2022-06-06_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).*\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/2022-06-06_prediction_transfert-des-voix.png \"Prédiction du transfert des voix\")\n",
    "\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, 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",
    "\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",
    "\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 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 car il y a moins de données disponibles.** \n",
    "\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": {
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   "source": [
    "datetime = '2022-06-06'\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": {
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     "shell.execute_reply": "2022-06-07T15:24:12.987660Z"
    }
   },
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:24:12.991370Z",
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    }
   },
   "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",
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       "      <th>Inscrits</th>\n",
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       "      <th>% Abs/Ins</th>\n",
       "      <th>...</th>\n",
       "      <th>Unnamed: 95</th>\n",
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       "      <td>231</td>\n",
       "      <td>Taipei</td>\n",
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       "      <td>1709</td>\n",
       "      <td>942</td>\n",
       "      <td>55.12</td>\n",
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       "      <td>64</td>\n",
       "      <td>54.70</td>\n",
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       "      <td>0</td>\n",
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       "      <td>DUPONT-AIGNAN</td>\n",
       "      <td>Nicolas</td>\n",
       "      <td>1</td>\n",
       "      <td>0.85</td>\n",
       "      <td>1.96</td>\n",
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       "      <th>69680</th>\n",
       "      <td>ZZ</td>\n",
       "      <td>Français établis hors de France</td>\n",
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       "      <td>234</td>\n",
       "      <td>Monterrey</td>\n",
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       "      <td>Bahamas (Nassau)</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": "2022-06-07T15:25:16.810976Z",
     "iopub.status.busy": "2022-06-07T15:25:16.810497Z",
     "iopub.status.idle": "2022-06-07T15:25:16.813148Z",
     "shell.execute_reply": "2022-06-07T15:25:16.812840Z"
    }
   },
   "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": "2022-06-07T15:25:16.817720Z",
     "iopub.status.busy": "2022-06-07T15:25:16.817249Z",
     "iopub.status.idle": "2022-06-07T15:25:16.822561Z",
     "shell.execute_reply": "2022-06-07T15:25:16.822111Z"
    }
   },
   "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",
       "        text-align: right;\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",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>18</td>\n",
       "      <td>266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>15</td>\n",
       "      <td>265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>246</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Nuls  Blancs  Abstentions\n",
       "0     1      16          108\n",
       "1     1       3           38\n",
       "2     5      18          266\n",
       "3     6      15          265\n",
       "4     8      10          246"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1 = T1[['Nuls', 'Blancs', 'Abstentions']].copy()\n",
    "df_1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:25:16.828184Z",
     "iopub.status.busy": "2022-06-07T15:25:16.827559Z",
     "iopub.status.idle": "2022-06-07T15:25:16.829939Z",
     "shell.execute_reply": "2022-06-07T15:25:16.830265Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .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",
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       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <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",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>246</td>\n",
       "    </tr>\n",
       "    <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",
       "    </tr>\n",
       "    <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",
       "    </tr>\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": "2022-06-07T15:25:16.833888Z",
     "iopub.status.busy": "2022-06-07T15:25:16.833285Z",
     "iopub.status.idle": "2022-06-07T15:25:16.835605Z",
     "shell.execute_reply": "2022-06-07T15:25:16.835931Z"
    }
   },
   "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": "2022-06-07T15:25:16.838861Z",
     "iopub.status.busy": "2022-06-07T15:25:16.838368Z",
     "iopub.status.idle": "2022-06-07T15:25:16.840551Z",
     "shell.execute_reply": "2022-06-07T15:25:16.840206Z"
    }
   },
   "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": "2022-06-07T15:25:16.844539Z",
     "iopub.status.busy": "2022-06-07T15:25:16.844065Z",
     "iopub.status.idle": "2022-06-07T15:25:16.846266Z",
     "shell.execute_reply": "2022-06-07T15:25:16.846591Z"
    }
   },
   "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": "2022-06-07T15:25:16.850817Z",
     "iopub.status.busy": "2022-06-07T15:25:16.850209Z",
     "iopub.status.idle": "2022-06-07T15:25:16.852359Z",
     "shell.execute_reply": "2022-06-07T15:25:16.852747Z"
    }
   },
   "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": "2022-06-07T15:25:16.856560Z",
     "iopub.status.busy": "2022-06-07T15:25:16.856049Z",
     "iopub.status.idle": "2022-06-07T15:25:16.865983Z",
     "shell.execute_reply": "2022-06-07T15:25:16.866310Z"
    }
   },
   "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": "2022-06-07T15:25:16.869480Z",
     "iopub.status.busy": "2022-06-07T15:25:16.869007Z",
     "iopub.status.idle": "2022-06-07T15:25:16.877880Z",
     "shell.execute_reply": "2022-06-07T15:25:16.878232Z"
    }
   },
   "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": "2022-06-07T15:25:16.882297Z",
     "iopub.status.busy": "2022-06-07T15:25:16.881817Z",
     "iopub.status.idle": "2022-06-07T15:25:16.884055Z",
     "shell.execute_reply": "2022-06-07T15:25:16.884386Z"
    }
   },
   "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": "2022-06-07T15:25:16.887546Z",
     "iopub.status.busy": "2022-06-07T15:25:16.887082Z",
     "iopub.status.idle": "2022-06-07T15:25:16.889287Z",
     "shell.execute_reply": "2022-06-07T15:25:16.889636Z"
    }
   },
   "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": "2022-06-07T15:25:16.892576Z",
     "iopub.status.busy": "2022-06-07T15:25:16.892114Z",
     "iopub.status.idle": "2022-06-07T15:25:16.898163Z",
     "shell.execute_reply": "2022-06-07T15:25:16.898490Z"
    }
   },
   "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": "2022-06-07T15:25:16.901754Z",
     "iopub.status.busy": "2022-06-07T15:25:16.901287Z",
     "iopub.status.idle": "2022-06-07T15:25:16.903573Z",
     "shell.execute_reply": "2022-06-07T15:25:16.903902Z"
    }
   },
   "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": "2022-06-07T15:25:16.906767Z",
     "iopub.status.busy": "2022-06-07T15:25:16.906292Z",
     "iopub.status.idle": "2022-06-07T15:25:16.908139Z",
     "shell.execute_reply": "2022-06-07T15:25:16.908485Z"
    }
   },
   "outputs": [],
   "source": [
    "# df_1 = df_1.drop(columns=['Nuls', 'Blancs'])#, 'Abstentions'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:25:16.911795Z",
     "iopub.status.busy": "2022-06-07T15:25:16.911257Z",
     "iopub.status.idle": "2022-06-07T15:25:16.913510Z",
     "shell.execute_reply": "2022-06-07T15:25:16.913845Z"
    }
   },
   "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": "2022-06-07T15:25:16.916837Z",
     "iopub.status.busy": "2022-06-07T15:25:16.916375Z",
     "iopub.status.idle": "2022-06-07T15:25:17.492673Z",
     "shell.execute_reply": "2022-06-07T15:25:17.493042Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:25:17.497012Z",
     "iopub.status.busy": "2022-06-07T15:25:17.496503Z",
     "iopub.status.idle": "2022-06-07T15:25:17.648521Z",
     "shell.execute_reply": "2022-06-07T15:25:17.648859Z"
    }
   },
   "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": "2022-06-07T15:25:17.653242Z",
     "iopub.status.busy": "2022-06-07T15:25:17.652772Z",
     "iopub.status.idle": "2022-06-07T15:25:38.897798Z",
     "shell.execute_reply": "2022-06-07T15:25:38.898145Z"
    }
   },
   "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": "2022-06-07T15:25:38.901972Z",
     "iopub.status.busy": "2022-06-07T15:25:38.901423Z",
     "iopub.status.idle": "2022-06-07T15:25:38.903617Z",
     "shell.execute_reply": "2022-06-07T15:25:38.903938Z"
    }
   },
   "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": "2022-06-07T15:25:38.907272Z",
     "iopub.status.busy": "2022-06-07T15:25:38.906719Z",
     "iopub.status.idle": "2022-06-07T15:25:38.908925Z",
     "shell.execute_reply": "2022-06-07T15:25:38.909249Z"
    }
   },
   "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": "2022-06-07T15:25:38.912685Z",
     "iopub.status.busy": "2022-06-07T15:25:38.912106Z",
     "iopub.status.idle": "2022-06-07T15:25:38.914395Z",
     "shell.execute_reply": "2022-06-07T15:25:38.914787Z"
    }
   },
   "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": "2022-06-07T15:25:38.918754Z",
     "iopub.status.busy": "2022-06-07T15:25:38.918281Z",
     "iopub.status.idle": "2022-06-07T15:25:38.920561Z",
     "shell.execute_reply": "2022-06-07T15:25:38.920951Z"
    }
   },
   "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": "2022-06-07T15:25:38.925026Z",
     "iopub.status.busy": "2022-06-07T15:25:38.924475Z",
     "iopub.status.idle": "2022-06-07T15:25:38.926771Z",
     "shell.execute_reply": "2022-06-07T15:25:38.927123Z"
    }
   },
   "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": "2022-06-07T15:25:38.930972Z",
     "iopub.status.busy": "2022-06-07T15:25:38.930502Z",
     "iopub.status.idle": "2022-06-07T15:25:38.935279Z",
     "shell.execute_reply": "2022-06-07T15:25:38.935639Z"
    },
    "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": "2022-06-07T15:25:38.938939Z",
     "iopub.status.busy": "2022-06-07T15:25:38.938373Z",
     "iopub.status.idle": "2022-06-07T15:25:38.940614Z",
     "shell.execute_reply": "2022-06-07T15:25:38.941026Z"
    }
   },
   "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": "2022-06-07T15:25:38.945251Z",
     "iopub.status.busy": "2022-06-07T15:25:38.944753Z",
     "iopub.status.idle": "2022-06-07T15:25:38.947167Z",
     "shell.execute_reply": "2022-06-07T15:25:38.947557Z"
    }
   },
   "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": "2022-06-07T15:25:38.953158Z",
     "iopub.status.busy": "2022-06-07T15:25:38.950297Z",
     "iopub.status.idle": "2022-06-07T15:25:38.955571Z",
     "shell.execute_reply": "2022-06-07T15:25:38.955907Z"
    }
   },
   "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": "2022-06-07T15:25:38.992324Z",
     "iopub.status.busy": "2022-06-07T15:25:38.982991Z",
     "iopub.status.idle": "2022-06-07T15:25:39.083868Z",
     "shell.execute_reply": "2022-06-07T15:25:39.084246Z"
    }
   },
   "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": "2022-06-07T15:25:39.087378Z",
     "iopub.status.busy": "2022-06-07T15:25:39.086881Z",
     "iopub.status.idle": "2022-06-07T15:25:39.088840Z",
     "shell.execute_reply": "2022-06-07T15:25:39.089195Z"
    }
   },
   "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": "2022-06-07T15:25:39.092885Z",
     "iopub.status.busy": "2022-06-07T15:25:39.092377Z",
     "iopub.status.idle": "2022-06-07T15:25:39.107548Z",
     "shell.execute_reply": "2022-06-07T15:25:39.107900Z"
    }
   },
   "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": "2022-06-07T15:25:39.111738Z",
     "iopub.status.busy": "2022-06-07T15:25:39.111268Z",
     "iopub.status.idle": "2022-06-07T15:25:39.126199Z",
     "shell.execute_reply": "2022-06-07T15:25:39.126568Z"
    }
   },
   "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": "2022-06-07T15:25:39.130381Z",
     "iopub.status.busy": "2022-06-07T15:25:39.129902Z",
     "iopub.status.idle": "2022-06-07T15:25:39.134417Z",
     "shell.execute_reply": "2022-06-07T15:25:39.134810Z"
    }
   },
   "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": "2022-06-07T15:25:39.138439Z",
     "iopub.status.busy": "2022-06-07T15:25:39.137962Z",
     "iopub.status.idle": "2022-06-07T15:25:39.152026Z",
     "shell.execute_reply": "2022-06-07T15:25:39.152369Z"
    }
   },
   "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": "2022-06-07T15:25:39.155987Z",
     "iopub.status.busy": "2022-06-07T15:25:39.155483Z",
     "iopub.status.idle": "2022-06-07T15:25:39.160995Z",
     "shell.execute_reply": "2022-06-07T15:25:39.161357Z"
    }
   },
   "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": "2022-06-07T15:25:39.164897Z",
     "iopub.status.busy": "2022-06-07T15:25:39.164403Z",
     "iopub.status.idle": "2022-06-07T15:25:39.166092Z",
     "shell.execute_reply": "2022-06-07T15:25:39.166560Z"
    }
   },
   "outputs": [],
   "source": [
    "df_12 = pd.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:25:39.171987Z",
     "iopub.status.busy": "2022-06-07T15:25:39.169547Z",
     "iopub.status.idle": "2022-06-07T15:25:39.174910Z",
     "shell.execute_reply": "2022-06-07T15:25:39.175241Z"
    }
   },
   "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": "2022-06-07T15:25:39.178685Z",
     "iopub.status.busy": "2022-06-07T15:25:39.178219Z",
     "iopub.status.idle": "2022-06-07T15:25:39.183917Z",
     "shell.execute_reply": "2022-06-07T15:25:39.184310Z"
    }
   },
   "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": "2022-06-07T15:25:39.187824Z",
     "iopub.status.busy": "2022-06-07T15:25:39.187267Z",
     "iopub.status.idle": "2022-06-07T15:25:39.192408Z",
     "shell.execute_reply": "2022-06-07T15:25:39.192726Z"
    }
   },
   "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": "2022-06-07T15:25:39.196012Z",
     "iopub.status.busy": "2022-06-07T15:25:39.195345Z",
     "iopub.status.idle": "2022-06-07T15:25:39.544779Z",
     "shell.execute_reply": "2022-06-07T15:25:39.545152Z"
    }
   },
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:25:39.557152Z",
     "iopub.status.busy": "2022-06-07T15:25:39.556392Z",
     "iopub.status.idle": "2022-06-07T15:25:40.235984Z",
     "shell.execute_reply": "2022-06-07T15:25:40.236320Z"
    }
   },
   "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": "2022-06-07T15:25:40.243790Z",
     "iopub.status.busy": "2022-06-07T15:25:40.243289Z",
     "iopub.status.idle": "2022-06-07T15:25:40.245779Z",
     "shell.execute_reply": "2022-06-07T15:25:40.246103Z"
    }
   },
   "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": "2022-06-07T15:25:40.249640Z",
     "iopub.status.busy": "2022-06-07T15:25:40.249055Z",
     "iopub.status.idle": "2022-06-07T15:25:40.251297Z",
     "shell.execute_reply": "2022-06-07T15:25:40.251775Z"
    }
   },
   "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": "2022-06-07T15:25:40.255278Z",
     "iopub.status.busy": "2022-06-07T15:25:40.254680Z",
     "iopub.status.idle": "2022-06-07T15:25:40.257022Z",
     "shell.execute_reply": "2022-06-07T15:25:40.257363Z"
    },
    "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": "2022-06-07T15:25:40.260669Z",
     "iopub.status.busy": "2022-06-07T15:25:40.260191Z",
     "iopub.status.idle": "2022-06-07T15:25:40.721846Z",
     "shell.execute_reply": "2022-06-07T15:25:40.722227Z"
    }
   },
   "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": "2022-06-07T15:25:40.726056Z",
     "iopub.status.busy": "2022-06-07T15:25:40.725489Z",
     "iopub.status.idle": "2022-06-07T15:25:40.727730Z",
     "shell.execute_reply": "2022-06-07T15:25:40.728056Z"
    }
   },
   "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": "2022-06-07T15:25:40.731789Z",
     "iopub.status.busy": "2022-06-07T15:25:40.731319Z",
     "iopub.status.idle": "2022-06-07T15:25:40.736335Z",
     "shell.execute_reply": "2022-06-07T15:25:40.736666Z"
    }
   },
   "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": "2022-06-07T15:25:40.740021Z",
     "iopub.status.busy": "2022-06-07T15:25:40.739475Z",
     "iopub.status.idle": "2022-06-07T15:25:40.741114Z",
     "shell.execute_reply": "2022-06-07T15:25:40.741591Z"
    }
   },
   "outputs": [],
   "source": [
    "train_loader = DataLoader(train_set, batch_size=32, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:25:40.744505Z",
     "iopub.status.busy": "2022-06-07T15:25:40.744035Z",
     "iopub.status.idle": "2022-06-07T15:25:40.749395Z",
     "shell.execute_reply": "2022-06-07T15:25:40.749722Z"
    }
   },
   "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": "2022-06-07T15:25:40.753112Z",
     "iopub.status.busy": "2022-06-07T15:25:40.752553Z",
     "iopub.status.idle": "2022-06-07T15:25:40.754792Z",
     "shell.execute_reply": "2022-06-07T15:25:40.755122Z"
    }
   },
   "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": "2022-06-07T15:25:40.758529Z",
     "iopub.status.busy": "2022-06-07T15:25:40.758029Z",
     "iopub.status.idle": "2022-06-07T15:25:40.761428Z",
     "shell.execute_reply": "2022-06-07T15:25:40.761773Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([ 628., 1000.,  862., 1024., 1285.,  901., 1036.,  839.,  483.,  859.,\n",
       "         1048., 1128., 1025., 1111.,  791.,  717., 1160., 1208.,  808.,  109.,\n",
       "          269.,  278., 1094.,  605., 1088.,  899.,  721.,  322., 1352.,  778.,\n",
       "          905.,   60.]),\n",
       " tensor([ 627., 1002.,  861., 1025., 1286.,  903., 1037.,  839.,  483.,  860.,\n",
       "         1047., 1131., 1025., 1111.,  791.,  717., 1158., 1209.,  808.,  109.,\n",
       "          270.,  278., 1094.,  605., 1088.,  899.,  720.,  323., 1352.,  778.,\n",
       "          905.,   61.]))"
