206 lines
5.8 KiB
Plaintext
206 lines
5.8 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "c49056b3-e2c2-471d-b998-14eb1cd1a082",
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"metadata": {},
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"source": [
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"# Exercice 1 : \n",
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"Autre fonctions d'erreurs : \n",
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"- Erreur résiduelle : ei = f(xi)-yi\n",
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"- Erreur logarithmique : ei = log(1+|f(xi)-yi|)\n",
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"- Erreur relative : ei = (f(xi)-yi)/yi\n",
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"\n",
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"# Exercice 2 : \n",
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"Autre fonctions de couts : \n",
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"- Erreur Log-Cosh, Log-Cosh est similaire à MAE pour de petites erreurs\n",
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"- Erreur Huber (𝛿=1), Huber réduit l’impact des grandes erreurs\n",
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"- Erreur de Poisson, Poisson est adaptée aux distributions asymétriques\n",
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" "
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]
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},
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{
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"cell_type": "markdown",
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"id": "3aa6d565-ac05-48ca-9f10-ece048a7eff2",
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"metadata": {},
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"source": [
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"# Exercice 3 : \n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 84,
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"id": "d8b00644-a239-44ba-9b4c-4982e624227f",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"iteration = 1\n",
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"a= 50 b= 75\n",
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"iteration = 2\n",
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"a= -25.75309997451889 b= 74.9568945\n",
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"iteration = 3\n",
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"a= 13.539805289078245 b= 74.97929653630847\n",
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"iteration = 4\n",
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"a= -6.841306604859323 b= 74.9677200103882\n",
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"iteration = 5\n",
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"a= 3.730314856415273 b= 74.97376806255475\n",
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"iteration = 6\n",
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"a= -1.7531534482568194 b= 74.9706742990146\n",
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"iteration = 7\n",
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"a= 1.0911050566712879 b= 74.97232236778468\n",
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"iteration = 8\n",
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"a= -0.3842033063747208 b= 74.97151086236455\n",
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"iteration = 9\n",
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"a= 0.3810346829632343 b= 74.97197513066288\n",
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"iteration = 10\n",
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"a= -0.015891986938224745 b= 74.97177765894565\n",
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"iteration = 11\n",
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"a= 0.1899926591360049 b= 74.9719234297637\n",
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"iteration = 12\n",
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"a= 0.08320088730389696 b= 74.97189116168829\n",
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"iteration = 13\n",
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"a= 0.13859343372153637 b= 74.97195124182983\n",
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"iteration = 14\n",
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"a= 0.10986146169209325 b= 74.97196342120678\n",
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"iteration = 15\n",
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"a= 0.12476462455318163 b= 74.97200044654436\n",
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"iteration = 16\n",
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"a= 0.1170343740876787 b= 74.97202458433483\n",
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"iteration = 17\n",
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"a= 0.12104400709218902 b= 74.97205540683525\n",
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"iteration = 18\n",
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"a= 0.11896419782388343 b= 74.97208276197472\n",
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"iteration = 19\n",
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"a= 0.12004296396127893 b= 74.97211191560189\n",
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"Paramètre a : 0.11948338652853815\n",
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"Paramètre b : 74.97214013633689\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"\n",
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"# Données d'exemple (à remplacer par vos propres données)\n",
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"# xi : les valeurs d'entrée\n",
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"# yi : les valeurs de sortie cibles\n",
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"xi = np.array([313, 2384, 342, 420]) # Exemple\n",
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"yi = np.array([124, 339, 179, 186]) # Exemple\n",
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"\n",
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"# Hyperparamètres\n",
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"alpha = 0.000001 # Taux d'apprentissage\n",
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"m = len(xi) # Nombre d'exemples\n",
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"\n",
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"# Initialisation des paramètres\n",
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"a = 50 # Paramètre a initial\n",
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"b = 75 # Paramètre b initial\n",
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"\n",
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"# Seuils d'arrêt\n",
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"epsilon_threshold = 1e-3\n",
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"\n",
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"# Initialisation des erreurs\n",
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"epsilon_1 = float('inf')\n",
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"epsilon_2 = float('inf')\n",
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"tmp = 0\n",
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"\n",
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"# Boucle principale\n",
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"while epsilon_1 > epsilon_threshold or epsilon_2 > epsilon_threshold:\n",
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" a_prev = a\n",
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" b_prev = b\n",
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" tmp += 1\n",
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" print(\"iteration = \",tmp)\n",
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" print(\"a=\",a,\" b=\",b)\n",
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" \n",
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"\n",
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"\n",
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" # Calcul des gradients et mise à jour des paramètres\n",
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" b = b - alpha * (1 / m) * np.sum(a * xi + b - yi)\n",
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" a = a - alpha * (1 / m) * np.sum((a * xi + b - yi) * xi)\n",
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"\n",
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" # Calcul des erreurs\n",
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" epsilon_1 = abs(a_prev - a)\n",
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" epsilon_2 = abs(b_prev - b)\n",
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"\n",
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"# Résultats finaux\n",
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"print(f\"Paramètre a : {a}\")\n",
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"print(f\"Paramètre b : {b}\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "10a19dd5-878c-4b92-b0e1-9b3324bb3407",
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"metadata": {},
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"source": [
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"| Itération | A | B |\n",
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"| :--------------- |:---------------:| -----:|\n",
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"| 1 | 50 | 75 |\n",
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"| 9 | 0.38103 | 74.97197 |\n",
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"| 19 | 0.12004 | 74.97214 |"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c9fed1c7-6c60-4589-8086-3f8fefec8fca",
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"metadata": {},
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"source": [
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"# Exercice 4 :\n",
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"## 1)\n",
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""
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]
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},
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{
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"cell_type": "markdown",
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"id": "04ea9f05-9b2d-43a9-86bf-afa9f17f0336",
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"metadata": {},
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"source": [
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"## 2)\n",
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"\n",
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"data : 01 11 10 00\n",
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"\n",
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"| _ | 01 | 11 | 10 | 00 |\n",
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"| :--------------- |:---------------:| -----:| -----:| -----:|\n",
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"| W0 | 2 | 1 | 1 | 0 |\n",
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"| W1 | 0 | 0 | 0 | 1 |\n",
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"| W2 | 0 | 1 | 1 | 1 |\n",
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"| RF |-2 | 0 | -1 | 0 |\n",
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"| RO | 0 | 0 | 0 | 0 |\n",
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"| RA | 1 | 0 | 1 | 0 |\n",
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"| W0' | 2+(1-0)*-1 = 1 | 1 | 1+(1-0)*-1 = 0 | 0 |\n",
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"| W1' | 0+(1-0)*0 = 0 | 0 | 0+(1-0)*1 = 1 | 1 |\n",
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"| W2' | 0+(1-0)*1 = 1 | 1 | 1+(1-0)*0 = 1 | 1 |"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d205f2d3-a9cb-4c8b-964d-a25f18f793d3",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.7"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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