORa6a2X3uucGMxbVRV+/q3XDYuv1/hximXEqOGVrQf/4ramhPf88LX49+firISxg4b1H7TdPymsaw0//09fiOSK9x8ntgu/+935Fgb2xub2vc7fo0t+YLYefAYz9Tvz19b7sT3qKU1P6/KKzsP8cjqHe3XfvzG8Q/ecgkAdZv28u0nN7XXffy8xwPJj9e8yveX13f6vA2rLGv/PN+3ouGkMDxu+KD2QPKNxzfwyy5heMboqvZA8pePvsSyTfs6rb9iUjX/91PXAfBHP1jD2i5h+JoZI/mXu/Jh+O5/XsGWvV3D8Fi+8R8WAfDev3+K3YeaO62/Y/4E/roQhl//v35BU0vnOWg+uGQyf/LOeeQSzPtvj9LVf7xhOv/ltks50NTC5f/t0UJYOtGC9zs3z+KTN81kR2MTN//Vr9pvKI//O/+XWy/hI9dOY93Og7zlr3/daT3An79rHu9fPJlV9ft55989edL5v3znAt5+xQSWbtzLB7+x9KT1//CRq7jpkjH86uVd/Md/WnHS+nv/4+tYPG0Ejz6/g9+999mT1j/46euYO7GaB5/bxv/7f08exvfL/9/rmTqqin9buZW/+NGLJ61f9kc3M3pYJd9fVs/f/mLdSevX/vdbGFxRyneWbuEfntjUaV1JwIY/eysA//T0Ju5d3tBp/bBBZe2B5B+f2sxDq0/+7B0PJN9+chO/evnkz97xQPLtJzaxfPPJn73jgeTbT27ixULr7XHXzBjZHii+s3QL9XuPtIfliPxn73gguX/VNvYdbobC5yMiaMml9v1/8sKrHGvNdfr8jCz8XIH8/5sdg3hEMHdC/ufe4WOt/NvKBg4da23/3AD8/lsu5pM3zWTb/qPtf8gpLQmGVpYxbFAZv/fm2bxzwSS27T/K//zxS+3Ljwea62aOYuqoKg4fa6Vh39FC2CljaEUZJecphPdnn3vrpdx94wy/dxowInX8iaSTLFq0KC1fvjzrMqSi05ZLtOVO/JX+eLAZWpkPXIeOtdLcmjsRRgt/5x4zLB84dx5soqk51x6EcylRXlLC5JH5FozNew5zuMNfkXMpMai8lNljhwGwZmsjR5rbToSlBMMHlzN3YjUAT63fw9GW1va/sOdSYvSwShZOzgfSHz+/Ix+2C/vnclA7YgiLp+VbYO5dXk/r8SBYuIbZY4fxuhkjyeUS33x8Y6faU4L5tTVcO3MUTS1t/N0v17f/9f34dtfNHMW1M0fReLSFv/npKyduOAutSG+8dCyLp41g96Fj/MMTG9tvZqPQQvOmOWOZO7GaVw80cd/y+vZWrY43vTPHDGXr/qM8snp7h9az/DHecMkYakcMoX7vER57ZdeJ45NvCbrpkjGMGTaILXuOsKxw03u8BQjgxtmjqRlSweY9h3l+24H2bprHj3HtzFFUVZaxec9hNuw63Kn2CFg8bQSVZaXU7z3S3t2yY+vcwskXUVoS1O89wu5DHbqKFs5x/N92e+NRDhxt7VR7SQTTC39tPv7ZOl53BJSVlDCuOv/Z23e4mZa2XHvLZZBfXz2kvP2zm0vpRG3kb94HlZcC5PflRO19sctnLpc43NzKwab866KqcsYMG0Tj0RYefG5bYXlL+/p3L5zEdbNG8eKOA9z1j8vbl7cV/sDxpTsX8I4rJvDk+t184Osnwm4EDK0o428/uJAbZ49mxeZ9fPnnr7QHmWGDyhg+qJx3LpjIhJrBvHqgiY27D7cvHzYo38W2rPScn8EjKWMRsSKltOiU6wwkZ2YgkSTpZCklmlpyHGxqYeigMoZUlLH70DGWbtjLwaYWDh1r5UAh2HxwyRRmjhnKk+t282ePvMihY/nlB5ryf5i4/5PXMr+2hnuX1fMH//bcSef68Wdu4OJxw/i/q7byrSc2MbwQZoZV5kPLp98wi+oh5by04yAbdx/qEHjyX0cMqSia1oZn6/fzf57cxO+95WIm1gw++w5SkThTILHLliRJ6rGIYHBFKYMrStuXjRpayVsvP/28GdfMHMUDn76u07JjrW2UleRbQF5/yWi+81tLTmqhGTs8P3arsqyE4YPKONjUyrb9R9vX//brZwDww2e38pVfrD/pvM//8Vuoqizjf//kZf7vqq2dWmiGDSrnf77nciKCx1/ZTcO+I51bcAaXX9CxHE9t2MO/P7OVP3rrpRfsnFLWDCSSJCkzlWUnAs2YYYPau22eyi1zx59xosCPXzed2+aNbw8qx0PNkEJomjJyCJdPqmlfvmn3EVoLT3KEfFfMHz67rdMxR1ZVsOL/fRMAn/zOSp5Yv7tT68y0UVX8+bsvb99/z6HmTt3RRg+rbO9OeLS5jcqykjO21qzasp8pI4cwsvAADWkgMJBIkqR+YURVBSOqKk67/l0LJ7U/fOBU/uxd8/jsrZd0CjPHx8lAfpzUyKEV7esPFILPcd+r28LKwiN7j5tfW8P9n7wWgHf+3RO89OpBhlYUBv0PKuN100e2P3zmrx59iac37uHG2aNfy+VLRctAIkmSRP7R3lWVp781eu9VtbyX2tOu/7ffvoajLW2dAktZh9aQj1wzlW37j7YHmYNNLQzv8GTJHz2/g+bWXPsjrKWBwkHtZ+GgdkmSJOncnGlQu8/RkyRJkpQZA4kkSZKkzBhIJEmSJGXGQCJJkiQpMwYSSZIkSZkxkEiSJEnKjIFEkiRJUmYMJJIkSZIyYyCRJEmSlBkDiSRJkqTMGEgkSZIkZcZAIkmSJCkzBhJJkiRJmTGQSJIkScqMgUSSJElSZgwkkiRJkjJjIJEkSZKUGQOJJEmSpMxESinrGvq0iNgFbO7lw1YDjb18zKwVwzX1hRqzqOF8n/N8Hb83jzsK2N1Lx1Lx6Qv/7xeD/vh9KoZr6is1Xug6LsT5/P3Ut0xJKY0+1QoDSQYi4p6U0ieyrqM3FcM19YUas6jhfJ/zfB2/N48bEctTSot641gqPn3h//1i0B+/T8VwTX2lxgtdx4U4n7+fioddtrLxQNYFnAfFcE19ocYsajjf5zxfx+8L/17qH/wsdU9//D4VwzX1lRovdB0X4nz+fioStpBI6vf8C5QkqS/y91OeLSSSBoJ7si5AkqRT8PcTtpBIkiRJypAtJJIkSZIyYyCRJEmSlBkDiSRJkqTMlGVdgCRdaBFxB/BWYDjwzZTSo9lWJEkSRMSlwO+QnzDxZymlr2Zc0gVhC4mkfiEivhUROyNiTZflt0TESxGxLiI+C5BSuj+ldBdwN/C+LOqVJA0MPfz9tDaldDfwXuDaLOrNgoFEUn/xbeCWjgsiohT4CnArMAe4MyLmdNjkc4X1kiSdL9+mB7+fIuIdwEPAwxe2zOwYSCT1Cymlx4C9XRYvBtallDaklJqB7wG3R95fAI+klFZe6FolSQNHT34/Fbb/YUrpVuCDF7bS7DiGRFJ/NhGo7/C+AVgCfBq4GaiOiJkppa9lUZwkacA65e+niHg98C6gkgHUQmIgkTTgpJS+BHwp6zokSeoopfRL4JcZl3HB2WVLUn+2Fajt8H5SYZkkSVny91MHBhJJ/dkyYFZETIuICuD9wA8zrkmSJH8/dWAgkdQvRMR3gaeAiyOiISI+nlJqBT4F/BhYC9ybUno+yzolSQOLv5/OLlJKWdcgSZIkaYCyhUSSJElSZgwkkiRJkjJjIJEkSZKUGQOJJEmSpMwYSCRJkiRlxkAiSZIkKTMGEkmSJEmZMZBIkiRJyoyBRJIkSVJm/j+wLb8YCl/yBQAAAABJRU5ErkJggg==\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, loss_test_l1, p_1, p_2, p_2_pred = fit_data(df_1, df_2, batch_size=batch_size_, num_epochs=num_epochs, 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": 90,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T17:13:41.147887Z",
     "iopub.status.busy": "2022-06-09T17:13:41.147382Z",
     "iopub.status.idle": "2022-06-09T17:13:41.149258Z",
     "shell.execute_reply": "2022-06-09T17:13:41.149563Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0. -0. -0. -0. -0. -0. -0.]\n"
     ]
    }
   ],
   "source": [
    "beta1s = 1 - (1 - beta1) * np.logspace(-1, 1, 7, base=10)\n",
    "print(np.log10(beta1s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T17:13:41.155752Z",
     "iopub.status.busy": "2022-06-09T17:13:41.155169Z",
     "iopub.status.idle": "2022-06-09T17:55:36.907634Z",
     "shell.execute_reply": "2022-06-09T17:55:36.907976Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.  1.  1.  1.  1.  1.  0.9]\n",
      "Pour beta1= 9.99e-01, loss_train=1.67e-02 / loss_test=1.65e-02; le temps de calcul est 350.914 s\n",
      "Pour beta1= 9.98e-01, loss_train=1.59e-02 / loss_test=1.60e-02; le temps de calcul est 345.636 s\n",
      "Pour beta1= 9.95e-01, loss_train=1.58e-02 / loss_test=1.57e-02; le temps de calcul est 360.138 s\n",
      "Pour beta1= 9.90e-01, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 365.451 s\n",
      "Pour beta1= 9.78e-01, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 363.748 s\n",
      "Pour beta1= 9.54e-01, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 364.457 s\n",