      ]
     },
     "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": "2022-06-07T15:25:40.765104Z",
     "iopub.status.busy": "2022-06-07T15:25:40.764561Z",
     "iopub.status.idle": "2022-06-07T15:25:40.767374Z",
     "shell.execute_reply": "2022-06-07T15:25:40.767701Z"
    }
   },
   "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": "2022-06-07T15:25:40.771511Z",
     "iopub.status.busy": "2022-06-07T15:25:40.770908Z",
     "iopub.status.idle": "2022-06-07T15:25:40.774322Z",
     "shell.execute_reply": "2022-06-07T15:25:40.774671Z"
    }
   },
   "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": "2022-06-07T15:25:40.779315Z",
     "iopub.status.busy": "2022-06-07T15:25:40.778830Z",
     "iopub.status.idle": "2022-06-07T15:25:40.780446Z",
     "shell.execute_reply": "2022-06-07T15:25:40.780784Z"
    },
    "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": "2022-06-07T15:25:40.784386Z",
     "iopub.status.busy": "2022-06-07T15:25:40.783840Z",
     "iopub.status.idle": "2022-06-07T15:25:40.786122Z",
     "shell.execute_reply": "2022-06-07T15:25:40.786454Z"
    }
   },
   "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": "2022-06-07T15:25:40.789757Z",
     "iopub.status.busy": "2022-06-07T15:25:40.789292Z",
     "iopub.status.idle": "2022-06-07T15:25:40.791048Z",
     "shell.execute_reply": "2022-06-07T15:25:40.791519Z"
    }
   },
   "outputs": [],
   "source": [
    "trans = TransfertVoix(N_1er, N_2eme)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:25:40.794481Z",
     "iopub.status.busy": "2022-06-07T15:25:40.794014Z",
     "iopub.status.idle": "2022-06-07T15:25:40.796880Z",
     "shell.execute_reply": "2022-06-07T15:25:40.797287Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[ 0.3305,  0.3652,  0.4048, -0.0413, -0.4238],\n",
      "        [ 0.1380,  0.2349, -0.2546,  0.3327,  0.1141],\n",
      "        [ 0.3261,  0.3922, -0.3465, -0.3615, -0.0037],\n",
      "        [ 0.1016,  0.3234, -0.0472,  0.4306, -0.3501],\n",
      "        [ 0.3084,  0.3406, -0.4130, -0.1961, -0.1918],\n",
      "        [-0.2415,  0.3251,  0.3102,  0.0231,  0.4256],\n",
      "        [-0.0628, -0.2723,  0.1410,  0.1751, -0.1231],\n",
      "        [-0.3144, -0.2962,  0.2878,  0.3564, -0.2769],\n",
      "        [ 0.0510,  0.3812, -0.1472,  0.4404,  0.2834],\n",
      "        [ 0.0727, -0.2868, -0.2901, -0.1054, -0.0379],\n",
      "        [-0.0401,  0.1732, -0.3409,  0.4243, -0.2642],\n",
      "        [-0.3493, -0.2887, -0.2481, -0.3591, -0.2288],\n",
      "        [ 0.3204, -0.3392,  0.2417,  0.2560, -0.2398],\n",
      "        [ 0.2108,  0.1209, -0.2809,  0.1173, -0.0223],\n",
      "        [-0.4216, -0.2395,  0.4291, -0.0034, -0.1912]], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "for p in trans.parameters():print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:25:40.800479Z",
     "iopub.status.busy": "2022-06-07T15:25:40.800005Z",
     "iopub.status.idle": "2022-06-07T15:25:40.802086Z",
     "shell.execute_reply": "2022-06-07T15:25:40.802408Z"
    }
   },
   "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": "2022-06-07T15:25:40.805439Z",
     "iopub.status.busy": "2022-06-07T15:25:40.804973Z",
     "iopub.status.idle": "2022-06-07T15:25:40.808221Z",
     "shell.execute_reply": "2022-06-07T15:25:40.808549Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.2341, 0.2423, 0.2521, 0.1614, 0.1101],\n",
       "        [0.2013, 0.2218, 0.1359, 0.2445, 0.1965],\n",
       "        [0.2631, 0.2811, 0.1343, 0.1323, 0.1892],\n",
       "        [0.1947, 0.2430, 0.1678, 0.2705, 0.1239],\n",
       "        [0.2682, 0.2769, 0.1304, 0.1619, 0.1626],\n",
       "        [0.1290, 0.2274, 0.2240, 0.1681, 0.2514],\n",
       "        [0.1906, 0.1546, 0.2337, 0.2418, 0.1794],\n",
       "        [0.1462, 0.1489, 0.2670, 0.2860, 0.1518],\n",
       "        [0.1681, 0.2339, 0.1379, 0.2481, 0.2121],\n",
       "        [0.2424, 0.1692, 0.1686, 0.2028, 0.2170],\n",
       "        [0.1863, 0.2306, 0.1379, 0.2964, 0.1489],\n",
       "        [0.1891, 0.2009, 0.2093, 0.1873, 0.2134],\n",
       "        [0.2532, 0.1309, 0.2340, 0.2374, 0.1446],\n",
       "        [0.2365, 0.2162, 0.1446, 0.2154, 0.1873],\n",
       "        [0.1366, 0.1639, 0.3199, 0.2076, 0.1720]], 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": "2022-06-07T15:25:40.811595Z",
     "iopub.status.busy": "2022-06-07T15:25:40.811084Z",
     "iopub.status.idle": "2022-06-07T15:25:40.814181Z",
     "shell.execute_reply": "2022-06-07T15:25:40.814524Z"
    },
    "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": "2022-06-07T15:25:40.818070Z",
     "iopub.status.busy": "2022-06-07T15:25:40.817508Z",
     "iopub.status.idle": "2022-06-07T15:25:40.819570Z",
     "shell.execute_reply": "2022-06-07T15:25:40.819916Z"
    }
   },
   "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": "2022-06-07T15:25:40.823788Z",
     "iopub.status.busy": "2022-06-07T15:25:40.823139Z",
     "iopub.status.idle": "2022-06-07T15:25:40.826087Z",
     "shell.execute_reply": "2022-06-07T15:25:40.826452Z"
    }
   },
   "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": "2022-06-07T15:25:40.829884Z",
     "iopub.status.busy": "2022-06-07T15:25:40.829315Z",
     "iopub.status.idle": "2022-06-07T15:25:40.831270Z",
     "shell.execute_reply": "2022-06-07T15:25:40.831659Z"
    }
   },
   "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": "2022-06-07T15:25:40.834649Z",
     "iopub.status.busy": "2022-06-07T15:25:40.834186Z",
     "iopub.status.idle": "2022-06-07T15:25:40.838987Z",
     "shell.execute_reply": "2022-06-07T15:25:40.839314Z"
    },
    "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": "2022-06-07T15:25:40.842473Z",
     "iopub.status.busy": "2022-06-07T15:25:40.841983Z",
     "iopub.status.idle": "2022-06-07T15:25:40.845511Z",
     "shell.execute_reply": "2022-06-07T15:25:40.845835Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.1975, 0.2105, 0.1953, 0.2002, 0.1966], 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": "2022-06-07T15:25:40.849094Z",
     "iopub.status.busy": "2022-06-07T15:25:40.848602Z",
     "iopub.status.idle": "2022-06-07T15:25:40.851735Z",
     "shell.execute_reply": "2022-06-07T15:25:40.852064Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.0185, 0.0504, 0.2546, 0.3703, 0.3062]), tensor(1.0000))"
      ]
     },
     "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": "2022-06-07T15:25:40.860214Z",
     "iopub.status.busy": "2022-06-07T15:25:40.858810Z",
     "iopub.status.idle": "2022-06-07T15:25:40.961502Z",
     "shell.execute_reply": "2022-06-07T15:25:40.961848Z"
    }
   },
   "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": "2022-06-07T15:25:40.965991Z",
     "iopub.status.busy": "2022-06-07T15:25:40.965482Z",
     "iopub.status.idle": "2022-06-07T15:25:40.968280Z",
     "shell.execute_reply": "2022-06-07T15:25:40.968700Z"
    }
   },
   "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([ 1.6700,  4.6054, 27.7749, 38.4502, 27.4996]))"
      ]
     },
     "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": "2022-06-07T15:25:40.972217Z",
     "iopub.status.busy": "2022-06-07T15:25:40.971677Z",
     "iopub.status.idle": "2022-06-07T15:25:40.974319Z",
     "shell.execute_reply": "2022-06-07T15:25:40.974687Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.1168)"
      ]
     },
     "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": "2022-06-07T15:25:40.978228Z",
     "iopub.status.busy": "2022-06-07T15:25:40.977670Z",
     "iopub.status.idle": "2022-06-07T15:25:40.979602Z",
     "shell.execute_reply": "2022-06-07T15:25:40.979950Z"
    }
   },
   "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": "2022-06-07T15:25:40.993131Z",
     "iopub.status.busy": "2022-06-07T15:25:40.992637Z",
     "iopub.status.idle": "2022-06-07T15:25:40.994319Z",
     "shell.execute_reply": "2022-06-07T15:25:40.994644Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch.nn.functional as F\n",
    "\n",
    "learning_rate = 0.1\n",
    "beta1, beta2 = 0.975, 0\n",
    "# beta1, beta2 = 0.9, 0.999 # décommenter pour utiliser Adam\n",
    "num_epochs = 2 ** 10 + 1\n",
    "batch_size = 200\n",
    "do_optim = False\n",
    "do_optim = True\n",
    "\n",
    "def pdf_loss(p_pred, p, weight, loss_type):\n",
    "    if loss_type=='kl':\n",
    "        ind_nonzero = (p==0) + (p_pred==0)\n",
    "        p[ind_nonzero] = 1.\n",
    "        p_pred[ind_nonzero] = 1.\n",
    "        kl_div = p * (p.log() - p_pred.log())\n",
    "        loss_train = (kl_div * weight[:, None]).sum()\n",
    "    elif loss_type=='l1':\n",
    "        div = torch.absolute(p - p_pred)\n",
    "        loss_train = (div * weight[:, None]).sum()\n",
    "    else: # 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": "code",
   "execution_count": 75,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:25:41.000090Z",
     "iopub.status.busy": "2022-06-07T15:25:40.999293Z",
     "iopub.status.idle": "2022-06-07T15:44:31.328084Z",
