From fa23d8e08e7f2688ae7a81ebaca1606895339970 Mon Sep 17 00:00:00 2001 From: Arthur DANJOU Date: Mon, 3 Mar 2025 16:34:14 +0100 Subject: [PATCH] Add TP1 in numerical methods --- M1/Numerical Methods/TP1.ipynb | 526 +++++++++++++++++++++++++++++++++ 1 file changed, 526 insertions(+) create mode 100644 M1/Numerical Methods/TP1.ipynb diff --git a/M1/Numerical Methods/TP1.ipynb b/M1/Numerical Methods/TP1.ipynb new file mode 100644 index 0000000..1e43814 --- /dev/null +++ b/M1/Numerical Methods/TP1.ipynb @@ -0,0 +1,526 @@ +{ + "cells": [ + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T14:27:00.244402Z", + "start_time": "2025-03-03T14:27:00.241231Z" + } + }, + "cell_type": "code", + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.integrate import odeint" + ], + "id": "fe01d49f9c6740ce", + "outputs": [], + "execution_count": 100 + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "## Exercise 2.18 : Numerical precision", + "id": "4a91fd48ddb1c4fc" + }, + { + "metadata": { + "collapsed": true, + "ExecuteTime": { + "end_time": "2025-03-03T15:03:25.306403Z", + "start_time": "2025-03-03T15:03:25.302289Z" + } + }, + "cell_type": "code", + "source": [ + "def f(t, x):\n", + " return 2 * np.power(np.abs(x), 1 / 2)\n", + "\n", + "\n", + "def f_exact(x, lam):\n", + " return np.power(x - lam, 2) * (x >= lam)" + ], + "id": "initial_id", + "outputs": [], + "execution_count": 169 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T15:26:11.555613Z", + "start_time": "2025-03-03T15:26:11.551621Z" + } + }, + "cell_type": "code", + "source": [ + "def euler_explicit(N, T, y0, f, args=()):\n", + " h = T / N\n", + " t = np.linspace(0, T, N + 1)\n", + " y = np.zeros(N + 1)\n", + " y[0] = y0\n", + " for n in range(N):\n", + " y[n + 1] = y[n] + h * f(t[n], y[n], *args)\n", + " return t, y" + ], + "id": "f447a3bdff49e850", + "outputs": [], + "execution_count": 217 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T15:26:18.887962Z", + "start_time": "2025-03-03T15:26:18.799687Z" + } + }, + "cell_type": "code", + "source": [ + "T = 10\n", + "N = 1000\n", + "u0 = 0\n", + "\n", + "t, sol_appr = euler_explicit(N, T, u0, f)\n", + "x = np.linspace(u0, T, 100)\n", + "\n", + "plt.scatter(t, sol_appr, label=\"Approximation\")\n", + "plt.plot(x, f_exact(x, T), label=\"Exact solution\", color=\"red\")\n", + "plt.legend()\n", + "plt.show()" + ], + "id": "957b7a23b6076f77", + "outputs": [ + { + "data": { + "text/plain": [ + "
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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "execution_count": 218 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T15:25:45.054499Z", + "start_time": "2025-03-03T15:25:45.049904Z" + } + }, + "cell_type": "code", + "source": [ + "def euler_implicit(N, T, y0):\n", + " h = T / N\n", + " t = np.linspace(0, T, N + 1)\n", + " y = np.zeros(N + 1)\n", + " y[0] = y0\n", + " for n in range(N):\n", + " y[n + 1] = np.power(h + np.sqrt(h ** 2 + y[n]), 2)\n", + " return t, y" + ], + "id": "57527c2e5eb6d17d", + "outputs": [], + "execution_count": 214 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T15:25:51.105580Z", + "start_time": "2025-03-03T15:25:51.038176Z" + } + }, + "cell_type": "code", + "source": [ + "T = 10\n", + "N = 1000\n", + "u0 = 0\n", + "\n", + "t, sol_appr = euler_implicit(N, T, u0)\n", + "x = np.linspace(0, T, 