      "Pour beta1= 9.00e-01, loss_train=1.51e-02 / loss_test=1.51e-02; le temps de calcul est 365.186 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, loss_test_l1, p_1, p_2, p_2_pred = fit_data(df_1, df_2, beta1=beta1_, num_epochs=num_epochs, 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": 92,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T17:55:36.914316Z",
     "iopub.status.busy": "2022-06-09T17:55:36.913107Z",
     "iopub.status.idle": "2022-06-09T18:40:12.856794Z",
     "shell.execute_reply": "2022-06-09T18:40:12.857158Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour beta2= 9.95e-01, loss_train=6.72e+00 / loss_test=6.12e+00; le temps de calcul est 377.528 s\n",
      "Pour beta2= 9.89e-01, loss_train=6.81e+00 / loss_test=6.21e+00; le temps de calcul est 381.881 s\n",
      "Pour beta2= 9.77e-01, loss_train=6.72e+00 / loss_test=6.13e+00; le temps de calcul est 387.187 s\n",
      "Pour beta2= 9.50e-01, loss_train=6.74e+00 / loss_test=6.13e+00; le temps de calcul est 372.071 s\n",
      "Pour beta2= 8.92e-01, loss_train=6.69e+00 / loss_test=6.09e+00; le temps de calcul est 380.279 s\n",
      "Pour beta2= 7.68e-01, loss_train=6.69e+00 / loss_test=6.15e+00; le temps de calcul est 378.869 s\n",
      "Pour beta2= 5.00e-01, loss_train=6.67e+00 / loss_test=6.06e+00; le temps de calcul est 397.812 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, loss_test_l1, p_1, p_2, p_2_pred = fit_data(df_1, df_2, beta2=beta2_, num_epochs=num_epochs, 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": 93,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-09T18:40:12.863639Z",
     "iopub.status.busy": "2022-06-09T18:40:12.863008Z",
     "iopub.status.idle": "2022-06-09T19:49:34.054862Z",
     "shell.execute_reply": "2022-06-09T19:49:34.055218Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 129  513 1153 2049 3201 4609]\n",
      "Pour num_epochs=129, loss_train=1.51e-02 / loss_test=1.51e-02; le temps de calcul est 46.162 s\n",
      "Pour num_epochs=513, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 183.287 s\n",
      "Pour num_epochs=1153, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 415.698 s\n",
      "Pour num_epochs=2049, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 732.785 s\n",
      "Pour num_epochs=3201, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 1148.116 s\n",
      "Pour num_epochs=4609, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 1634.783 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, loss_test_l1, 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"
  },
  "nteract": {
   "version": "0.28.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}