     "shell.execute_reply": "2022-06-07T15:44:31.328487Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss_type='l1'\n",
      "Iteration: 0 / 1025 - Loss: 7.22832e-01\n",
      "Iteration: 32 / 1025 - Loss: 1.43086e-01\n",
      "Iteration: 64 / 1025 - Loss: 1.12373e-01\n",
      "Iteration: 96 / 1025 - Loss: 1.01625e-01\n",
      "Iteration: 128 / 1025 - Loss: 9.65180e-02\n",
      "Iteration: 160 / 1025 - Loss: 9.36830e-02\n",
      "Iteration: 192 / 1025 - Loss: 9.18777e-02\n",
      "Iteration: 224 / 1025 - Loss: 9.05986e-02\n",
      "Iteration: 256 / 1025 - Loss: 8.96218e-02\n",
      "Iteration: 288 / 1025 - Loss: 8.88417e-02\n",
      "Iteration: 320 / 1025 - Loss: 8.81919e-02\n",
      "Iteration: 352 / 1025 - Loss: 8.76354e-02\n",
      "Iteration: 384 / 1025 - Loss: 8.71523e-02\n",
      "Iteration: 416 / 1025 - Loss: 8.67224e-02\n",
      "Iteration: 448 / 1025 - Loss: 8.63410e-02\n",
      "Iteration: 480 / 1025 - Loss: 8.59988e-02\n",
      "Iteration: 512 / 1025 - Loss: 8.56887e-02\n",
      "Iteration: 544 / 1025 - Loss: 8.54069e-02\n",
      "Iteration: 576 / 1025 - Loss: 8.51503e-02\n",
      "Iteration: 608 / 1025 - Loss: 8.49141e-02\n",
      "Iteration: 640 / 1025 - Loss: 8.46974e-02\n",
      "Iteration: 672 / 1025 - Loss: 8.44969e-02\n",
      "Iteration: 704 / 1025 - Loss: 8.43127e-02\n",
      "Iteration: 736 / 1025 - Loss: 8.41402e-02\n",
      "Iteration: 768 / 1025 - Loss: 8.39811e-02\n",
      "Iteration: 800 / 1025 - Loss: 8.38336e-02\n",
      "Iteration: 832 / 1025 - Loss: 8.36956e-02\n",
      "Iteration: 864 / 1025 - Loss: 8.35658e-02\n",
      "Iteration: 896 / 1025 - Loss: 8.34453e-02\n",
      "Iteration: 928 / 1025 - Loss: 8.33324e-02\n",
      "Iteration: 960 / 1025 - Loss: 8.32257e-02\n",
      "Iteration: 992 / 1025 - Loss: 8.31259e-02\n",
      "Iteration: 1024 / 1025 - Loss: 8.30311e-02\n",
      "Erreur ~ 8.5%\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: 3.66513e-01\n",
      "Iteration: 32 / 1025 - Loss: 4.06888e-02\n",
      "Iteration: 64 / 1025 - Loss: 2.47049e-02\n",
      "Iteration: 96 / 1025 - Loss: 2.01747e-02\n",
      "Iteration: 128 / 1025 - Loss: 1.81133e-02\n",
      "Iteration: 160 / 1025 - Loss: 1.69389e-02\n",
      "Iteration: 192 / 1025 - Loss: 1.61797e-02\n",
      "Iteration: 224 / 1025 - Loss: 1.56463e-02\n",
      "Iteration: 256 / 1025 - Loss: 1.52477e-02\n",
      "Iteration: 288 / 1025 - Loss: 1.49342e-02\n",
      "Iteration: 320 / 1025 - Loss: 1.46774e-02\n",
      "Iteration: 352 / 1025 - Loss: 1.44596e-02\n",
      "Iteration: 384 / 1025 - Loss: 1.42704e-02\n",
      "Iteration: 416 / 1025 - Loss: 1.41023e-02\n",
      "Iteration: 448 / 1025 - Loss: 1.39510e-02\n",
      "Iteration: 480 / 1025 - Loss: 1.38135e-02\n",
      "Iteration: 512 / 1025 - Loss: 1.36877e-02\n",
      "Iteration: 544 / 1025 - Loss: 1.35715e-02\n",
      "Iteration: 576 / 1025 - Loss: 1.34643e-02\n",
      "Iteration: 608 / 1025 - Loss: 1.33652e-02\n",
      "Iteration: 640 / 1025 - Loss: 1.32730e-02\n",
      "Iteration: 672 / 1025 - Loss: 1.31873e-02\n",
      "Iteration: 704 / 1025 - Loss: 1.31077e-02\n",
      "Iteration: 736 / 1025 - Loss: 1.30336e-02\n",
      "Iteration: 768 / 1025 - Loss: 1.29642e-02\n",
      "Iteration: 800 / 1025 - Loss: 1.28994e-02\n",
      "Iteration: 832 / 1025 - Loss: 1.28386e-02\n",
      "Iteration: 864 / 1025 - Loss: 1.27819e-02\n",
      "Iteration: 896 / 1025 - Loss: 1.27287e-02\n",
      "Iteration: 928 / 1025 - Loss: 1.26787e-02\n",
      "Iteration: 960 / 1025 - Loss: 1.26315e-02\n",
      "Iteration: 992 / 1025 - Loss: 1.25868e-02\n",
      "Iteration: 1024 / 1025 - Loss: 1.25446e-02\n",
      "Erreur ~ 9.4%\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: 4.75533e-01\n",
      "Iteration: 32 / 1025 - Loss: 4.71563e-02\n",
      "Iteration: 64 / 1025 - Loss: 2.94258e-02\n",
      "Iteration: 96 / 1025 - Loss: 2.46616e-02\n",
      "Iteration: 128 / 1025 - Loss: 2.23430e-02\n",
      "Iteration: 160 / 1025 - Loss: 2.09098e-02\n",
      "Iteration: 192 / 1025 - Loss: 1.99136e-02\n",
      "Iteration: 224 / 1025 - Loss: 1.91731e-02\n",
      "Iteration: 256 / 1025 - Loss: 1.85991e-02\n",
      "Iteration: 288 / 1025 - Loss: 1.81408e-02\n",
      "Iteration: 320 / 1025 - Loss: 1.77670e-02\n",
      "Iteration: 352 / 1025 - Loss: 1.74570e-02\n",
      "Iteration: 384 / 1025 - Loss: 1.71962e-02\n",
      "Iteration: 416 / 1025 - Loss: 1.69739e-02\n",
      "Iteration: 448 / 1025 - Loss: 1.67822e-02\n",
      "Iteration: 480 / 1025 - Loss: 1.66149e-02\n",
      "Iteration: 512 / 1025 - Loss: 1.64677e-02\n",
      "Iteration: 544 / 1025 - Loss: 1.63367e-02\n",
      "Iteration: 576 / 1025 - Loss: 1.62193e-02\n",
      "Iteration: 608 / 1025 - Loss: 1.61132e-02\n",
      "Iteration: 640 / 1025 - Loss: 1.60164e-02\n",
      "Iteration: 672 / 1025 - Loss: 1.59281e-02\n",
      "Iteration: 704 / 1025 - Loss: 1.58466e-02\n",
      "Iteration: 736 / 1025 - Loss: 1.57711e-02\n",
      "Iteration: 768 / 1025 - Loss: 1.57010e-02\n",
      "Iteration: 800 / 1025 - Loss: 1.56359e-02\n",
      "Iteration: 832 / 1025 - Loss: 1.55748e-02\n",
      "Iteration: 864 / 1025 - Loss: 1.55175e-02\n",
      "Iteration: 896 / 1025 - Loss: 1.54631e-02\n",
      "Iteration: 928 / 1025 - Loss: 1.54120e-02\n",
      "Iteration: 960 / 1025 - Loss: 1.53639e-02\n",
      "Iteration: 992 / 1025 - Loss: 1.53184e-02\n",
      "Iteration: 1024 / 1025 - Loss: 1.52752e-02\n",
      "Erreur ~ 9.2%\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"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "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.show()\n",
    "\n",
    "plt.savefig(datetime + '_prediction_transfert-des-voix.png');"
   ]
  },
  {
   "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.\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": "2022-06-07T15:44:31.332067Z",
     "iopub.status.busy": "2022-06-07T15:44:31.331595Z",
     "iopub.status.idle": "2022-06-07T15:44:31.333589Z",
     "shell.execute_reply": "2022-06-07T15:44:31.333970Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Erreur ~ 9.2%\n"
     ]
    }
   ],
   "source": [
    "print(f'Erreur ~ {loss_test_l1.item()*100:.1f}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'erreur est relativement importante mais il faut la rapporter au fait que c'est l'erreur moyenne 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": "2022-06-07T15:44:31.338401Z",
     "iopub.status.busy": "2022-06-07T15:44:31.337851Z",
     "iopub.status.idle": "2022-06-07T15:44:31.340260Z",
     "shell.execute_reply": "2022-06-07T15:44:31.340587Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.18286577, 0.16729486, 0.11276119, 0.18168885, 0.3553894 ],\n",
       "       [0.10578601, 0.39069578, 0.10077849, 0.13080464, 0.271935  ],\n",
       "       [0.00344546, 0.00621037, 0.8816372 , 0.02954521, 0.07916182],\n",
       "       [0.21767128, 0.1882733 , 0.13536943, 0.15730421, 0.30138186],\n",
       "       [0.09274884, 0.3301721 , 0.08587237, 0.23497622, 0.25623044],\n",
       "       [0.00124446, 0.0027219 , 0.00471753, 0.98637056, 0.00494557],\n",
       "       [0.09245634, 0.20131236, 0.06422006, 0.14247535, 0.49953586],\n",
       "       [0.0013067 , 0.00243068, 0.00325917, 0.00464122, 0.98836225],\n",
       "       [0.01998847, 0.07687607, 0.06536892, 0.20999263, 0.6277739 ],\n",
       "       [0.01395538, 0.07435784, 0.22482768, 0.61757296, 0.06928608],\n",
       "       [0.12706338, 0.17374808, 0.15964091, 0.31094083, 0.22860679],\n",
       "       [0.01293025, 0.05386738, 0.03123457, 0.87230545, 0.02966237],\n",
       "       [0.0233942 , 0.0729494 , 0.055519  , 0.7168975 , 0.1312399 ],\n",
       "       [0.18697052, 0.17323582, 0.1881812 , 0.17383054, 0.27778187],\n",
       "       [0.07051493, 0.25680584, 0.10501669, 0.11811366, 0.44954893]],\n",
       "      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": "2022-06-07T15:44:31.344568Z",
     "iopub.status.busy": "2022-06-07T15:44:31.343983Z",
     "iopub.status.idle": "2022-06-07T15:44:31.346134Z",
     "shell.execute_reply": "2022-06-07T15:44:31.346460Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.       , 0.9999999, 1.       , 1.0000001, 1.       , 1.       ,\n",
       "        1.       , 1.       , 1.       , 1.       , 1.       , 1.       ,\n",
       "        1.       , 0.9999999, 1.       ], 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": [
    "Nous allons nous inspirer d'[un graphique de la galerie matplotlib](https://matplotlib.org/stable/gallery/misc/table_demo.html#sphx-glr-gallery-misc-table-demo-py) pour représenter la proportion de reports de voix en fonction de chacun des choix éfféctués au deuxième tour :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:44:31.359094Z",
     "iopub.status.busy": "2022-06-07T15:44:31.353927Z",
     "iopub.status.idle": "2022-06-07T15:44:31.895349Z",
     "shell.execute_reply": "2022-06-07T15:44:31.895685Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x936 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13, 13))\n",
    "\n",
    "columns = df_2.columns\n",
    "rows = df_1.columns\n",
    "\n",