100)\n", + "\n", + "plt.scatter(t, sol_appr, label=\"Approximation\")\n", + "plt.plot(x, f_exact(x, T), label=\"Exact solution\", color=\"red\")\n", + "plt.plot(x, x ** 2, label=\"Square function\", color=\"green\")\n", + "plt.legend()\n", + "plt.show()" + ], + "id": "2ff29a8872a51c89", + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ], + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "execution_count": 216 + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "## Exercise 2.19 : SIR model, schema order", + "id": "ecea2cd935dea93a" + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T15:25:14.888616Z", + "start_time": "2025-03-03T15:25:14.884827Z" + } + }, + "cell_type": "code", + "source": [ + "def F(y, t, a, r):\n", + " S, I, R = y\n", + " dS = -r * S * I\n", + " dI = r * S * I - a * I\n", + " dR = a * I\n", + " return np.array([dS, dI, dR])" + ], + "id": "61588e94b56ea779", + "outputs": [], + "execution_count": 208 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T15:25:15.302160Z", + "start_time": "2025-03-03T15:25:15.298178Z" + } + }, + "cell_type": "code", + "source": [ + "def euler_explicit_sir(N, T, u0, f, args):\n", + " t = np.linspace(0, T, N + 1)\n", + " y = np.zeros((N + 1, len(y0)))\n", + " y[0] = y0\n", + " h = T / N\n", + " for i in range(N):\n", + " y[i + 1] = y[i] + h * F(y[i], t[i], *args)\n", + " return t, y" + ], + "id": "a32f0facb958a1a0", + "outputs": [], + "execution_count": 209 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T15:25:15.672410Z", + "start_time": "2025-03-03T15:25:15.667465Z" + } + }, + "cell_type": "code", + "source": [ + "def heun_sir(N, T, u0, f, args):\n", + " t = np.linspace(0, T, N + 1)\n", + " y = np.zeros((N + 1, len(y0)))\n", + " y[0] = y0\n", + " h = T / N\n", + " for i in range(N):\n", + " k1 = h * F(y[i], t[i], *args)\n", + " k2 = h * F(y[i] + k1, t[i + 1], *args)\n", + " y[i + 1] = y[i] + 0.5 * (k1 + k2)\n", + " return t, y" + ], + "id": "ca061c36b09f7200", + "outputs": [], + "execution_count": 210 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T15:25:16.031135Z", + "start_time": "2025-03-03T15:25:16.028109Z" + } + }, + "cell_type": "code", + "source": [ + "def runge_kutta_order_4_sir(N, T, u0, f, args):\n", + " t = np.linspace(0, T, N + 1)\n", + " y = np.zeros((N + 1, len(y0)))\n", + " y[0] = y0\n", + " h = T / N\n", + " for i in range(N):\n", + " k1 = h * F(y[i], t[i], *args)\n", + " k2 = h * F(y[i] + 0.5 * k1, t[i] + 0.5 * h, *args)\n", + " k3 = h * F(y[i] + 0.5 * k2, t[i] + 0.5 * h, *args)\n", + " k4 = h * F(y[i] + k3, t[i + 1], *args)\n", + " y[i + 1] = y[i] + (k1 + 2 * k2 + 2 * k3 + k4) / 6\n", + " return t, y" + ], + "id": "afc8571b14a6b464", + "outputs": [], + "execution_count": 211 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T15:31:50.573137Z", + "start_time": "2025-03-03T15:31:50.483307Z" + } + }, + "cell_type": "code", + "source": [ + "t0, T = 52, 60\n", + "N = 150\n", + "\n", + "y0 = np.array([10e6, 10, 0], dtype=np.float64) # Initial conditions: S, I, R\n", + "a = 0.33 # Recovery rate\n", + "r = 0.5 # Infection rate\n", + "t = np.linspace(t0, T, N)\n", + "\n", + "sol = odeint(F, y0, t, args=(a, r))\n", + "\n", + "plt.plot(t, sol[:, 0], label='S(t)')\n", + "plt.plot(t, sol[:, 1], label='I(t)')\n", + "plt.plot(t, sol[:, 2], label='R(t)')\n", + "plt.legend()\n", + "plt.show()" + ], + "id": "3ff4bbd4286d2b69", + "outputs": [ + { + "data": { + "text/plain": [ + "
