mirror of
https://github.com/ArthurDanjou/ArtStudies.git
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- Updated import order in Point_Fixe.ipynb for consistency. - Changed lambda functions to regular function definitions for clarity in Point_Fixe.ipynb. - Added numpy import in TP1_EDO_EulerExp.ipynb, TP2_Lokta_Volterra.ipynb, and TP3_Convergence.ipynb for better readability. - Modified for loops in TP1_EDO_EulerExp.ipynb and TP2_Lokta_Volterra.ipynb to include strict=False for compatibility with future Python versions.
351 lines
122 KiB
Plaintext
351 lines
122 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 273,
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"id": "98d26b7b-0ddb-4ef8-93af-106818267229",
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"metadata": {
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"tags": []
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},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"import scipy.optimize as opt\n",
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"import scipy.special as sp\n",
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"import scipy.stats as stats"
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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": 2,
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"id": "bf2aad2a-b9ad-4d38-9763-4182752b5d54",
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"metadata": {
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"tags": []
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},
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"outputs": [],
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"source": [
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"def f(L, z):\n",
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" x, y = L[0], L[1]\n",
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" return (\n",
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" np.power(z * x, 2)\n",
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" + np.power(y / z, 2)\n",
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" - np.cos(2 * np.pi * x)\n",
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" - np.cos(2 * np.pi * y)\n",
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" )"
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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": 3,
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"id": "bc00dbe1-2edf-4a90-839e-1aa8d53fc7dc",
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"metadata": {
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"tags": []
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},
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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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" message: Optimization terminated successfully.\n",
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" success: True\n",
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" status: 0\n",
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" fun: -1.0125323577209524\n",
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" x: [ 1.409e-07 1.975e+00]\n",
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" nit: 6\n",
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" jac: [ 7.048e-06 3.651e-06]\n",
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" hess_inv: [[ 2.137e-02 2.198e-04]\n",
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" [ 2.198e-04 2.546e-02]]\n",
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" nfev: 30\n",
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" njev: 10\n"
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]
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}
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],
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"source": [
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"res2 = opt.minimize(f, x0=(1, 2), args=2, method=\"BFGS\")\n",
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"print(res2)"
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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": 65,
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"id": "9a50016b-d8c1-489d-affe-81bae33463dc",
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"metadata": {
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"tags": []
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},
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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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" message: ['requested number of basinhopping iterations completed successfully']\n",
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" success: True\n",
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" fun: -2.0\n",
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" x: [ 1.358e-09 6.023e-10]\n",
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" nit: 100\n",
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" minimization_failures: 0\n",
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" nfev: 3369\n",
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" njev: 1123\n",
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" lowest_optimization_result: message: Optimization terminated successfully.\n",
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" success: True\n",
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" status: 0\n",
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" fun: -2.0\n",
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" x: [ 1.358e-09 6.023e-10]\n",
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" nit: 7\n",
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" jac: [ 4.172e-07 3.278e-07]\n",
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" hess_inv: [[ 2.140e-02 3.244e-04]\n",
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" [ 3.244e-04 2.532e-02]]\n",
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" nfev: 30\n",
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" njev: 10\n"
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]
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}
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],
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"source": [
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"mk = {\"method\": \"BFGS\", \"args\": 2}\n",