    "# Get some shades for the colors\n",
    "colors = plt.cm.tab20c(np.linspace(0, 1, len(rows)))\n",
    "n_rows = len(rows)\n",
    "\n",
    "index = np.arange(len(columns)) + 0.3\n",
    "bar_width = 0.4\n",
    "\n",
    "# Initialize the vertical-offset for the stacked bar chart.\n",
    "y_offset = np.zeros(len(columns))\n",
    "\n",
    "# Plot bars and create text labels for the table\n",
    "cell_text = []\n",
    "for row in range(n_rows):\n",
    "    ax.bar(index, M[row]*100, bar_width, bottom=y_offset, color=colors[row])\n",
    "    y_offset = y_offset + M[row]*100\n",
    "    cell_text.append([f'{x*100:1.1f}%' for x in M[row]])\n",
    "ax.set_ylim(0, 100)\n",
    "\n",
    "# Add a table at the bottom of the axes\n",
    "the_table = ax.table(cellText=cell_text,\n",
    "                      rowLabels=rows,\n",
    "                      rowColours=colors,\n",
    "                      colLabels=columns,\n",
    "                      loc='bottom')\n",
    "\n",
    "# Adjust layout to make room for the table:\n",
    "plt.subplots_adjust(left=0.2, bottom=0.2)\n",
    "\n",
    "plt.ylabel(\"Pourcentage de report des voix\")\n",
    "plt.yticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.xticks([])\n",
    "plt.title(\"Report des voix par résultat du 2nd tour\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ces données correspondent aux intuitions qu'on peut se faire quand au report des votes. Notamment on remarque que la plupart des individus qui s'abstiennent au second tour se sont abstenus au premier (avec une légère proportion de \"Mélenchon\" qui se sont abstenus). Remarquez aussi que les électeurs de \"Macron\" ou \"Le Pen\" au premier tour ont voté pour la même personne au deuxième tour. Environ un quart des électeurs de \"Le Pen\" au second tour s'était abstenu au premier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:44:31.900369Z",
     "iopub.status.busy": "2022-06-07T15:44:31.899788Z",
     "iopub.status.idle": "2022-06-07T15:44:31.902030Z",
     "shell.execute_reply": "2022-06-07T15:44:31.902352Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[18.3, 16.7, 11.3, 18.2, 35.5],\n",
       "       [10.6, 39.1, 10.1, 13.1, 27.2],\n",
       "       [ 0.3,  0.6, 88.2,  3. ,  7.9],\n",
       "       [21.8, 18.8, 13.5, 15.7, 30.1],\n",
       "       [ 9.3, 33. ,  8.6, 23.5, 25.6],\n",
       "       [ 0.1,  0.3,  0.5, 98.6,  0.5],\n",
       "       [ 9.2, 20.1,  6.4, 14.2, 50. ],\n",
       "       [ 0.1,  0.2,  0.3,  0.5, 98.8],\n",
       "       [ 2. ,  7.7,  6.5, 21. , 62.8],\n",
       "       [ 1.4,  7.4, 22.5, 61.8,  6.9],\n",
       "       [12.7, 17.4, 16. , 31.1, 22.9],\n",
       "       [ 1.3,  5.4,  3.1, 87.2,  3. ],\n",
       "       [ 2.3,  7.3,  5.6, 71.7, 13.1],\n",
       "       [18.7, 17.3, 18.8, 17.4, 27.8],\n",
       "       [ 7.1, 25.7, 10.5, 11.8, 45. ]], dtype=float32)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(precision=1)\n",
    "np.set_printoptions(suppress=True)\n",
    "M*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On observe aussi quelques points intéressants dans les votes nuls qui proviennent majoritairement de 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",
    "\n",
    "Muni de cette matrice de transition, on peut maintenant opérer une transformation de telle sorte à ce que nous allons regarder la distribution du report de voix pour chacun des choix qui sont faits au premier tour."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:44:31.906461Z",
     "iopub.status.busy": "2022-06-07T15:44:31.905958Z",
     "iopub.status.idle": "2022-06-07T15:44:31.908264Z",
     "shell.execute_reply": "2022-06-07T15:44:31.908612Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[18.3, 10.6,  0.3, 21.8,  9.3,  0.1,  9.2,  0.1,  2. ,  1.4, 12.7,\n",
       "         1.3,  2.3, 18.7,  7.1],\n",
       "       [16.7, 39.1,  0.6, 18.8, 33. ,  0.3, 20.1,  0.2,  7.7,  7.4, 17.4,\n",
       "         5.4,  7.3, 17.3, 25.7],\n",
       "       [11.3, 10.1, 88.2, 13.5,  8.6,  0.5,  6.4,  0.3,  6.5, 22.5, 16. ,\n",
       "         3.1,  5.6, 18.8, 10.5],\n",
       "       [18.2, 13.1,  3. , 15.7, 23.5, 98.6, 14.2,  0.5, 21. , 61.8, 31.1,\n",
       "        87.2, 71.7, 17.4, 11.8],\n",
       "       [35.5, 27.2,  7.9, 30.1, 25.6,  0.5, 50. , 98.8, 62.8,  6.9, 22.9,\n",
       "         3. , 13.1, 27.8, 45. ]], dtype=float32)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MT = M.T\n",
    "MT /= MT.sum(axis=0)\n",
    "MT*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:44:31.974381Z",
     "iopub.status.busy": "2022-06-07T15:44:31.929377Z",
     "iopub.status.idle": "2022-06-07T15:44:32.469813Z",
     "shell.execute_reply": "2022-06-07T15:44:32.470167Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(25, 8))\n",
    "\n",
    "columns = df_1.columns\n",
    "rows = df_2.columns\n",
    "\n",
    "# named colors: https://matplotlib.org/stable/gallery/color/named_colors.html\n",
    "colors = ['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, MT[row]*100, bar_width, bottom=y_offset, color=colors[row], linewidth=1)\n",
    "    y_offset = y_offset + MT[row]*100\n",
    "    cell_text.append([f'{x*100:1.1f}%' for x in MT[row]])\n",
    "ax.set_ylim(0, 100)\n",
    "\n",
    "# Add a table at the bottom of the axes\n",
    "the_table = ax.table(cellText=cell_text,\n",
    "                      rowLabels=rows,\n",
    "                      rowColours=colors,\n",
    "                      colLabels=columns,\n",
    "                      loc='bottom')\n",
    "\n",
    "# Adjust layout to make room for the table:\n",
    "plt.subplots_adjust(left=0.2, bottom=0.2)\n",
    "\n",
    "plt.ylabel(\"Pourcentage de report des voix\")\n",
    "plt.yticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.xticks([])\n",
    "plt.title(\"Report des voix par résultat du 1er tour\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut aussi se restreindre aux votes exprimés :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:44:32.474856Z",
     "iopub.status.busy": "2022-06-07T15:44:32.474279Z",
     "iopub.status.idle": "2022-06-07T15:44:32.476573Z",
     "shell.execute_reply": "2022-06-07T15:44:32.476897Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[34.3, 47.8, 99.5, 22.2,  0.5, 25.1, 89.9, 57.6, 96.7, 84.5, 38.5,\n",
       "        20.8],\n",
       "       [65.7, 52.2,  0.5, 77.8, 99.5, 74.9, 10.1, 42.4,  3.3, 15.5, 61.5,\n",
       "        79.2]], dtype=float32)"
      ]
     },
     "execution_count": 83,
     "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": 84,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T15:44:32.512777Z",
     "iopub.status.busy": "2022-06-07T15:44:32.512242Z",
     "iopub.status.idle": "2022-06-07T15:44:32.811116Z",
     "shell.execute_reply": "2022-06-07T15:44:32.811457Z"
    },
    "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=0.2, bottom=0.2)\n",
    "\n",
    "plt.ylabel(\"Pourcentage de report des voix\")\n",
    "plt.yticks(np.linspace(0, 100, 6, endpoint=True))\n",
    "plt.xticks([])\n",
    "plt.title(\"Report des voix exprimées connaissant le choix exprimé au 1er tour\")\n",
    "plt.savefig(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.** \n",
    "\n",
    "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`).\n"
   ]
  },
  {
   "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": "2022-06-07T15:44:32.815879Z",
     "iopub.status.busy": "2022-06-07T15:44:32.815312Z",
     "iopub.status.idle": "2022-06-07T15:44:32.818259Z",
     "shell.execute_reply": "2022-06-07T15:44:32.818588Z"
    },
    "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 = 48807 personnes.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(f\"\"\"\n",
    "Total des voix au 1er tour= {x_1.sum():.0f}, dont Macron = {x_1[:, 5].sum():.0f} (soit une pourcentage de {x_1[:, 5].sum()/x_1.sum()*100:.2f}%), \n",
    "-> nombre de reports de Macron du 1er vers Le Pen au 2eme = {x_1[:, 5].sum()*MT[1, 2]:.0f} personnes.\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Influence des parametres\n",
    "\n",
    "Finalement, 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": "2022-06-07T15:44:32.824192Z",
     "iopub.status.busy": "2022-06-07T15:44:32.823122Z",
     "iopub.status.idle": "2022-06-07T15:50:52.893154Z",
     "shell.execute_reply": "2022-06-07T15:50:52.893491Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAIN: Loss avec do_optim=True = 1.70e-02 / Loss avec alternative choice do_optim=False = 1.70e-02 \n",
      "TEST: Loss avec do_optim=True = 1.67e-02 / Loss avec alternative choice do_optim=False = 1.67e-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": "2022-06-07T15:50:52.897099Z",
     "iopub.status.busy": "2022-06-07T15:50:52.896527Z",
     "iopub.status.idle": "2022-06-07T15:50:52.898857Z",
     "shell.execute_reply": "2022-06-07T15:50:52.899182Z"
    }
   },
   "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": "2022-06-07T15:50:52.904972Z",
     "iopub.status.busy": "2022-06-07T15:50:52.904139Z",
     "iopub.status.idle": "2022-06-07T16:36:21.590029Z",