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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "execution_count": 228 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T15:33:44.002798Z", + "start_time": "2025-03-03T15:33:43.645747Z" + } + }, + "cell_type": "code", + "source": [ + "errors_EE = []\n", + "errors_H = []\n", + "errors_RK4 = []\n", + "\n", + "h_list = [0.05, 0.01, 0.1, 0.5, 1, 2, 4]\n", + "\n", + "\n", + "def calculate_errors(sol_exact, sol_appr):\n", + " return np.max(\n", + " np.power(np.abs(sol_appr - sol_exact), 2)[np.isfinite(np.power(np.abs(sol_appr - sol_exact), 2))]\n", + " )\n", + "\n", + "\n", + "for h in h_list:\n", + " N = int(T / h)\n", + " t = np.linspace(0, T, N + 1)\n", + "\n", + " _, sol_appr_EE = euler_explicit_sir(N, T, y0, F, args=(a, r))\n", + " _, sol_appr_H = heun_sir(N, T, y0, F, args=(a, r))\n", + " _, sol_appr_RK4 = runge_kutta_order_4_sir(N, T, y0, F, args=(a, r))\n", + " sol_exact = odeint(F, y0, t, args=(a, r))\n", + "\n", + " errors_EE.append(calculate_errors(sol_exact, sol_appr_EE))\n", + " errors_H.append(calculate_errors(sol_exact, sol_appr_H))\n", + " errors_RK4.append(calculate_errors(sol_exact, sol_appr_RK4))\n", + "\n", + "plt.plot(errors_EE, label=\"Euler Explicit\")\n", + "plt.plot(errors_H, label=\"Heun\")\n", + "plt.plot(errors_RK4, label=\"Runge Kutta order 4\")\n", + "plt.yscale('log')\n", + "plt.xscale('log')\n", + "plt.legend()\n", + "plt.show()" + ], + "id": "c147c62e0a55bf28", + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/tp/_ld5_pzs6nx6mv1pbjhq1l740000gn/T/ipykernel_61968/732581197.py:3: RuntimeWarning: overflow encountered in scalar multiply\n", + " dS = -r * S * I\n", + "/var/folders/tp/_ld5_pzs6nx6mv1pbjhq1l740000gn/T/ipykernel_61968/732581197.py:4: RuntimeWarning: overflow encountered in scalar multiply\n", + " dI = r * S * I - a * I\n", + "/var/folders/tp/_ld5_pzs6nx6mv1pbjhq1l740000gn/T/ipykernel_61968/732581197.py:4: RuntimeWarning: invalid value encountered in scalar subtract\n", + " dI = r * S * I - a * I\n", + "/var/folders/tp/_ld5_pzs6nx6mv1pbjhq1l740000gn/T/ipykernel_61968/122785292.py:10: RuntimeWarning: overflow encountered in power\n", + " np.power(np.abs(sol_appr - sol_exact), 2)[np.isfinite(np.power(np.abs(sol_appr - sol_exact), 2))]\n" + ] + }, + { + "ename": "OverflowError", + "evalue": "cannot convert float infinity to integer", + "output_type": "error", + "traceback": [ + "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m", + "\u001B[0;31mOverflowError\u001B[0m Traceback (most recent call last)", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/IPython/core/formatters.py:340\u001B[0m, in \u001B[0;36mBaseFormatter.__call__\u001B[0;34m(self, obj)\u001B[0m\n\u001B[1;32m 338\u001B[0m \u001B[38;5;28;01mpass\u001B[39;00m\n\u001B[1;32m 339\u001B[0m \u001B[38;5;28;01melse\u001B[39;00m:\n\u001B[0;32m--> 340\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[43mprinter\u001B[49m\u001B[43m(\u001B[49m\u001B[43mobj\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 341\u001B[0m \u001B[38;5;66;03m# Finally look for special method names\u001B[39;00m\n\u001B[1;32m 342\u001B[0m method \u001B[38;5;241m=\u001B[39m get_real_method(obj, \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39mprint_method)\n", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/IPython/core/pylabtools.py:152\u001B[0m, in \u001B[0;36mprint_figure\u001B[0;34m(fig, fmt, bbox_inches, base64, **kwargs)\u001B[0m\n\u001B[1;32m 