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"res = opt.basinhopping(f, x0=(1, 2), minimizer_kwargs=mk)\n",
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"print(res)"
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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": 92,
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"id": "4bbd6193-9658-421a-a746-81b9fd530f2c",
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"metadata": {
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"tags": []
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},
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"outputs": [
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{
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"data": {
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",
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"<Figure size 1800x500 with 3 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.figure(figsize=(18, 5))\n",
|
|
"for i, nb_repl in enumerate([100, 1000, 10000]):\n",
|
|
" plt.subplot(1, 3, i + 1)\n",
|
|
" sample_X1 = np.random.normal(0, 1, nb_repl)\n",
|
|
" sample_X2 = np.random.normal(3, np.sqrt(5), nb_repl)\n",
|
|
" sample_e = np.random.normal(0, np.sqrt(1 / 4), nb_repl)\n",
|
|
" Y = 5 * sample_X1 - 4 * sample_X2 + 2 + sample_e\n",
|
|
"\n",
|
|
" intervalle = np.linspace(np.min(Y), np.max(Y), 100)\n",
|
|
" plt.hist(Y, bins=intervalle, density=True, label=\"Echantillon de Y\")\n",
|
|
"\n",
|
|
" densite = stats.norm(-10, np.sqrt(105.25)).pdf\n",
|
|
" plt.plot(intervalle, densite(intervalle), label=\"Fonction densité\")\n",
|
|
"\n",
|
|
" plt.title(f\"Graphique de la somme de gaussiennes pour N={nb_repl}\")\n",
|
|
" plt.legend()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 172,
|
|
"id": "508aa866-d4ed-42a6-8f01-09c9b8721566",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def theta_hat(Y):\n",
|
|
" return np.mean(Y)\n",
|
|
"\n",
|
|
"\n",
|
|
"def sigma_hat(Y):\n",
|
|
" return 1 / nb_repl * np.sum(np.power(Y - theta_hat(Y), 2))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 173,
|
|
"id": "eb62aac4-2a4f-4ae8-84e9-702bc212315e",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def log_likehood_gauss(X, Y):\n",
|
|
" theta, sigma_2 = X[0], X[1]\n",
|
|
" return (\n",
|
|
" 1 / 2 * np.log(2 * np.pi)\n",
|
|
" + 1 / 2 * np.log(sigma_2)\n",
|
|
" + 1 / (2 * nb_repl * sigma_2) * np.sum(np.power(Y - theta, 2))\n",
|
|
" )"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 204,
|
|
"id": "ae68062d-1c5d-4881-b750-afaefd62b8af",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"[-10.15254483 105.22161157]\n",
|
|
"[-10.152550623018831, 105.22156995434973]\n",
|
|
"True\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"nb_repl = 5000\n",
|
|
"sample_X1 = np.random.normal(0, 1, nb_repl)\n",
|
|
"sample_X2 = np.random.normal(3, np.sqrt(5), nb_repl)\n",
|
|
"sample_e = np.random.normal(0, np.sqrt(1 / 4), nb_repl)\n",
|
|
"Y = 5 * sample_X1 - 4 * sample_X2 + 2 + sample_e\n",
|
|
"\n",
|
|
"mk = {\"method\": \"BFGS\", \"args\": Y}\n",
|
|
"res = opt.basinhopping(log_likehood_gauss, x0=(-1, 98.75), minimizer_kwargs=mk)\n",
|
|
"print(res.x)\n",
|
|
"print([theta_hat(Y), sigma_hat(Y)])\n",
|
|
"print(np.allclose([theta_hat(Y), sigma_hat(Y)], res.x))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 258,
|
|
"id": "2ce462b1-00e8-4386-bb8c-163f2ba69e68",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def simule(a, b, n):\n",
|
|
" X = np.random.gamma(a, 1 / b, n)\n",
|
|
" intervalle = np.linspace(0, np.max(X), 100)\n",
|
|
" plt.hist(X, bins=intervalle, density=True, label=\"Echantillon de X\")\n",
|
|
"\n",
|
|
" densite = stats.gamma.pdf(intervalle, a, 0, 1 / b)\n",
|
|
" plt.plot(intervalle, densite, label=\"Fonction densité Gamma(2, 1)\")\n",
|
|
" plt.legend()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 259,
|
|
"id": "b8861952-f676-4b38-8f24-ecd71b137bfd",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"simule(2, 1, 10000)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 290,
|
|
"id": "dcb07fde-0af2-46e0-b009-bf4d799249c1",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def log_likehood_gamma(X, sample):\n",
|
|
" a, b = X[0], X[1]\n",
|
|
" n = len(sample)\n",
|
|
" return (\n",
|
|
" -n * a * np.log(b)\n",
|
|
" + n * np.log(sp.gamma(a))\n",
|
|
" - (a - 1) * np.sum(np.log(sample))\n",
|
|
" + b * np.sum(sample)\n",
|
|
" )"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 296,
|
|
"id": "ea041002-cc5c-47e1-aa52-9a607def05d2",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"[1.99590773 0.96694005]\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"/tmp/ipykernel_360/437431687.py:4: RuntimeWarning: invalid value encountered in log\n",
|
|
" return -n*a*np.log(b) + n * np.log(sp.gamma(a)) - (a-1) * np.sum(np.log(sample)) + b * np.sum(sample)\n",
|
|
"/tmp/ipykernel_360/437431687.py:4: RuntimeWarning: divide by zero encountered in log\n",
|
|
" return -n*a*np.log(b) + n * np.log(sp.gamma(a)) - (a-1) * np.sum(np.log(sample)) + b * np.sum(sample)\n",
|
|
"/tmp/ipykernel_360/437431687.py:4: RuntimeWarning: invalid value encountered in log\n",
|
|
" return -n*a*np.log(b) + n * np.log(sp.gamma(a)) - (a-1) * np.sum(np.log(sample)) + b * np.sum(sample)\n",
|
|
"/tmp/ipykernel_360/437431687.py:4: RuntimeWarning: divide by zero encountered in log\n",
|
|
" return -n*a*np.log(b) + n * np.log(sp.gamma(a)) - (a-1) * np.sum(np.log(sample)) + b * np.sum(sample)\n",
|
|
"/tmp/ipykernel_360/437431687.py:4: RuntimeWarning: invalid value encountered in log\n",
|
|
" return -n*a*np.log(b) + n * np.log(sp.gamma(a)) - (a-1) * np.sum(np.log(sample)) + b * np.sum(sample)\n",
|
|
"/tmp/ipykernel_360/437431687.py:4: RuntimeWarning: divide by zero encountered in log\n",
|
|
" return -n*a*np.log(b) + n * np.log(sp.gamma(a)) - (a-1) * np.sum(np.log(sample)) + b * np.sum(sample)\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"nb_repl = 1000\n",
|
|
"a, b = 2, 1\n",
|
|
"\n",
|
|
"sample = np.random.gamma(a, 1 / b, nb_repl)\n",
|
|
"mk = {\"method\": \"BFGS\", \"args\": sample}\n",
|
|
"res = opt.basinhopping(log_likehood_gamma, x0=(1, 1), minimizer_kwargs=mk)\n",
|
|
"print(res.x)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "abfb9307-2531-4e48-818d-169ebe17072b",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"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": "3.10.8"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|