     "shell.execute_reply": "2022-06-07T16:36:21.590438Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour learning_rate= 1.00e-02, loss_train=2.67e-02 / loss_test=2.51e-02; le temps de calcul est 389.154 s\n",
      "Pour learning_rate= 2.15e-02, loss_train=2.19e-02 / loss_test=2.12e-02; le temps de calcul est 398.443 s\n",
      "Pour learning_rate= 4.64e-02, loss_train=1.88e-02 / loss_test=1.82e-02; le temps de calcul est 387.635 s\n",
      "Pour learning_rate= 1.00e-01, loss_train=1.70e-02 / loss_test=1.67e-02; le temps de calcul est 386.607 s\n",
      "Pour learning_rate= 2.15e-01, loss_train=1.62e-02 / loss_test=1.59e-02; le temps de calcul est 389.846 s\n",
      "Pour learning_rate= 4.64e-01, loss_train=1.55e-02 / loss_test=1.55e-02; le temps de calcul est 389.328 s\n",
      "Pour learning_rate= 1.00e+00, loss_train=1.52e-02 / loss_test=1.52e-02; le temps de calcul est 387.267 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_, 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": "2022-06-07T16:36:21.596580Z",
     "iopub.status.busy": "2022-06-07T16:36:21.595771Z",
     "iopub.status.idle": "2022-06-07T17:22:22.750344Z",
     "shell.execute_reply": "2022-06-07T17:22:22.750715Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 25 100 225 400 625 900]\n",
      "Pour batch_size= 25, loss_train=1.73e-02 / loss_test=1.70e-02; le temps de calcul est 903.227 s\n",
      "Pour batch_size= 100, loss_train=1.71e-02 / loss_test=1.68e-02; le temps de calcul est 442.299 s\n",
      "Pour batch_size= 225, loss_train=1.71e-02 / loss_test=1.68e-02; le temps de calcul est 378.735 s\n",
      "Pour batch_size= 400, loss_train=1.69e-02 / loss_test=1.67e-02; le temps de calcul est 342.802 s\n",
      "Pour batch_size= 625, loss_train=1.72e-02 / loss_test=1.69e-02; le temps de calcul est 335.740 s\n",
      "Pour batch_size= 900, loss_train=1.70e-02 / loss_test=1.67e-02; le temps de calcul est 357.972 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results_train, results_test = [], []\n",
    "batch_sizes = (batch_size * np.arange(1, N_scan) ** 2) // 8\n",
    "print(batch_sizes)\n",
    "for batch_size_ in batch_sizes:\n",
    "    tic = time.time()\n",
    "    trans, loss_train, loss_test, loss_test_l1, p_1, p_2, p_2_pred = fit_data(df_1, df_2, batch_size=batch_size_, verbose=False)\n",
    "    print(f'Pour batch_size= {batch_size_}, {loss_train=:.2e} / {loss_test=:.2e}; le temps de calcul est {time.time()-tic:.3f} s')\n",
    "    results_train.append(loss_train)\n",
    "    results_test.append(loss_test)\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (13, 8))\n",
    "ax.plot(batch_sizes, results_train, '--')\n",
    "ax.plot(batch_sizes, results_test)\n",
    "ax.set_xlabel = 'batch size'\n",
    "ax.set_ylabel = 'Loss'\n",
    "ax.set_yscale('log');\n",
    "ax.set_xscale('log');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T17:22:22.755134Z",
     "iopub.status.busy": "2022-06-07T17:22:22.754549Z",
     "iopub.status.idle": "2022-06-07T17:22:22.756556Z",
     "shell.execute_reply": "2022-06-07T17:22:22.756901Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.  1.  1.  1.  0.9 0.9 0.7]\n"
     ]
    }
   ],
   "source": [
    "beta1s = 1 - (1 - beta1) * np.logspace(-1, 1, 7, base=10)\n",
    "print(beta1s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-07T17:22:22.762750Z",
     "iopub.status.busy": "2022-06-07T17:22:22.762138Z",
     "iopub.status.idle": "2022-06-07T18:08:12.126508Z",
     "shell.execute_reply": "2022-06-07T18:08:12.126871Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.  1.  1.  1.  0.9 0.9 0.7]\n",
      "Pour beta1= 9.98e-01, loss_train=1.52e-02 / loss_test=1.52e-02; le temps de calcul est 392.081 s\n",
      "Pour beta1= 9.95e-01, loss_train=1.55e-02 / loss_test=1.55e-02; le temps de calcul est 390.999 s\n",
      "Pour beta1= 9.88e-01, loss_train=1.61e-02 / loss_test=1.58e-02; le temps de calcul est 390.219 s\n",
      "Pour beta1= 9.75e-01, loss_train=1.70e-02 / loss_test=1.67e-02; le temps de calcul est 390.164 s\n",
      "Pour beta1= 9.46e-01, loss_train=1.89e-02 / loss_test=1.83e-02; le temps de calcul est 392.275 s\n",
      "Pour beta1= 8.84e-01, loss_train=2.09e-02 / loss_test=2.01e-02; le temps de calcul est 401.328 s\n",
      "Pour beta1= 7.50e-01, loss_train=2.61e-02 / loss_test=2.48e-02; le temps de calcul est 392.114 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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TYcsiyM+Cptc5U6/a3Alezcr7NrkFhby55TgzVqQQGeblze/1wxhDoc/iVfkQERGRKkqlww+VDj+y05w1H+umQ9phiG0MPSc5U6+iarmdLuj5fJZzWXkkxIRzISuP259eybBujRjfL5G6MRFuxxMREREpVyodfqh0lICvEL5835l6dXAFhERAp+HO6Ee99m6nqxSOXbjEH97Zzfs7TxLq8TCsWyOmDEymeUINt6OJiIiIlAuVDj9UOkrp1C6nfGx7GQqyIXGAUz5a3w4eHZb3bQ6ezWLmyhRe3XiM/EIfn//0RhrWjHQ7loiIiMg1q3alwxgzFLgDiAVmWWs/LO5alY4yunQeNs13tt3NOAY1m0KvqdB1NETGu50u6J3NzGXFl2cY1q0xAM98vI829WO4uW09LToXERGRSqnMpcMY0wSYD9QDLDDdWvt0Mdd6gQ1AqrX2zmsIOxu4Ezhtre1w2fODgacBLzDTWvvnEtwrHvgfa+2k4q5R6bhGhQWw9x3nwMEjqyA0CjqPdHa9SmjtdrpKISe/kNv+sYLD5y6RnBDN1AHJDO3aiIhQjRyJiIhI5XEtpaMB0MBau8kYEwNsBIZaa3dd5drHgR5A7JWlwxhTF8i21l687LkW1tr9V7nPQCATmP9V6SgqNF8CtwDHgPXASGvtLmNMR+BPV9xmorX2tDHmb8BCa+2m4n6PKh3l6MRWWDsdtr8ChbmQfAP0+Q60uAU8HrfTBbWCQh/v7jjJ9BUH2JGaQZ0a4Twzsgt9m9dxO5qIiIhIiRRXOr71p0Br7YmvfmAvKgy7gUZXeYPGONOZZhZzq0HAG8aY8KLrpwD/LOY9VwDnr3i6F7DfWptirc0DFgP3FF2/3Vp75+UP4Iwx5kngPX+FQ8pZg84w9Fl4fBfc+Es4swdeGg7/6u6MhORkuJ0waIV4PdzduSFvPdKfhZN706lx3NeLzL88dZHUtGyXE4qIiIiUTakOXDDGJAJdgbVX+fY/gJ8AMVd7rbX2FWNMErDEGPMKMBFn1KKkGgFHL/v6GNDbz/WPAjcDcUUjKs9feYEx5i7grhYtWpQihpRIdB0Y+GPo9xjsetM57fz9n8Ly30PXh5y1H7Wbu50yKBlj6NeiDv1a/N8Ix/97aydrU85zV+eGTB2YTNsGsS4mFBERESmdEs93McbUAJYCj1lrM6743lfrLzb6u4e19i9ADvAccLe1NrP0kUvGWvuMtba7tfbhqxWOomvestZOjYuLC1QM8YY6p5pP/gimLIc2Q2D9LPhnN1j4AOz/GKroZgbl6cn7OjH2ukQ+2HmS259eyZhZa1l/6MrBQBEREZHgVKLSYYwJxSkcC621r13lkn7A3caYQzjTnm40xiy4yn0GAB2A14FflzJrKtDksq8bFz0nlUWj7jBsOvxgJwx6Ao5vgQXD4Nlezg5YuQHroJVe4/gofnVXO1Y/cRM/vq01u09cZOvRNMBZC1JQ6HM3oIiIiIgfJVlIboB5wHlr7WPfekNjrgd+dJWF5F2Bl3B2pToILAQOWGt/Wcx9EoG3L1tIHoKzkPwmnLKxHhhlrd35bZm+jRaSu6QgF3a+AWufg+ObITwOuo2BXlMgPtHtdEEtJ78QgIhQLy9vOMozH+9jcv8khvdsQlRYqWZNioiIiJSbMi8kxxnFGIMzerGl6DGk6KbvGmMaljBDFDDcWnvAWusDxgKHiwm7CFgNtDbGHDPGTLLWFgCPAB/gLGZ/uTwKh7goJBw6j4Apn8Ckj6DFTbDmOXi6CywaBSmfaepVMSJCvV9vp9s4PpL6sRH85q1d9P3zcp76cC9nM3NdTigiIiLyf6rs4YCloZGOIJKeChtmw8Y5cOkc1G3nnPfRcTiERbmdLqhtOHSeF1ak8NGuU3RtWpPXv9vP7UgiIiJSzVS7E8lLQ6UjCOVnw46lzja7p7Y7J5x3Gwc9J0PNJt/++mps/+lMMnLy6dY0nvTsfH715g7G902ka1OdEi8iIiKBpdLhh0pHELMWDq+Ctc/DnrcBA23vhN4PQ9PrwBi3Ewa1tSnnmDJ/Axk5BfRKqsW0gcnc0LouHo/+3ERERKT8qXT4odJRSaQdgfUzYeM8yEmD+p2c8tHhPgiNcDtd0MrMLWDJ+qPMWpnC8fQcWtWrwWvf7UeNcC04FxERkfKl0uGHSkclk3cJti1xDhw8sxuiakP3Cc7Uq9gGbqcLWvmFPt7edpytR9P5zd3tAfh49yl6JtUiNiLU5XQiIiJSFah0+KHSUUlZCwdXOFOv9r4HHi+0uwd6fwca99DUq29xNjOXPn/8mIhQL6N6N2VivyTqx2nESERERMpOpcMPlY4q4PxBZ+rVphchNx0adnOmXrW/F0LC3E4XtHakpvPCihTe2XYcr8dwd+dGPH5rKxrVjHQ7moiIiFRCKh1+qHRUIbmZsHWRM/Xq3D6oUQ96THSmX8XUcztd0Dp6/hKzPj/I0k3HeP+xgTSqGcnFnHxqhIdgNGIkIiIiJaTS4YdKRxXk80HKcmfL3f0fgSfUWXDeexo06uZ2uqCVnVdIZJhz6OCYWWvJyM5n2qDm3Na+Pl7teCUiIiLfQqXDD5WOKu7sflg3HbYshLxMaNLbKR9t7wavFlBfjbWWl9YdYcaKFA6du0Sz2lFMHpDMA90bf30SuoiIiMiVVDr8UOmoJnLSYctLztSrCwchpiH0nATdx0N0HbfTBaVCn+XDnSd5fkUKW4+m8fMhbZg6sLnbsURERCRIqXT4odJRzfh8sO9DZ9erlE/AGw4dH3BGPxp0cjtdULLWsu7gedo0iCUuMpR3t59gbco5Jg9IpkmtKLfjiYiISJBQ6fBDpaMaO70H1r0AWxdD/iVo1s/Z9ar1EPDq8Lzi/Gv5Pp7+eB+FPsuQjg2YNrA5HRvHuR1LREREXKbS4YdKh5B9wdlud90MSD8CcU2g1xToOgaiarmdLiidTM9hzhcHeWntES7mFvBQ76b84d6ObscSERERF6l0+KHSIV/zFToHDa59Hg6thJBI6DzCGf2o29btdEEpIyefRWuP0LRWFLd3bEBmbgEf7TrJnZ0aEur1uB1PREREKpBKhx8qHXJVJ3c45WP7K1CQA0mDnPLR6jbn9HO5qiXrj/DTpdtpGBfBxP5JPNirKTXCNVVNRESkOlDp8EOlQ/zKOgeb5jknnmekQnwi9JoKXUdDhNYxXMlay6d7z/D8ZwdYe/A8MREhjO7TjB/d2lpnfYiIiFRxKh1+qHRIiRTmw563nS13j6yG0GjoMsrZ9apOS7fTBaUtR9OYvuIAaZfyeWlKHwDOZuZSp0a4y8lEREQkEFQ6/FDpkFI7vhnWTocdr0JhHrS42Zl61fwm8Ggdw5XyC32Eej2cyshhwF8+YWDLBB4elEyPRC3SFxERqUpUOvxQ6ZAyyzwDG+c4U68yT0HtFtBrGnQZCeExbqcLOumX8pn1xUHmrz5E2qV8ujeLZ+rAZG5pWw+Ppl6JiIhUeiodfqh0yDUryINdbzoLz1M3QHiss+aj1xSolex2uqBzKa+AVzYcY+bnKaReyOazH9+gQwZFRESqAJUOP1Q6pFwd2+CUj52vO1vwtrrNmXqVfD0Y/Wv+5QoKfWw5mvb1NKufvLqVZrWjGd27GXFRoS6nExERkdJS6fBDpUMCIuOEM/Vqw2zIOgMJbZxdrzo/CGHRbqcLOnkFPqa+uIFP954hKszLiJ5NmNQ/icbxGgERERGpLFQ6/FDpkIAqyIUdr8Ha5+DEVmeb3W5joecUiG/mdrqgs/tEBjNWpLBs63Es8Oyorgzu0MDtWCIiIlICKh1+qHRIhbAWjq51pl7tWgZYaD3EmXqV2F9Tr65wPC2buasO8Z1BzYmPDmNtyjnyCy39WtTG6M9KREQkKKl0+KHSIRUu/RisnwUb50L2eajXwTnvo+MDEBrpdrqgNHHuepbvOU37hrFMHZjMHR0bEOLV9sQiIiLBRKXDD5UOcU1+Nmx/BdY8D6d3QmQt6D4eek6CuMZupwsquQWFvLE5lekrUjhwJotGNSP5yeDW3NOlkdvRREREpIhKhx8qHeI6a+HQ587Uq73vAgba3gV9vgNNemvq1WV8PsvHe04zfcUB7u3amFG9m5KTX0hmboFOOhcREXGZSocfKh0SVC4chvUzYNN8yEmHBl2cdR8dhkGIfqi+nM9n8XgM81cf4g/v7Oa+7o2ZMiCZpDraHUxERMQNKh1+qHRIUMrLgq2LYe0LcHYvRCdA9wnO1KuY+m6nCyopZzKZsTKFpZtSyS/0cVu7+kwdlEy3pvFuRxMREalWVDr8UOmQoGYtpHzqTL368gPweKH9vc7oR+Nv/G+6Wjt9MYd5qw7x4urDtKhbg9e+28/tSCIiItWKSocfKh1SaZw7AOtmwOYFkHcRGvVwyke7eyAkzO10QSMrt4AzF3NJrBPN2cxcJsxZz5jrmnFPl4aEh3jdjiciIlJlqXT4odIhlU7uRdiyyBn9OH8AatR3pl11nwA1EtxOF1R2Hc/gh69sZfeJDOrGhDOhXxKjejclLjLU7WgiIiJVjkqHHyodUmn5fHDgY6d87P83eMOgw/3OmR8Nu7idLmhYa1m57yzTV6Tw+f6zxESE8PlPbiQuSsVDRESkPBVXOkLcCCMi5cTjgZa3OI8zX8K66bDlJdj6EjS9zikfbe4Cb/X+n7oxhoGtEhjYKoEdqemsSTn3deGY+8VB+jSvTZv6sS6nFBERqbo00oFGOqSKyU6DLQudXa/SDkNsI+g52Tl0MKqW2+mCSvqlfPo9uZzM3AKub53AtIHN6ZNcC6NzUURERMpE06v8UOmQKslX6Ox2tfZ5OPgZhERAp+HQaxrU7+B2uqBxISuPBWsOM2/1Ic5m5tGpcRx/ub+TRj5ERETKQKXDD5UOqfJO7YJ1L8DWJVCQDYkDnF2vWt/ubMEr5OQXsnTTMV5cfZgFk3tTp0Y4R85dIiEmnMgw/RmJiIiUhEqHHyodUm1cOu+cdL5+JqQfhZpNoecU6DYGInWQHjiLzr+aXnX/c6s4cCaTsdclMq5vIrWitS2xiIiIPyodfqh0SLVTWAB733WmXh3+AkKjoPODzuhHQmu30wWNdQfPM33FAf69+zQRoR6G92jC5P7JNK0d5XY0ERGRoKTS4YdKh1RrJ7Y5U6+2vQKFuZB8g1M+Wt7q7I4l7Dt1kRkrU3h9cyq/GNKW8f2S/mNERERERBwqHX6odIgAWWdh41xYPwsuHof4JGfL3S4PQYQWVQOcysghNiKUyDAvL609wltbjzN1UDLXt0pQAREREaH40qF/xhQRR3QdGPgjeGwb3D8batSF95+Ap9rCuz+Bs/vdTui6erERXy8qDw/xcPBsFhPmrOf2p1eydOMx8gp8LicUEREJThrpQCMdIsVK3Qhrp8OOpeDLd6Zc9Z4GyTdq6hWQV+Djra3Hmb4ihb2nLnJz27rMHNfT7VgiIiKu0fQqP1Q6RL7FxVOwcY4z9SrrNNRpBb2mQueREF7D7XSus9by6ZdnCA/x0Ld5HS5k5TFjZQrj+yZSNzbC7XgiIiIVRqXDD5UOkRIqyINdb8Ca5+D4JgiPg66jodcUqJXkdrqg8e72Ezzy0iZCPB6Gdm3I1IHJtKgb43YsERGRgFPp8EOlQ6SUrIVjG2Dtc7DrTef089a3O7teJQ0ELarm8LksZq48yCsbj5KT7+PmtvV4bnQ3Qr2aliYiIlWXSocfKh0i1yDjuDPtauMcuHQOEto66z46jYAwnWdxLjOX+asPc/TCJZ4a3gWALUfT6NgoDq9H5UxERKoWlQ4/VDpEykF+jrPgfO1zcHI7RNSE7uOg52Tn5HMB4Oj5Swz66yc0qx3NlAHJDOvWiIhQr9uxREREyoVKhx8qHSLlyFo4sto57Xz3W85zbe50pl4161vtp14VFPp4f+dJpq9IYduxdOrUCGN830TG9k0kNiLU7XgiIiLXRKXDD5UOkQBJOwrrZzqHDuakQf2OTvnocD+EVu9dnay1rEk5zwsrDrBq/zlW/vQG6sVGUOizmnYlIiKVlkqHHyodIgGWdwm2vwxrX4DTuyCqNnSfAD0nQWxDt9O57lRGDvWKttYdM2st8VFhTB2YTIdGcS4nExERKR2VDj9UOkQqiLVwcIVTPva+Cx4vtLvHGf1o3FNTrwp9PPn+Hl5ae4SsvEIGtKzD1IHJ9G9RB1PN/2xERKRyUOnwQ6VDxAXnDzpTrza9CLnp0LAr9P4OtB8KIeFup3NVenY+L609wuwvDnLmYi5/ua8Tw3s2cTuWiIjIt1Lp8EOlQ8RFuZmwdZEz+nFuH0TXdaZddZ8AMfXcTueq3IJC3tx8nNs71icmIpT3d5zkeFo2I3o2ITo8xO14IiIi31AtS4cxZihwBxALzLLWfni161Q6RIKAzwcpnzi7Xu37EDyh0GGYM/WqUTe30wWFn766jSUbjhIXGcqYPs0Y1zeRhJjqPSokIiLB5ZpKhzGmCTAfqAdYYLq19unSXlOKsLOBO4HT1toOV3xvMPA04AVmWmv/XIL7xQP/Y62ddLXvq3SIBJlzB2DddNi8EPIuQuNezoGD7e4Bb/XeVnbj4QtMX3GAD3edItTr4bGbW/Ld61u4HUtERAS49tLRAGhgrd1kjIkBNgJDrbW7SnlNXSDbWnvxsudaWGv3X/F+A4FMYP7lpcMY4wW+BG4BjgHrgZE4BeRPV8SeaK09XfS6vwELrbWbrvb7U+kQCVI5GbDlJVj3ApxPgZgG/zf1KrqO2+lclXImkxkrD9K3eW3u6tyQjJx89p3KpHuzeLejiYhINVau06uMMW8C/7LWflSaa4wxDwAPA0OstbnGmCnAMGvt7Vd5fSLw9hWl4zrgN9ba24q+/hmAtfbKwvHV9Qb4M/CRtfbfxWVV6RAJcj4f7P/ImXp1YDl4w6HjA87oR4NObqcLCjNWpPCHd3fTMzGeqQObc1Obunh03oeIiFSw4kpHqVciFpWBrsDa0l5jrX3FGJMELDHGvAJMxBm1KKlGwNHLvj4G9PZz/aPAzUBc0YjK81fkvAu4q0ULTU0QCWoeD7S6zXmc3uNMvdq6CLYsgGb9nPLR+g7wVt/F1aN6NyXEa5i58iBT5m+geUI0UwcmM7xHE223KyIirivVSIcxpgbwGfAHa+1r13DNYmAI0Nxae6aYaxL55kjH/cBga+3koq/HAL2ttY+U+DdxFRrpEKmEsi/A5gVOAUk7AnFNoOdk6DYWomq5nc41BYU+3tl+ghc+S6F2jTBenOT8u0xuQSHhIV6X04mISFVX3EiHpxQ3CAWW4qyNKK5MlOSaAUAH4HXg1yV9/yKpwOWb1Tcuek5EqpvIeOj7KHx/Czz4EsQnwr9/DU+1g2Xfh1O7vu0OVVKI18M9XRrxzvf7869Rzq5fx9Oy6f3Hj/n927s4npbtckIREamOSlQ6itZGzAJ2W2ufuoZrugLTgXuACUBtY8zvS5F3PdDSGJNkjAkDHgSWleL1IlLVeLzQ5g4Y/zZ8ZxV0egC2LYHnroN5d8Ged8FX6HbKCmeMIS7S2emr0GcZ1CqBOasOMfAvn/D4ki3sPpHhckIREalOSrp7VX9gJbAd8BU9/XNr7bvGmHeByUBycddcdp9+QIa1dnvR16HAeGvtjCvebxFwPVAHOAX82lo7q+h7Q4B/4OxYNdta+4fS/7b/k6ZXiVQxl87DpnmwbiZkHIOazaDXVOg6GiJrup3ONccuXGLW5wdZsv4oeQU+1v78JmrX0DkfIiJSfqrl4YAlpdIhUkUVFsCet53Tzo+sgtBo6DISek2DhFZup3NN2qU81h48z23t6wPwu7d30bVpTQa3r0+It8SzbkVERL5BpcMPlQ6RauD4FmfR+fZXoDAPmt/knHbe4mZnd6xqKjO3gLv/+TkpZ7NoUiuSyf2TeaBHY6LCqu9OYCIiUnYqHX6odIhUI5lnYONcWD8TMk9CrebOlrtdRkF4jNvpXFHos3y06xQvrDjA5iNpxEeF8sKYHvRKqr67gImISNmodPih0iFSDRXkwe5lzoGDx9ZDWIyz5qPXFKjd3O10rrDWsuHwBeZ+cYg/DutIXGQoW446JaRZ7Wi344mISCWg0uGHSodINXdso1M+dr4OvgJoeSv0eRiSb4BqfrDe0Ge/YNuxNG7v0ICpA5Pp3KSm25FERCSIqXT4odIhIgBcPAkbZjuPrDNQp7Uz9arzgxBWPf+l/1RGDnO+OMTCtYe5mFNAn+Ra/ODmVvROru12NBERCUIqHX6odIjIfyjIdUY91jwHJ7ZARJxz0nnPKRDfzO10rriYk8+S9UeZ9flBfnBLK4b3aEJOfiEeYwgLqb4L8UVE5D+pdPih0iEiV2UtHF0Ha5+DXcsAC62HOLteJfavllOv8gudY5hCvR5mfX6QGStSmNg/kZG9mhITEepyOhERcVtxpUN7IoqIFMcYaNrbeaSnwoZZsGGOc/ZH3fbO1KtOwyE00u2kFSb0snM82jeMJTkhmj++u4d/fryfUX2aMrFfEvViI1xMKCIiwUgjHWikQ0RKIT8btr/qLDw/tQMi46H7eOg5GeIau53OFduPpfPCigO8u/0E1zWvzcLJfdyOJCIiLtH0Kj9UOkSk1KyFw1845WPPO4CBtnc5U6+a9qmWU6+OnLtEVl4BbRvEciojh/9+YweT+ifRK6kWphr+eYiIVEeaXiUiUp6McdZ1JPaHC4edwwY3zYNdb0CDzk75aD8MQqvPVKOmtaO+/vX+05lsOHyBD3edokuTmjw8KJlb2tXH61H5EBGpjjTSgUY6RKSc5GXBtiWw9gU4swei6kCPic4jtoHb6Spcdl4hr246xowVKRw5f4nmCdG88/0BRIR63Y4mIiIBoulVfqh0iEi5shYOfgZrnocv3wePF9rf64x+NP7G38NVXqHP8sHOk+w5eZHHb2kFwJtbUhnYMoH46DCX04mISHlS6fBDpUNEAuZ8CqybAZsXQG4GNOoOvb8D7e6BkOr5A3dqWjb9n1xORIiXET2bMKl/Ek1qRX37C0VEJOipdPih0iEiAZd7EbYudhaen9sPNepBj0nQYwLUqOt2ugq39+RFpq9IYdnWVHwWhnRswM9ub0PDmtVn+2ERkapIpcMPlQ4RqTA+HxxY7pSP/R+BNww63OdMvWrYxe10Fe5EejZzvjjE65tT+fCxgcRHh3EuM5da0WHa8UpEpBJS6fBDpUNEXHF2H6ybDltegrxMaNLHOXCw7V3grV6ne+cX+gj1erDWMvTZL8grtEwbmMwdnRr8x4GEIiIS3FQ6/FDpEBFX5aTD5oWw7gW4cAhiG0HPSdBtPETXdjtdhfL5LEs3HWP6ihT2nc6kUc1IJvZP4sGeTYgO1y7vIiLBTqXDD5UOEQkKvkLY96Ez9SrlUwiJgI4POFOv6ndwO12F8vksn+w9zQsrUlh38Dx/vLcjo3o3dTuWiIh8C5UOP1Q6RCTonN7tnPexdTEUZEOz/tDnYWg9xNmCtxrZfOQCbRvEEhHqZfG6I2w5msaUgck0T6jhdjQREbmCSocfKh0iErQunXe22103A9KPQFxT6DUFuo2ByHi301W4Zz7ex78+2U9+oY9b2tZj2qBkujer5XYsEREpotLhh0qHiAS9wgL48j3nwMHDn0NoFHQa4Uy9qtvG7XQV6szFXOavPsT81YdJz85nTJ9m/G5o9Zp+JiISrFQ6/FDpEJFK5eR2Z93HtlegMBeSr3cOHGx5K3iqz05Pl/IKeHn9UZITajCwVQLnMnP5aNcphnZtRERo9ZqCJiISLFQ6/FDpEJFKKescbJoL62bCxeMQn+RsudtlFETEuZ2uws1bdYhfL9tJQkw44/smMrp3M+KiqtfWwyIiblPp8EOlQ0QqtcJ82P2Ws/D86BoIq+EUj17ToE4Lt9NVGGstqw6c4/nPDrBy31miw7yM6t2Unw9pq4MGRUQqiEqHHyodIlJlHN/slI8dS6EwD1rc4qz7aH5jtZp6tfN4OjNWpJBX6ON/H+oOQGpaNo1qRrqcTESkalPp8EOlQ0SqnMzTsGEObJgFmaegdktn6lXnkRBefbaa9fksHo/h4Nksbvrbp/RvmcDDA5O5rnltjX6IiASASocfKh0iUmUV5MGuN2DNc3B8E4THQtcxzra7tZLcTldh0rPzWbDmMHO+OMTZzFw6Nopj6sBkbu9QnxBv9RkBEhEJNJUOP1Q6RKRaOLbBKR+73nBOP299uzP6kTQIqsm/+ufkF/L65lRmrEjhWFo2X/z0RhJiwt2OJSJSZah0+KHSISLVSsYJZ9rVhjlw6SwktHXKR6cREBbldroK4fNZdp/MoH1DZ5evKfM30LZBLOOua0btGiohIiJlpdLhh0qHiFRL+Tmw8zVn9OPkNoioCd3GOlOvajZ1O12Fyc4r5PuLN/PRrlOEh3h4oEdjJvdPJrFOtNvRREQqHZUOP1Q6RKRasxaOrHEOHNz9FmChzR3OgYPN+labqVf7T2cyc2UKr21KJd/nY+bYHtzUtp7bsUREKhWVDj9UOkREiqQddaZebZwL2RegXkdn6lXHByA0wu10FeJ0Rg4L1h7h4UHJRIWF8O9dp8gr9HFb+/p4PdWjgImIlJVKhx8qHSIiV8jPhm0vO6Mfp3dBVG3oPh56TIK4Rm6nq1AT5qzjk71naFIrkkn9knigRxOiw0PcjiUiEpRUOvxQ6RARKYa1cGilc+DgnnfAeKDdPc6Bg016VYupV4U+y0e7TjFjZQobD18gNiKEJ25vy6je1Wfdi4hISRVXOvRPNSIiUjxjIGmg87hwCNbNgE0vOgvQG3Z1ykf7eyGk6u745PUYBneoz+AO9dl05AIzV6YQFxkKQPqlfI6nZ9O2QazLKUVEgptGOtBIh4hIqeRmwrYlzujH2b0QXRd6THQeMdVr4fWzn+znrx/sZUDLOkwekMzAlnV00rmIVGuaXuWHSoeISBlYCymfwJrnYd8H4Al1Rj36PAyNurudrkKkXcpj4dojzFt1iNMXc2ldL4YpA5O5v3tjt6OJiLhCpcMPlQ4RkWt07oAz9WrzAsi7CI17OlOv2t0D3lC30wVcbkEhb209wcyVKTSIi2DOhF6AcwJ6RKjX5XQiIhVHpcMPlQ4RkXKSkwFbFzlTr84fgJgG0HMSdJ8A0XXcThdw1loycgqIiwzl6PlLDHl6JcO6NWJi/ySa1dZhgyJS9al0+KHSISJSznw+2P9vZ8vdAx+DNxw63u+c+dGgs9vpKsSxC5f4+0f7WLY1lUKf5bb29Zk8IJnuzeLdjiYiEjAqHX6odIiIBNCZvbBuOmxZBPlZ0LSvUz7a3Aneqr+J4qmMHOatOsSCNYfJzi9k9c9uok6Nqrvbl4hUbyodfqh0iIhUgOw0Z83HuumQdhhiG0OvydBtHETVcjtdwGXlFrDpyAUGtEwA4EevbKVjozge6NGYqLCqX75EpHpQ6fBDpUNEpAL5CuHL952pVwdXQEgkdBrujH7Ua+92ugqRlVvAmFlr2XQkjbjIUEb3acq46xKpGxvhdjQRkWui0uGHSoeIiEtO7XLKx7YlUJDjHELY+2FoNRg8VX/Xp42HzzNjxUE+2HWSUI+HGeN6MKhVgtuxRETKTKXDD5UOERGXXToPm+bBupmQcQxqNoNeU6HraIis6Xa6gDt0Not5qw/x+C2tiIkIZeW+MwD0b6HDBkWkclHp8EOlQ0QkSBQWwN53nAMHj6yC0GjoMhJ6TYOEVm6nqzAPzVzDF/vP0aZ+DFMGJHNX54aEhXjcjiUi8q1UOvxQ6RARCUIntsLa6bD9FSjMheY3Qu/vQIubwVO1fwDPLSjkzS3HmbkyhS9PZVIvNpyfDm7DsG466VxEgptKhx8qHSIiQSzrLGycA+tnwcUTUCvZGfnoMgoiYt1OF1DWWlbsO8uMFSnc370xQ7s24mJOPmmX8mlSK8rteCIi36DS4YdKh4hIJVCYD7vedE47P7YOwmKg60PO2o/azd1OF3DWWowxvPDZAZ58fw+3d2jA5AFJdG2qwwZFJHiodPih0iEiUsmkbnTKx47XwFcALW91ttxtfiNU8YXXJ9NzmLvqEAvXHuZiTgE9msUzZWAyt7Wv73Y0ERGVDn9UOkREKqmLp2DDbOeRdRrqtIbeU6HTgxBew+10AZWZW8DL648y+4uDJNaOZsHk3gAUFPoI8VbtNS8iErxUOvxQ6RARqeQKcmHn67DmOTixBcLjoNsY6DUF4hPdThdQBYU+zl/Ko25MBMfTsrn7X1/wYM8mjO3bjLoxOmxQRCqWSocfKh0iIlWEtXBsvVM+dr0J1geth0CfhyFxQJWfenXobBZ/fHc3H+0+RajHw9CuDZk8IJlW9WLcjiYi1YRKhx8qHSIiVVB6qjPtauMcuHQO6rZ31n10fADCqvbOTwfPZjH784O8svEoBYWWtT+/ido1wt2OJSLVgEqHHyodIiJVWH427FjqHDh4ajtExkO3cc7Uq7iqfe7F+aw81h08x+AODQD4zbKddGocx52ddNigiASGSocfKh0iItWAtXB4Fax9Hva8DRhoeyf0fhiaXlflp15l5RYw9Nkv2Hc6k/qxEYzvl8jIXk2Jiwx1O5qIVCEqHX6odIiIVDNpR2D9TNg4D3LSoH4np3x0uA9Cq+7ia5/P8tm+M8xYkcKqA+eIDvMyfWwP+rWo43Y0EakiVDr8UOkQEamm8i7BtiXOmR9ndkNUHegxAXpMhNiGbqcLqB2p6cxbdYhf3tGOuKhQ1h08T1iIhy5NarodTUQqMZUOP1Q6RESqOWvh4Apn6tXe98B4oM0Qp3wkXQ+eqr/+4cHpq1mTcp5eibWYPCCJm9vWw+Op2lPORKT8VcvSYYwZCtwBxAKzrLUfXu06lQ4REfna+YPOjlebFzi7XtVKhu4ToMtDEF3b7XQBk5lbwJL1R5n9+UFS07JJqhPNj29rzZCODdyOJiKVSHGlo9z+6cYY08QY84kxZpcxZqcx5r+u4V6zjTGnjTE7rvK9wcaYvcaY/caYJ/zdx1r7hrV2CvAwMKKseUREpBqplQS3/BYe3w3DZkKN+vDRf8NTbWDpFDiyxhkZqWJqhIcwqX8Sn/34ev45siuxESFk5hQAcCmvgDMXc11OKCKVWbmNdBhjGgANrLWbjDExwEZgqLV212XX1AWyrbUXL3uuhbV2/xX3GghkAvOttR0ue94LfAncAhwD1gMjAS/wpysiTbTWni563d+AhdbaTVfLrpEOERHx6/Ru58yPrYshNwPqtnOmXnUaARGxbqcLCGst1oLHY5j1+UGefH8Pw7o2YvKAJFrU1WGDInJ1FT69yhjzJvAva+1Hlz33AM6owxBrba4xZgowzFp7+1Venwi8fUXpuA74jbX2tqKvfwZgrb2ycHx1vQH+DHxkrf33Vb5/F3BXixYtpuzbt6/sv1kREake8rKcMz/Wz4ITWyA0Gjre7xSQhl3cThcwB89mMXNlCq9uPEZugY8bWicwZWAyfZtr1ysR+U8VWjqKCsMKoIO1NuOK7/0E6Au8AjwC3GKtzSzmHleWjvuBwdbayUVfjwF6W2sfKSbH94FxOCMiW6y1z1/tOo10iIhIqaVuckY/tr8KBdnQsBv0nATth1XZE8/PZeayYM0R5q8+RIu6NVgy7TrAGRUxVfycExEpmQorHcaYGsBnwB+sta8Vc81iYAjQ3Fp7pphrErnG0lFSKh0iIlJm2WnOtrsbZsOZPRAeB11