149\u001B[0m \u001B[38;5;28;01mfrom\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[38;5;21;01mmatplotlib\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mbackend_bases\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[38;5;28;01mimport\u001B[39;00m FigureCanvasBase\n\u001B[1;32m 150\u001B[0m FigureCanvasBase(fig)\n\u001B[0;32m--> 152\u001B[0m \u001B[43mfig\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mcanvas\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mprint_figure\u001B[49m\u001B[43m(\u001B[49m\u001B[43mbytes_io\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[43mkw\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 153\u001B[0m data \u001B[38;5;241m=\u001B[39m bytes_io\u001B[38;5;241m.\u001B[39mgetvalue()\n\u001B[1;32m 154\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m fmt \u001B[38;5;241m==\u001B[39m \u001B[38;5;124m'\u001B[39m\u001B[38;5;124msvg\u001B[39m\u001B[38;5;124m'\u001B[39m:\n", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/matplotlib/backend_bases.py:2164\u001B[0m, in \u001B[0;36mFigureCanvasBase.print_figure\u001B[0;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001B[0m\n\u001B[1;32m 2161\u001B[0m \u001B[38;5;66;03m# we do this instead of `self.figure.draw_without_rendering`\u001B[39;00m\n\u001B[1;32m 2162\u001B[0m \u001B[38;5;66;03m# so that we can inject the orientation\u001B[39;00m\n\u001B[1;32m 2163\u001B[0m \u001B[38;5;28;01mwith\u001B[39;00m \u001B[38;5;28mgetattr\u001B[39m(renderer, \u001B[38;5;124m\"\u001B[39m\u001B[38;5;124m_draw_disabled\u001B[39m\u001B[38;5;124m\"\u001B[39m, nullcontext)():\n\u001B[0;32m-> 2164\u001B[0m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mfigure\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mdraw\u001B[49m\u001B[43m(\u001B[49m\u001B[43mrenderer\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 2165\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m bbox_inches:\n\u001B[1;32m 2166\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m bbox_inches \u001B[38;5;241m==\u001B[39m \u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mtight\u001B[39m\u001B[38;5;124m\"\u001B[39m:\n", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/matplotlib/artist.py:95\u001B[0m, in \u001B[0;36m_finalize_rasterization..draw_wrapper\u001B[0;34m(artist, renderer, *args, **kwargs)\u001B[0m\n\u001B[1;32m 93\u001B[0m \u001B[38;5;129m@wraps\u001B[39m(draw)\n\u001B[1;32m 94\u001B[0m \u001B[38;5;28;01mdef\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[38;5;21mdraw_wrapper\u001B[39m(artist, renderer, \u001B[38;5;241m*\u001B[39margs, \u001B[38;5;241m*\u001B[39m\u001B[38;5;241m*\u001B[39mkwargs):\n\u001B[0;32m---> 95\u001B[0m result \u001B[38;5;241m=\u001B[39m \u001B[43mdraw\u001B[49m\u001B[43m(\u001B[49m\u001B[43martist\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mrenderer\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[43margs\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[38;5;241;43m*\u001B[39;49m\u001B[43mkwargs\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 96\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m renderer\u001B[38;5;241m.\u001B[39m_rasterizing:\n\u001B[1;32m 97\u001B[0m renderer\u001B[38;5;241m.