GOqMfCa3dThcQOfmFnM3MpXF8FKczcnjghdWM6tWUkb2bEhuhwwZFqrOALyQvepNQYCnO+oniCscAoAPwOvDrUr5FKtDksq8bFz0nIiLijsia0HsafHcNTHgPWt7iTL96thfMuaNoJKRqLcKOCPXSON4ZzcnIyadhXCR/em8Pff+0nN+9vYtjFy65nFBEgk15LiQ3wDzgvLX2sWKu6Qq8BNwJHAQWAgestb+8yrWJfHOkIwRnIflNOGVjPTDKWrvzWrJrpENERMpV5hnYstDZevfCIefQwW5joPt4iE90OVxg7EhNZ8bKFN7edgKvMaz5+U3Uig5zO5aIVLCAT68yxvQHVgLbAV/R0z+31r572TX9gAxr7fair0OB8dbaGVfcaxFwPVAHOAX82lo7q+h7Q4B/4OxYNdta+4drza7SISIiAeHzQcpy2DAH9r7rbLXb4mZn6lXLW8Eb4nbCcnc8LZvVB85xX/fGAPzPB3vp0qQmN7apq8MGRaqBank4YEmpdIiISMClp8Km+bBpHlw8AbGNoNs46DYWYqvmAXyZuQXc9vcVpKZlk5wQzaT+SdzXrTERoV63o4lIgKh0+KHSISIiFaawAL58HzbMggPLwXihzRBn9CPpevCU63JL1+UX+nh3+wlmrjzI9tR0akWH8b8PdaNPctU93V2kOlPp8EOlQ0REXHE+BTbOhc0L4NI5qJUM3SdAl4cgumr9UG6tZe3B88z94hB/GtaR+Ogwth5NIzo8hBZ1a7gdT0TKiUqHHyodIiLiqoJc2LXM2Xb3yCrwhkP7oc7oR5PeUEXPwBj+wmrWHTzPTW3qMnlAMn2Sa+m8D5FKTqXDD5UOEREJGqd3O+Vj62LIzYC67Zzy0WkERMS6na5cnc3M5cXVh3lxzWHOZ+XRoVEsP7ylNTe0qet2NBEpI5UOP1Q6REQk6ORlOWd8bJgFJ7ZCaDR0vN8pIA27uJ2uXOXkF/LaplRmrkxh0oAkHurdjJz8QvILfcTosEGRSkWlww+VDhERCWqpm5zRj+2vQkE2NOrulI/2wyAsyu105cbnsxRaS6jXw/zVh/jr+3t5sFcTJvRLomHNSLfjiUgJqHT4odIhIiKVQnYabFviFJAzeyA8DrqMdApIQmu305WrXcczeP6zA7yz/QQAd3ZqwJQByXRoFOdyMhHxR6XDD5UOERGpVKyFw6uc8rHrTfDlQ7P+0GMCtL0bQqrOSeDHLlxi7heHWLz+KK3q1eC17/ZzO5KI+KHS4YdKh4iIVFqZZ2DLQtg4By4cgugE6Doauo+H+ESXw5WfjJx8zlzMpXlCDc5m5jJu9jpG92nGvV0b6bBBkSCi0uGHSoeIiFR6Ph+kLIcNc2Dvu85oSIubnalXLW8Fb4jbCcvN7hMZ/PjVrexIzaB2dBhjr0tkdJ+m1K4R7nY0kWpPpcMPlQ4REalS0lNh03zYNA8unoDYRtBtHHQbC7EN3E5XLqy1rE45x8yVB1m+5zSRoV5WPXEj8dFVZ2qZSGWk0uGHSoeIiFRJhQXw5XvO2o8Dy8F4oc0QZ/Qj6XrweNxOWC72n77IqgPnGHtdIgDPf3aArk1q0itJhw2KVLTiSkfVGWsVERGR/+QNgbZ3OY/zKbBxLmxeALvfglrJ0H0CdHkIomu7nfSatKgbQ4u6MQBk5hYwc2UKZzPz6Nw4jskDkrm9Q31CvFWjYIlUVhrpQCMdIiJSjRTkwq5lzqGDR1aDNxzaD3VGP5r0hiowMpCdV8jSTceY9flBDp7NolHNSJ4Z2YXuzWq5HU2kytP0Kj9UOkREpFo6tcvZ9WrrYsjNgLrtnPLRaQRExLqd7pr5fJZ/7z7FvNWH+MeIriTEhLPnZAaxEaE6bFAkQFQ6/FDpEBGRai0vyzntfMMsOLEVQqOh4/1OAWnYxe105WrEC6vZePgCd3ZqwGQdNihS7lQ6/FDpEBERKZK6ySkf25dCQTY06u6Uj/bDICzK7XTX7NiFS8z54hCL1x0hK6+Qvs1r8+iNLbmueeVe1yISLFQ6/FDpEBERuUJ2Gmxb4ux8dWYPhMdBl5FOAUlo7Xa6a5aenc/idUeY88UhHh6UzPh+SeQV+PBZq8MGRa6BSocfKh0iIiLFsBYOr3LKx643wZcPzfpDjwnQ9m4IqdznYuQV+LBYwkO8LFp3hL99uLfosMFm1NKZHyKlptLhh0qHiIhICWSegS0LnFPP0w5DdAJ0HQ3dx0N8otvprtnGwxf45/J9fLr3DBGhHu7v3phJ/ZNJqhPtdjSRSkOlww+VDhERkVLw+SBluVM+9r7rjIa0uNmZetXyVud8kEps36mLzFx5kNc3p9K2YSxvfq+f25FEKg2VDj9UOkRERMooPRU2zYdN8+DiCYht5Ix8dB0DsQ3cTndNzlzM5WxmLm0bxJJ2KY+HF2xkdJ9mDG6vwwZFiqPS4YdKh4iIyDUqLIAv33PWfhxYDsYLbYY4ox9J14Oncv+Qvv1YOo8u2sShc5doHB/JxH5JDO/ZhBrhlXtUR6S8qXT4odIhIiJSjs4dgI1zYfMCyD4PtZKh+wTo8hBEV96taQuLDhucsSKFDYcvEBcZymc/vp6aUVpwLvIVlQ4/VDpEREQCoCAXdi1zzv04shq84dB+qDP60aQ3GON2wjLbfOQCq1PO8d3rWwDw4upDdG9Wi3YNK/9J7iLXQqXDD5UOERGRADu1CzbOga2LITcD6rZ3tt3tNAIiKvcP6hdz8un75+VczCmgf4s6TB6QxKBWCZhKXKpEykqlww+VDhERkQqSmwk7ljqjHye2Qmg0dLzfGf1o2MXtdGWWfimfl9YdYe6qg5zKyKVVvRr89f7OdG5S0+1oIhVKpcMPlQ4REREXpG5yysf2pVCQDY26O+Wj/TAIi3I7XZnkFfh4a+tx5q0+xPQxPagfF0HKmUzio8KI12GDUg2odPih0iEiIuKi7DTYtgTWz4KzeyEiDjqPcqZfJbR2O901Gzl9DVuOphUdNphEog4blCpMpcMPlQ4REZEgYC0cXuVsu7vrTfDlQ7P+TvloezeEVM6Rgr0nLzJzZQpvbjlOvs/HLW3r8d0bWtBFU6+kClLp8EOlQ0REJMhknoEtC5xTz9MOQ3QCdB3tHDwYn+h2ujI5nZHDvNWHWLDmCI/c0IIpA5MpKPRhjMHr0aJzqRpUOvxQ6RAREQlSPh+kLIf1s53DB62FFjc7az9a3greync436W8AgyGyDAvr248xtMff8mkfkk80KMJ0TpsUCo5lQ4/VDpEREQqgfRU2DQfNs2DiycgtpEz8tF1DMQ2cDtdmXyx/yxPffQlGw9fIDYihIf6NGN830TqxUa4HU2kTFQ6/FDpEBERqUQKC5xRjw2z4cByMF5oMwR6TIKkQeDxuJ2w1DYevsDMlSl8sPMkHRvF8eYj/d2OJFImKh1+qHSIiIhUUucOwMa5sHkBZJ+HWsnQfQJ0eQiia7udrtSOnLvEuaxcujaNJz07nx++vJWx1zVjQMs6OmxQKgWVDj9UOkRERCq5/BzY/ZZz7seR1eANh/ZDnbUfTXpDJfyBffORC0x7cSOnL+bSpn4Mvx/agR6JtdyOJeKXSocfKh0iIiJVyKldsHEObF0MuRlQt72z7W6nERAR63a6UsktKGTZluP8c/l+zlzMZdb4HvRtXsftWCLFUunwQ6VDRESkCsrNhB1LndGPE1shNBo63u+MfjTs4na6UjlzMZeHZq6hZb0Ynh3Vze04IsVS6fBDpUNERKSKS93oLDzfvhQKsqFRd6d8tB8GYVFupyuRC1l5RIV7CQ/x4vNZPDrbQ4JQcaWj8m3vICIiIlJajbrDPc/CD/fA7X9xRkHe/B481QbeewLO7HU74beKjw4jPMRL2qU8hj23iuV7TrkdSaTEVDpERESk+oisCb2nwffWwvh3ocUtsH4mPNsL5twB21+Fgjy3U/plMPisZdqLG/lw50m344iUiKZXoelVIiIi1VrmGdiyADbMgbTDEJ0AXUc7Bw/GJ7qd7qrSs/MZN3sdO1LT+efIrtzesXIejihVj9Z0+KHSISIiIvh8kLIc1s92Dh+0Flrc7Kz9aHkreEPcTvgfLubkM37OerYcTeP50d25pV09tyOJFFs6gut/PSIiIiJu8XicktHiZkhPhU3zYdM8WDwSYhs5Ix9dx0BscIwqxESEMm9iL371xg46NKpcWwFL9aORDjTSISIiIsUozIcv33d2vjqwHIwX2gyBHpMgaZBTVIJEoc+y4dB5eidXvpPYperQ7lUiIiIipeUNhbZ3wZjX4dFNcN334NAX8OJQ+Fd3+OIZyDrndkoA5nxxkAdnrOHl9UfdjiLyDSodIiIiIiVRuznc+jt4fDcMmwE16sFH/w1PtYXXpsKRNc46EJeM7tOMAS0T+MnSbby09ohrOUSuRtOr0PQqERERKaNTu2DjHNi6GHIzoG576DEBOo2AiIpfZ5GTX8h3F25i+Z7T/Pae9oy9LrHCM0j1pt2r/FDpEBERkWuSmwk7lsKGWXBiK4RGQ8f7oeckaNC5YqMUFPK9hZv5Yv9ZPvvx9dSNjajQ95fqTaXDD5UOERERKTepG52F59uXQkG2cxp6j4nQfhiERVVIhLwCH1+eukiHRnEV8n4iX1Hp8EOlQ0RERMpddhpsWwLrZ8HZvRARB51HOdOvElpXWIyFaw+TkV3Ad65vXmHvKdWXzukQERERqUiRNaH3NOg1FQ6vckY/1s+Etc9B4gCnfLS5C0LCAhbBWsv6g+d5Y8txCgp9PHpTy4C9l4g/Kh0iIiIigWQMJPZzHpl/hi0LYMMceHUiRCdA19HOwYPxiQF4a8PfhnfBYwx/++hLCnyWx25uiTGm3N9LxB9Nr0LTq0RERKSC+XzOYYMbZsOX7zlb7ba42Vn70eo28HjL9e0KfZYnlm7jlY3H+N4NzfnxbW3K9f4iX9H0KhEREZFg4fFAy5udR3oqbJoPm+bB4pEQ2xi6j4OuYyC2Qbm8nddjePK+ToR4PdSMDNx0LpHiaKQDjXSIiIhIECjMhy/fdxaep3wCxgtthkCPSZA0yCkq18ha+/XUqqPnL9E4PlJTraRcFTfSoRPJRURERIKBNxTa3gVj34BHN8F134NDX8CLQ+Ff3WHfR9f8FpcXjiFPr+T/vbUL/QO0VASVDhEREZFgU7s53Po7eHw3DJsJIRHw0gjYvKBcbt84PpIRPZswd9UhfvnGDnw+FQ8JLK3pEBEREQlWoRHQ6QFoPRiWjIE3vweZp6D/486uWGVkjOEXd7QlxOvh+c8OUOiz/PHejng8mmolgaGRDhEREZFgFx4Do16Gjg/Ax7+F937q7IB1DYwx/HRwax69sQWL1x9l4boj5RRW5Js00iEiIiJSGYSEwb3TIbourHkWsk7DvS9ASHiZb2mM4Ye3tqZVvRgGd6hfjmFF/pNGOkREREQqC48HBv8Rbvkd7HwdFt4PORnXfNu7Ojck1OvhbGYuT76/h4LCaxtFEbmSSoeIiIhIZdPv+84ox+FVMHcIXDxVLrddvvs0z316gO8v3ky+ioeUI5UOERERkcqo84MwcgmcS4FZt8C5A9d8y+E9m/DLO9ry7vaTPPLSJvIKVDykfKh0iIiIiFRWLW+GcW9BXibMuhVSN13zLScPSOY3d7Xjg52n+O7CjeQWFJZDUKnuVDpEREREKrPG3WHihxAWBXPvhP0fX/Mtx/dL4vdDO3DwbBYXcwrKIaRUdyodIiIiIpVdnRYw6SOolQwvDYdtL1/zLUf3acY73x9AnRrhFBT6yMnXiIeUXZUtHcaYocaYGcaYJcaYW93OIyIiIhJQMfVhwjvQ9Dp4bQqs+uc13zIi1Iu1lh++spWJc9eTnafiIWVTotJhjJltjDltjNnh55ofGGN2GmN2GGMWGWMiyhLI33sZYwYbY/YaY/YbY57wdx9r7RvW2inAw8CIsmQRERERqVQi4mD0Umg3FD78JXzwi3I5RHBQqwTWpJxj/Jx1ZOVqupWUXklHOuYCg4v7pjGmEfB9oIe1tgPgBR684pq6xpiYK55rUdL3MsZ4gWeB24F2wEhjTDtjTEdjzNtXPOpe9tJfFr1OREREpOoLCYf7Z0OvqbD6X/D6NCjIu6ZbDuvWmL+P6ML6Q+cZP2cdmSoeUkolKh3W2hXA+W+5LASINMaEAFHA8Su+Pwh4wxgTDmCMmQJ8Y9zPz3v1AvZba1OstXnAYuAea+12a+2dVzxOG8eTwHvW2qtu5WCMucsYMz09Pf1bfmsiIiIilYjHC7f/BW78b9j+MiwaAbmZ13TLe7o04p8ju7HpSBrfWbARa205hZXqIKQ8bmKtTTXG/A9wBMgGPrTWfnjFNa8YY5KAJcaYV4CJwC2leJtGwNHLvj4G9PZz/aPAzUCcMaaFtfb5q+R+C3irR48eU0qRQ0RERCT4GQMDfwQ16sFb/wXz7oRRr0CNhDLf8o5ODfB6DLWiwzDGlGNYqerKZSG5MSYeuAdIAhoC0caY0VdeZ639C5ADPAfcba29tsrth7X2GWttd2vtw1crHCIiIiLVQrcx8OBLcHoPzL4Vzh+8ptsN7lCfXkm1AHhjcyppl65t6pZUD+W1e9XNwEFr7RlrbT7wGtD3youMMQOADsDrwK9L+R6pQJPLvm5c9JyIiIiI+NN6MIxbBtkXnEMET2y95lseT8vmJ0u3MWrGWs5nqXiIf+VVOo4AfYwxUcYZa7sJ2H35BcaYrsB0nBGRCUBtY8zvS/Ee64GWxpgkY0wYzkL1ZeWSXkRERKSqa9ILJn4A3jCYcwekfHZNt2tYM5IZY3tw4Ewmo2as4WxmbjkFlaqopFvmLgJWA62NMceMMZOKnn/XGNPQWrsWeBXYBGwvuu/0K24TBQy31h6w1vqAscDhkr6XtbYAeAT4AKfQvGyt3Vnq37GIiIhIdZXQGiZ9CHGNYcF9sGPpNd1uUKsEZo3ryaFzWYycvoYzF1U85OqMdh6AHj162A0bNrgdQ0RERKRiZF+ARSPhyBq4/UnoPe2abrf6wDkmzVvP7+7pwH3dG5dTSKmMjDEbrbU9vvG8SodKh4iIiFRD+dmwdDLseRv6Pw43/crZ8aqMTmfkUDfWORva57N4PNrdqjoqrnSU15oOEREREalMQiNh+HzoPgE+fwre/B4U5pf5dl8VjvWHznPHPz8nNS27vJJKFaDSISIiIlJdebxw59/h+p/BloWweBTkZV3TLUM8hmMXLjHihdUcPX+pnIJKZafSISIiIlKdGQPXPwF3PAX7/w3z7oZL58t8u65N41k4uTcXcwp4cPoaDp+7thIjVYNKh4iIiIhAz0nOdKuT252zPNKOlPlWnRrXZOHk3mTlFTDihTWcSNdUq+pOpUNEREREHG3vgrFvQNZpp3icKvvpBB0axbFoSh9ubleXhBrh5ZdRKiWVDhERERH5P836woT3nV/Pvh0OfVHmW7VtEMvvh3YkxOvhVEYO+09fLKeQUtmodIiIiIjIf6rXzjlEMKYevHgv7Fp2zbd8bPEWRrywhr0nVTyqI5UOEREREfmmmk1h4gfQoBO8Mg7Wz7qm2/3h3g6EeA0PTl/NruMZ5RRSKguVDhERERG5uqhaMHYZtLwV3nkcPvkjlPFg6eSEGiyZeh2RoV5GzVzDjtT0cg4rwUylQ0RERESKFxYFIxZCl9Hw2ZPw9mNQWFCmWyXWiWbJtOuIDgvht2/twpaxwEjlE+J2ABEREREJct4QuOdfzhqPlX+DrLNw30znVPNSalIriiXT+hAR6sUYE4CwEow00iEiIiIi384YuOlXcPtfYM87zgLz7AtlulXj+Cjq1Agnv9DH40u2sP5Q2Q8jlMpBpUNERERESq73NLh/NqRudLbUTU8t863Ss/PZcjSNcbPXsTblXDmGlGCj0iEiIiIipdNhGIxeCunHnEMEz+wt023q1Ahn8dQ+NKwZyfg561m1/2w5B5VgodIhIiIiIqWXNBAmvAu+fKd4HFlbptvUjY1g0ZQ+NK0VxYS561m570w5B5VgoNIhIiIiImXToJNziGBUbZh/D+x9r0y3SYgJ56UpvencuCYxEaHlHFKCgUqHiIiIiJRdfKJTPOq2hcUPwab5ZbpN7RrhLJnWhy5NagJw+FxW+WUU16l0iIiIiMi1ia4D496C5Oth2aOw4q9lOkTwqy10X9t0jJuf+owPdp4s56DiFpUOEREREbl24TVg5GLoNAKW/x7e/TH4Cst0q5va1qN9wzi+t3AT720/Uc5BxQ0qHSIiIiJSPkLCYOjz0PdRWD8DXp0A+Tmlvk1cZCgvTupF5yY1eWTRZt7aejwAYaUiqXSIiIiISPnxeODW38Otf4Bdb8LC+yEnvdS3iYkIZd7EXnRvGs8PlmzhyLlLAQgrFSXE7QAiIiIiUgX1fQRq1IU3vgNz7oDRr0JM/VLdokZ4CHMn9mTlvrM0rR0VoKBSETTSISIiIiKB0Wk4jHoZzqfArFvg7P5S3yIqLITb2jtlZdX+s7y84Wh5p5QKoNIhIiIiIoHT4iYY/zbkXYLZt8KxjWW+1fzVh/nJq9tYuPZwOQaUiqDSISIiIiKB1aibc5ZHWA2Ydyfs+6hMt/nHg124sU1dfvH6DuavPlS+GSWgVDpEREREJPBqN4dJHzn/uehB2LKo1LeICPXy3Ohu3NKuHr96cyezPz8YgKASCCodIiIiIlIxYurB+HehWV9442H44ulSHyIYHuLl2VHdGNy+PjuOp2PLcAihVDztXiUiIiIiFSciFh56FV5/GD76FVw85Wyx6yn5v4WHhXj456iueIzBGMPFnHxiIkIDGFqulUY6RERERKRihYTDfbOg98Ow5ll4bQoU5JXqFqFeD16P4WxmLnc88znPfLwvQGGlPGikQ0REREQqnscDg/8MNerBx/8PLp2FEQsgPKZUt4mPCqNHYjxPffQlBT7LD25uiTEmQKGlrFQ6RERERMQdxsCAx53isexRmHsnPPSKc6hgCXk9hr/e35kQj+GZj/dR6PPxo1tbq3gEGU2vEhERERF3dX0IRi6Gs1/CrFudwwRLwesx/HlYJ0b2asqznxxg3qpDgckpZabSISIiIiLua3UrjF0GOWlO8Ti+pVQv93gMfxjagZ8ObsM9XRoFJKKUnUqHiIiIiASHJj1h4ocQEgFz74ADn5Tq5R6P4TvXNyc+OozcgkLe33EyQEGltFQ6RERERCR4JLRyDhGs2QwWPgDbXy3TbWZ/foiHF2zkjc2p5RxQykKlQ0RERESCS2wDmPAuNOkFSyfB6v8t9S0m9U+iV1ItfrJ0GxsPXwhASCkNlQ4RERERCT6RNWH0a9D2LvjgZ/DRr0t1enlYiIfnR3enfmwE017cwLELlwKXVb6VSoeIiIiIBKfQCHhgHvSYCF/8A974DhTml/jltaLDmD2+B7kFPh5fshVbitIi5UvndIiIiIhI8PJ44Y6nIKYBfPIHyDoLw+dBWHSJXt6ibgwvjOlO3Zhwnd3hIo10iIiIiEhwMwYG/QTuehoOfAzz7oKscyV+ed/mdWhRNwZrLWtTSv46KT8qHSIiIiJSOXQfDyMWwKmdMPtWuHC4VC9ftvU4I6av4eUNRwOTT4ql0iEiIiIilUebO2DMG5B1xjlE8OSOEr/0jo4N6N+iDr94fTtrNOJRoVQ6RERERKRyaXYdTPzAWe8x53Y4uLJELwvxenj2oW40qRXFdxZs5PC5rAAHla+odIiIiIhI5VO3LUz60FlgvmAY7HyjRC+Liwxl9rieWGDq/I0UFPoCGlMcKh0iIiIiUjnFNYaJ70PDrvDKeFg3o0QvS6wTzXMPdecng1sT4tWPwxVBf8oiIiIiUnlF1XLWeLQaDO/+CJb/vkSHCF7XvDY3ta0HwP7TFwMcUlQ6RERERKRyC4tydrXqOgZW/BXe+j4UFpTopesPnefWv6/gxTWl2wlLSkeHA4qIiIhI5ecNgbv/CTH1neKRdRbunw2hkX5f1q1pPDe0rstvlu0ksXYUA1omVFDg6kUjHSIiIiJSNRgDN/4ShvwP7H0PFj8EBbl+X+L1GJ4e2ZWWdWvw3YWb2H86s4LCVi8qHSIiIiJStfSa4ox6HPgYXpkAhfl+L68RHsLMcT0ID/Ewad56Lub4v15KT6VDRERERKqebmOKRjzegdenga/Q7+WN46N4YUx3RvVqSo1wrUAob/oTFREREZGqqdcUyL8EH/0KQiLg7n+Bp/h/c+/erBbdm9UC4HRGDgkx4RhjKiptlaaRDhERERGpuvr9Fwx6ArYshPd+XKLtdA+ezeLmpz5j1ucHKyBg9aCRDhERERGp2q5/whnxWPWMs5vVLb9zFp0Xo1mtKPq1qMMf3t1NUp3or8/zkLLTSIeIiIiIVG3GwC2/hZ5TYNU/4dM/+73c4zH8bXhn2jeM5fuLNrPnZEYFBa26VDpEREREpOozBm7/C3QZDZ/9GT7/h9/Lo8JCmDm2JzUiQpg0dwNnM/1vvSv+aXqViIiIiFQPHg/c/QwUZMO/fw2hUdB7arGX14+LYObYnry45pB2tLpG+tMTERERkerD44V7X4D8HGdheWiks71uMTo2juMv93cGICu3gKgwr3a0KgNNrxIRERGR6sUbCg/MgeY3wbJHYfur3/qSC1l53P2vz/nfTw9UQMCqR6VDRERERKqfkHAYsQCa9YPXpsLut/xeXjMqlI6N4vjrB3t5b/uJCgpZdah0iIiIiEj1FBYFoxZDo27wygTY9+9iLzXG8Of7OtG1aU1+8PIWdqSmV2DQyk+lQ0RERESqr/AYeOhVqNsWljwEB1cWe2lEqJfpY3pQOzqcSfPWcyojpwKDVm4qHSIiIiJSvUXWhDFvQHwivDQCjq4r9tKEmHBmjutBUp3oikpXJah0iIiIiIhE14axb0JMPVhwHxzfUuylbRvEsmhKH+rFRlDos/h8tuJyVlIqHSIiIiIiADH1YewyiKgJL94Lp3YVe6kxhtyCQibPW88//v1lxWWspFQ6RERERES+UrMJjHvT2d1q/j1wdn+xl4Z5PdSNieCZ5ft5c0tqBYasfFQ6REREREQuVyvZmWplfTD/brhw+KqXGWP43dAO9E6qxY9f3cbGwxcqOGjlodIhIiIiInKlhNYw9g3Iy4J5d0HG8ateFhbi4fnR3WkQF8G0Fzdw7MKlis1ZSah0iIiIiIhcTf2OMPo1uHQe5t0Nmaevell8dBizxvUkLjKUtEv5FRyyclDpEBEREREpTuPu8NArkJEK84c6BeQqWtStwYc/GESHRnEAWKsdrS6n0iEiIiIi4k+z6+DBl+DcflgwDHKufhq512Ow1vKn93bzp/f2VHDI4KbSISIiIiLybZrfAMPnw8ntsHC4s9bjKowxXMotZPqKFJasP1LBIYOXSoeIiIiISEm0Hgz3zYRj62DRSMjPueplv76rHQNa1uEXr+9gTcq5Cg4ZnFQ6RERERERKqv29MPQ5OLgCXh4LBXnfuCTE6+Ffo7rRrHYUDy/YyKGzVx8VqU5UOkRERERESqPzg3DnU7DvA1g6CQoLvnFJXGQos8b1JDzEw95TF10IGVxC3A4QKMaYocAdQCwwy1r7obuJRERERKTK6DHRmV71wc/gze/C0OfB85//np9YJ5rPfnwDEaFel0IGjxKNdBhjZhtjThtjdvi5pqYx5lVjzB5jzG5jzHVlDVXc+xljBhtj9hpj9htjnvB3D2vtG9baKcDDwIiyZhERERERuarrvgs3/hK2LYF3fgBX2SY3ItSLtZalG48x+/ODLoQMDiWdXjUXGPwt1zwNvG+tbQN0BnZf/k1jTF1jTMwVz7Uo6fsZY7zAs8DtQDtgpDGmXdH3Ohpj3r7iUbfopb8sep2IiIiISPka+GMY8EPYOBfe/9lViwfA8r2n+eO7u9l+7Orb7VZ1JSod1toVwNVPQgGMMXHAQGBW0fV51tq0Ky4bBLxhjAkves0U4J+leL9ewH5rbYq1Ng9YDNxTdP12a+2dlz+AM8aYJ4H3rLWbSvL7FBEREREptRv/G3p/B9Y+B8t/941vG2P449COJMSE819LNpOdV+hCSHeV10LyJOAMMMcYs9kYM9MYE335BdbaV4APgCXGmIeAicADpXiPRsDRy74+VvRccR4FbgbuN8Y8fLULjDF3GWOmp6dXz8YpIiIiIuXAGBj8J+g+Hlb+DVb89RuXxEWF8rfhnTl4Novfv7Or4jO6rLxKRwjQDXjOWtsVyAK+sebCWvsXIAd4DrjbWptZTu//DdbaZ6y13a21D1trny/mmrestVPj4uICFUNEREREqgNj4I6/Q6cHYfnvYfU3Z/f3bV6HqQOSWbj2CLuOZ7gQ0j3ltXvVMeCYtXZt0devcpXSYYwZAHQAXgd+DTxSivdIBZpc9nXjoudERERERNzn8cA9z0JBNnzwcwiNdHa5uszjt7aib4s6tGsY61JId5TLSIe19iRw1BjTuuipm4D/GDcyxnQFpuOsw5gA1DbG/L4Ub7MeaGmMSTLGhAEPAsuuObyIiIiISHnxhsCwmdDyNnj7cdiy6D++HR7iZVCrBABSzmRii1l4XtWUdMvcRcBqoLUx5pgxZlLR8+8aYxoWXfYosNAYsw3oAvzxittEAcOttQestT5gLHC4pO9nrS3AGRn5AGdnrJettTtL8XsVEREREQm8kDAYPh+SBjpneOx8/RuX7EhN57Z/rODFNVf9cbjKMdWlXfnTo0cPu2HDBrdjiIiIiEhVkpcFC+6DY+thxEJo/X8nQlhrmTB3PasPnOPtR/vTsl6MnxtVHsaYjdbaHlc+X14LyUVERERE5HJh0TDqZajfEV4eC/s//vpbxhj+cn8nosND+K/FW8gtqNrb6Kp0iIiIiIgESkQsjH4N6rSCxaPg4Mqvv1U3JoIn7+vErhMZPPXhly6GDDyVDhERERGRQIqqBWPfgPhEeGkEHFnz9bduaVeP0X2aEh7qrdKLyrWmA63pEBEREZEKcPEUzB3i/OfYN6Fxd8BZ32GMcTlc+dCaDhERERERN8XUg7HLILo2LLgXTmwF+LpwfL7vLL9ZtrNKjniodIiIiIiIVJS4RjDuLQiPhflD4dT/nQCx9Vgac1cd4rVNVe/8a5UOEREREZGKVLMpjFsGIeEw/x444ywif3hQc3ol1eLXy3Zy9Pwll0OWL5UOEREREZGKVivZGfHAwLy74NwBvB7DU8M7Y4DHlmyhoNDndspyo9IhIiIiIuKGOi2dEQ9fPsy7Gy4cpnF8FL8b2oGNhy/w1rbjbicsNyodIiIiIiJuqdsWxrwBeZkw705IP8bQro2YO6EnQ7s0cjtduVHpEBERERFxU4NOMOZ1yE5zplpdPMn1retijCE1LZus3AK3E14zlQ4REREREbc16gajlzpneMy7GzLPkH4pnyFPr+R3b+9yO901U+kQEREREQkGTXrBQ69A2hGYfw9xXOSh3k1ZvP4o7+846Xa6a6LSISIiIiISLBL7wchFcG4/vDiUx/rXo2OjOJ54bRunMnLcTldmKh0iIiIiIsGk+Q0wYgGc2kXYovt4elhzcvIL+X9v7fz21wYplQ4RERERkWDT6lYYPg9ObCX5/fE8NqAh0WEhFPqs28nKRKVDRERERCQYtbkD7psJx9bx8PFf8Nd7WuL1GLdTlYlKh4iIiIhIsGp/L9z7Ahz6HN76PtuPpbP/9EW3U5VaiNsBRERERETEj07D4XwKfPon/nd7S/KTbmTmuJ5upyoVjXSIiIiIiAS7/j+A2i35c8Q8Pt99lG3H0txOVCoqHSIiIiIiwS4kHO76B3E5qfw4Yhn/+Pc+txOVikqHiIiIiEhlkNgfujzEeLOMY3s3svnIBbcTlZhKh4iIiIhIZXHL7/BExPG3yDkcPpvpdpoSU+kQEREREaksomtjbv09HX17GGo/djtNial0iIiIiIhUJl1GQbP+2I9+xaZde91OUyIqHSIiIiIilYkxcOff8eVd4siix9hw6Lzbib6VSoeIiIiISGWT0Apf38cY6l3FR28vcjvNt1LpEBERERGphEIH/Yj0yKaMPP00675MdTuOXyodIiIiIiKVUWgEEfc+Q6LnFMeW/dbtNH6pdIiIiIiIVFLhrW5gX/07uSvzVS4c2uZ2nGKpdIiIiIiIVGJNRz6Ft04L4gvPuR2lWCFuBxARERERkbILj6sH310NnuAdTwjeZCIiIiIiUjJBXDhApUNERERERAJMpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERAJKpUNERERERALKWGvdzuA6Y8wZ4LDLMeoAZ13OIMFFnwm5Gn0u5Er6TMiV9JmQK1XkZ6KZtTbhyidVOoKEMWaDtbaH2zkkeOgzIVejz4VcSZ8JuZI+E3KlYPhMaHqViIiIiIgElEqHiIiIiIgElEpH8JjudgAJOvpMyNXocyFX0mdCrqTPhFzJ9c+E1nSIiIiIiEhAaaRDREREREQCSqWjAhhjBhtj9hpj9htjnrjK9/9ujNlS9PjSGJN22fcKL/vesgoNLgFTgs9EU2PMJ8aYzcaYbcaYIZd972dFr9trjLmtYpNLoJT1M2GMSTTGZF/298TzFZ9eAqEEn4lmxpiPiz4PnxpjGl/2vXHGmH1Fj3EVm1wC6Ro/F/qZoooxxsw2xpw2xuwo5vvGGPNM0edlmzGm22Xfq9i/J6y1egTwAXiBA0AyEAZsBdr5uf5RYPZlX2e6/XvQo+I/EzhzL79T9Ot2wKHLfr0VCAeSiu7jdfv3pIern4lEYIfbvwc9XPlMvAKMK/r1jcCLRb+uBaQU/Wd80a/j3f496eHu56Loa/1MUcUewECgW3H/PwAMAd4DDNAHWFv0fIX/PaGRjsDrBey31qZYa/OAxcA9fq4fCSyqkGTilpJ8JiwQW/TrOOB40a/vARZba3OttQeB/UX3k8rtWj4TUjWV5DPRDlhe9OtPLvv+bcBH1trz1toLwEfA4ArILIF3LZ8LqYKstSuA834uuQeYbx1rgJrGmAa48PeESkfgNQKOXvb1saLnvsEY0wznX6+XX/Z0hDFmgzFmjTFmaMBSSkUqyWfiN8BoY8wx4F2cEbCSvlYqn2v5TAAkFU27+swYMyCgSaWilOQzsRUYVvTre4EYY0ztEr5WKqdr+VyAfqaojor7zFT43xMqHcHlQeBVa23hZc81s84JkqOAfxhjmrsTTSrYSGCutbYxztDoi8YY/e+1eivuM3ECaGqt7Qo8DrxkjIn1cx+pOn4EDDLGbAYGAalAof+XSDXg73OhnynENfohJvBSgSaXfd246LmreZArplZZa1OL/jMF+BToWv4RpYKV5DMxCXgZwFq7GogA6pTwtVL5lPkzUTTV7lzR8xtx5nu3CnhiCbRv/UxYa49ba4cVFc5fFD2XVpLXSqV1LZ8L/UxRPRX3manwvydUOgJvPdDSGJNkjAnDKRbf2DHCGNMGZyHP6sueizfGhBf9ug7QD9hVIaklkErymTgC3ARgjGmL8wPmmaLrHjTGhBtjkoCWwLoKSy6BUubPhDEmwRjjLXo+GeczkVJhySVQvvUzYYypc9kI6M+A2UW//gC4tej/Q+KBW4uek8qvzJ8L/UxRbS0DxhbtYtUHSLfWnsCFvydCAnlzAWttgTHmEZz/Ir04O1PtNMb8Fthgrf3qL4sHcRYIX35aY1vgBWOMD6cg/tlaq78gKrkSfiZ+CMwwxvwAZwHx+KLPxk5jzMs4/0dRAHzviul4Ugldy2fCGDMQ+K0xJh/wAQ9ba/0tKpRKoISfieuBPxljLLAC+F7Ra88bY36H8wMqwG/1magaruVzgX6mqJKMMYtw/juvU7Tm79dAKIC19nmcNYBDcDaeuQRMKPpehf89oRPJRUREREQkoDS9SkREREREAkqlQ0REREREAkqlQ0REREREAkqlQ0REREREAkqlQ0REREREAkqlQ0REREREAkqlQ0REREREAkqlQ0REREREAur/A5i1fKlxqzjZAAAAAElFTkSuQmCC\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_, 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": "2022-06-07T18:08:12.133285Z",
     "iopub.status.busy": "2022-06-07T18:08:12.132680Z",
     "iopub.status.idle": "2022-06-07T18:55:09.419351Z",
     "shell.execute_reply": "2022-06-07T18:55:09.419735Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour beta2= 9.95e-01, loss_train=1.51e-02 / loss_test=1.52e-02; le temps de calcul est 401.157 s\n",
      "Pour beta2= 9.89e-01, loss_train=1.50e-02 / loss_test=1.53e-02; le temps de calcul est 402.233 s\n",
      "Pour beta2= 9.77e-01, loss_train=1.50e-02 / loss_test=1.51e-02; le temps de calcul est 402.146 s\n",
      "Pour beta2= 9.50e-01, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 401.846 s\n",
      "Pour beta2= 8.92e-01, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 401.336 s\n",
      "Pour beta2= 7.68e-01, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 404.640 s\n",
      "Pour beta2= 5.00e-01, loss_train=1.50e-02 / loss_test=1.50e-02; le temps de calcul est 403.597 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_, 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": "2022-06-07T18:55:09.426392Z",
     "iopub.status.busy": "2022-06-07T18:55:09.425801Z",
     "iopub.status.idle": "2022-06-07T20:08:59.588061Z",
     "shell.execute_reply": "2022-06-07T20:08:59.588455Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 129  513 1153 2049 3201 4609]\n",
      "Pour num_epochs=129, loss_train=2.39e-02 / loss_test=2.27e-02; le temps de calcul est 50.230 s\n",
      "Pour num_epochs=513, loss_train=1.86e-02 / loss_test=1.82e-02; le temps de calcul est 200.644 s\n",
      "Pour num_epochs=1153, loss_train=1.69e-02 / loss_test=1.66e-02; le temps de calcul est 442.471 s\n",
      "Pour num_epochs=2049, loss_train=1.63e-02 / loss_test=1.61e-02; le temps de calcul est 775.202 s\n",
      "Pour num_epochs=3201, loss_train=1.58e-02 / loss_test=1.57e-02; le temps de calcul est 1208.351 s\n",
      "Pour num_epochs=4609, loss_train=1.56e-02 / loss_test=1.55e-02; le temps de calcul est 1753.045 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"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}