\u001B[39mstop_rasterizing()\n", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/matplotlib/artist.py:72\u001B[0m, in \u001B[0;36mallow_rasterization..draw_wrapper\u001B[0;34m(artist, renderer)\u001B[0m\n\u001B[1;32m 69\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m artist\u001B[38;5;241m.\u001B[39mget_agg_filter() \u001B[38;5;129;01mis\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m \u001B[38;5;28;01mNone\u001B[39;00m:\n\u001B[1;32m 70\u001B[0m renderer\u001B[38;5;241m.\u001B[39mstart_filter()\n\u001B[0;32m---> 72\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[43mdraw\u001B[49m\u001B[43m(\u001B[49m\u001B[43martist\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mrenderer\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 73\u001B[0m \u001B[38;5;28;01mfinally\u001B[39;00m:\n\u001B[1;32m 74\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m artist\u001B[38;5;241m.\u001B[39mget_agg_filter() \u001B[38;5;129;01mis\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m \u001B[38;5;28;01mNone\u001B[39;00m:\n", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/matplotlib/figure.py:3154\u001B[0m, in \u001B[0;36mFigure.draw\u001B[0;34m(self, renderer)\u001B[0m\n\u001B[1;32m 3151\u001B[0m \u001B[38;5;66;03m# ValueError can occur when resizing a window.\u001B[39;00m\n\u001B[1;32m 3153\u001B[0m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39mpatch\u001B[38;5;241m.\u001B[39mdraw(renderer)\n\u001B[0;32m-> 3154\u001B[0m \u001B[43mmimage\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43m_draw_list_compositing_images\u001B[49m\u001B[43m(\u001B[49m\n\u001B[1;32m 3155\u001B[0m \u001B[43m \u001B[49m\u001B[43mrenderer\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;28;43mself\u001B[39;49m\u001B[43m,\u001B[49m\u001B[43m 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\u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/matplotlib/image.py:132\u001B[0m, in \u001B[0;36m_draw_list_compositing_images\u001B[0;34m(renderer, parent, artists, suppress_composite)\u001B[0m\n\u001B[1;32m 130\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m not_composite \u001B[38;5;129;01mor\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m has_images:\n\u001B[1;32m 131\u001B[0m \u001B[38;5;28;01mfor\u001B[39;00m a \u001B[38;5;129;01min\u001B[39;00m artists:\n\u001B[0;32m--> 132\u001B[0m \u001B[43ma\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mdraw\u001B[49m\u001B[43m(\u001B[49m\u001B[43mrenderer\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 133\u001B[0m \u001B[38;5;28;01melse\u001B[39;00m:\n\u001B[1;32m 134\u001B[0m \u001B[38;5;66;03m# Composite any adjacent images together\u001B[39;00m\n\u001B[1;32m 135\u001B[0m image_group \u001B[38;5;241m=\u001B[39m []\n", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/matplotlib/artist.py:72\u001B[0m, in \u001B[0;36mallow_rasterization..draw_wrapper\u001B[0;34m(artist, renderer)\u001B[0m\n\u001B[1;32m 69\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m artist\u001B[38;5;241m.\u001B[39mget_agg_filter() \u001B[38;5;129;01mis\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m \u001B[38;5;28;01mNone\u001B[39;00m:\n\u001B[1;32m 70\u001B[0m renderer\u001B[38;5;241m.\u001B[39mstart_filter()\n\u001B[0;32m---> 72\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[43mdraw\u001B[49m\u001B[43m(\u001B[49m\u001B[43martist\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mrenderer\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 73\u001B[0m \u001B[38;5;28;01mfinally\u001B[39;00m:\n\u001B[1;32m 74\u001B[0m \u001B[38;5;28;01mif\u001B[39;00m artist\u001B[38;5;241m.\u001B[39mget_agg_filter() \u001B[38;5;129;01mis\u001B[39;00m \u001B[38;5;129;01mnot\u001B[39;00m 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Return the list of ticks that will be drawn.\u001B[39;00m\n\u001B[1;32m 1274\u001B[0m \u001B[38;5;124;03m\"\"\"\u001B[39;00m\n\u001B[1;32m 1275\u001B[0m major_locs \u001B[38;5;241m=\u001B[39m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39mget_majorticklocs()\n\u001B[0;32m-> 1276\u001B[0m major_labels \u001B[38;5;241m=\u001B[39m \u001B[38;5;28;43mself\u001B[39;49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mmajor\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mformatter\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mformat_ticks\u001B[49m\u001B[43m(\u001B[49m\u001B[43mmajor_locs\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 1277\u001B[0m major_ticks \u001B[38;5;241m=\u001B[39m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39mget_major_ticks(\u001B[38;5;28mlen\u001B[39m(major_locs))\n\u001B[1;32m 1278\u001B[0m \u001B[38;5;28;01mfor\u001B[39;00m tick, loc, label \u001B[38;5;129;01min\u001B[39;00m \u001B[38;5;28mzip\u001B[39m(major_ticks, major_locs, major_labels):\n", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/matplotlib/ticker.py:216\u001B[0m, in \u001B[0;36mFormatter.format_ticks\u001B[0;34m(self, values)\u001B[0m\n\u001B[1;32m 214\u001B[0m \u001B[38;5;250m\u001B[39m\u001B[38;5;124;03m\"\"\"Return the tick labels for all the ticks at once.\"\"\"\u001B[39;00m\n\u001B[1;32m 215\u001B[0m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39mset_locs(values)\n\u001B[0;32m--> 216\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m [\u001B[38;5;28mself\u001B[39m(value, i) \u001B[38;5;28;01mfor\u001B[39;00m i, value \u001B[38;5;129;01min\u001B[39;00m \u001B[38;5;28menumerate\u001B[39m(values)]\n", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/matplotlib/ticker.py:216\u001B[0m, in \u001B[0;36m\u001B[0;34m(.0)\u001B[0m\n\u001B[1;32m 214\u001B[0m \u001B[38;5;250m\u001B[39m\u001B[38;5;124;03m\"\"\"Return the tick labels for all the ticks at once.\"\"\"\u001B[39;00m\n\u001B[1;32m 215\u001B[0m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39mset_locs(values)\n\u001B[0;32m--> 216\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m [\u001B[38;5;28;43mself\u001B[39;49m\u001B[43m(\u001B[49m\u001B[43mvalue\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mi\u001B[49m\u001B[43m)\u001B[49m \u001B[38;5;28;01mfor\u001B[39;00m i, value \u001B[38;5;129;01min\u001B[39;00m \u001B[38;5;28menumerate\u001B[39m(values)]\n", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/matplotlib/ticker.py:1066\u001B[0m, in \u001B[0;36mLogFormatterMathtext.__call__\u001B[0;34m(self, x, pos)\u001B[0m\n\u001B[1;32m 1064\u001B[0m \u001B[38;5;66;03m# only label the decades\u001B[39;00m\n\u001B[1;32m 1065\u001B[0m fx \u001B[38;5;241m=\u001B[39m math\u001B[38;5;241m.\u001B[39mlog(x) \u001B[38;5;241m/\u001B[39m math\u001B[38;5;241m.\u001B[39mlog(b)\n\u001B[0;32m-> 1066\u001B[0m is_x_decade \u001B[38;5;241m=\u001B[39m \u001B[43m_is_close_to_int\u001B[49m\u001B[43m(\u001B[49m\u001B[43mfx\u001B[49m\u001B[43m)\u001B[49m\n\u001B[1;32m 1067\u001B[0m exponent \u001B[38;5;241m=\u001B[39m \u001B[38;5;28mround\u001B[39m(fx) \u001B[38;5;28;01mif\u001B[39;00m is_x_decade \u001B[38;5;28;01melse\u001B[39;00m np\u001B[38;5;241m.\u001B[39mfloor(fx)\n\u001B[1;32m 1068\u001B[0m coeff \u001B[38;5;241m=\u001B[39m \u001B[38;5;28mround\u001B[39m(b \u001B[38;5;241m*\u001B[39m\u001B[38;5;241m*\u001B[39m (fx \u001B[38;5;241m-\u001B[39m exponent))\n", + "File \u001B[0;32m/opt/anaconda3/envs/homl3/lib/python3.10/site-packages/matplotlib/ticker.py:2237\u001B[0m, in \u001B[0;36m_is_close_to_int\u001B[0;34m(x)\u001B[0m\n\u001B[1;32m 2236\u001B[0m \u001B[38;5;28;01mdef\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[38;5;21m_is_close_to_int\u001B[39m(x):\n\u001B[0;32m-> 2237\u001B[0m \u001B[38;5;28;01mreturn\u001B[39;00m math\u001B[38;5;241m.\u001B[39misclose(x, \u001B[38;5;28;43mround\u001B[39;49m\u001B[43m(\u001B[49m\u001B[43mx\u001B[49m\u001B[43m)\u001B[49m)\n", + "\u001B[0;31mOverflowError\u001B[0m: cannot convert float infinity to integer" + ] + }, + { + "data": { + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "execution_count": 233 + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": "## Exercise 2.20 : Stability of Euler Explicit", + "id": "ee44f24a438fb7b6" + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T14:53:50.580505Z", + "start_time": "2025-03-03T14:53:50.577743Z" + } + }, + "cell_type": "code", + "source": [ + "def euler_implicit(N, T, u0, lam):\n", + " h = T / N\n", + " t = np.linspace(0, T, N + 1)\n", + " u = np.zeros(N + 1)\n", + " u[0] = u0\n", + " for n in range(N):\n", + " u[n + 1] = u[n] / (1 - lam * h)\n", + " return t, u" + ], + "id": "4484c71f50b8e691", + "outputs": [], + "execution_count": 164 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-03-03T14:54:19.153842Z", + "start_time": "2025-03-03T14:54:18.967497Z" + } + }, + "cell_type": "code", + "source": [ + "def f(t, x, lam):\n", + " return x * lam\n", + "\n", + "\n", + "T = 10 * 2 * np.pi\n", + "lam = 1j\n", + "N = 400\n", + "x0 = 1\n", + "\n", + "t, x_appr_EE = euler_explicit(N, T, x0, f, args=(lam,))\n", + "_, x_appr_EI = euler_implicit(N, T, x0, lam)\n", + "x_exact = x0 * np.exp(lam * t)\n", + "\n", + "# Plot the real parts\n", + "plt.figure(figsize=(12, 6))\n", + "plt.subplot(1, 2, 1)\n", + "plt.plot(t, np.real(x_appr_EI), label='Numerical Solution by EI')\n", + "plt.plot(t, np.real(x_appr_EE), label='Numerical Solution by EE')\n", + "plt.plot(t, np.real(x_exact), label='Exact Solution', linestyle='--')\n", + "plt.xlabel('Time')\n", + "plt.ylabel('Real Part')\n", + "plt.legend()\n", + "plt.title('Real Part of the Solution')\n", + "\n", + "# Plot the imaginary parts\n", + "plt.subplot(1, 2, 2)\n", + "plt.plot(t, np.imag(x_appr_EI), label='Numerical Solution by EI')\n", + "plt.plot(t, np.imag(x_appr_EE), label='Numerical Solution by EE')\n", + "plt.plot(t, np.imag(x_exact), label='Exact Solution', linestyle='--')\n", + "plt.xlabel('Time')\n", + "plt.ylabel('Imaginary Part')\n", + "plt.legend()\n", + "plt.title('Imaginary Part of the Solution')\n", + "\n", + "plt.show()" + ], + "id": "1b8a3146e7060c52", + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/tp/_ld5_pzs6nx6mv1pbjhq1l740000gn/T/ipykernel_61968/3352565519.py:7: ComplexWarning: Casting complex values to real discards the imaginary part\n", + " u[n + 1] = u[n] + h * f(t[n], u[n], *args)\n" + ] + }, + { + "data": { + "text/plain": [ + "
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" 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