259 lines
65 KiB
Plaintext
259 lines
65 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"id": "cd0f878e-2083-45d6-9537-13801b9f4ee9",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"import numpy as np\n",
|
|
"import matplotlib.pyplot as plt"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"id": "2aa18b72-6f8f-4512-8fe4-c29a3c3b17c3",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"relax=1/10"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"id": "ee56c13e-1946-47d3-8bdc-3045dc591009",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def fexamen(x):\n",
|
|
" f = np.array([ \n",
|
|
" x[0]**2 + x[1]**2 - 9 , \n",
|
|
" -x[0] + x[1] - 1\n",
|
|
" ])\n",
|
|
" J = np.array([\n",
|
|
" [ 2*x[0], 2*x[1] ],\n",
|
|
" [ -1, 1]\n",
|
|
" ])\n",
|
|
" \n",
|
|
" return f, J"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 55,
|
|
"id": "ca6950a5-a648-4654-98c2-b692750c30e9",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def NewtonRnRelax(fct, x0, tol=1e-6):\n",
|
|
" k=1\n",
|
|
" x=x0\n",
|
|
" listX = []\n",
|
|
" fx, Jx = fct(x)\n",
|
|
" \n",
|
|
" while np.linalg.norm(fx) >= tol and k < 1000:\n",
|
|
" listX.append(x)\n",
|
|
" # JxInv = np.linalg.inv(Jx)\n",
|
|
" # x = x - (relax * np.dot(JxInv, fx))\n",
|
|
" x = x - (relax * np.linalg.solve(Jx, fx))\n",
|
|
" \n",
|
|
" fx, Jx = fct(x)\n",
|
|
" k+=1\n",
|
|
" \n",
|
|
" listX.append(x)\n",
|
|
" return listX\n",
|
|
" "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 56,
|
|
"id": "3c9a95c9-40d7-4efa-93d2-01067473e8b8",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"[1.56155298 2.56155289]\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"x0 = np.array([10, 0]) \n",
|
|
"l = NewtonRnRelax(fexamen, x0)\n",
|
|
"print(l[-1])\n",
|
|
"theta = np.linspace(0, 2*np.pi, 40)\n",
|
|
"r = 3\n",
|
|
"x=r*np.cos(theta)\n",
|
|
"y=r*np.sin(theta)\n",
|
|
"plt.plot(x,y)\n",
|
|
"\n",
|
|
"# tracé droite\n",
|
|
"x = np.linspace(-5, 5, 40)\n",
|
|
"y=x+1\n",
|
|
"plt.plot(x,y)\n",
|
|
"\n",
|
|
"plt.plot([x[0] for x in l], [x[1] for x in l], 'or')\n",
|
|
"\n",
|
|
"plt.xlabel('x1')\n",
|
|
"plt.ylabel('x2')\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 36,
|
|
"id": "e5402726-5acd-4c1a-9a1d-c6cebc91da0c",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Intersection du cercle et de la droite: [1.56155298 2.56155289]\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Intersection cercle et droite\n",
|
|
"\n",
|
|
"print(\"Intersection du cercle et de la droite:\", l[-1])\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 41,
|
|
"id": "2be93022-5a6c-436a-bcaa-c88cb1b89501",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"[-2.56155291 -1.56155295]\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Autre intersection (autre x0)\n",
|
|
"x0 = np.array([-4, -4])\n",
|
|
"l = NewtonRnRelax(fexamen, x0)\n",
|
|
"print(l[-1])\n",
|
|
"\n",
|
|
"theta = np.linspace(0, 2*np.pi, 40)\n",
|
|
"r = 3\n",
|
|
"x=r*np.cos(theta)\n",
|
|
"y=r*np.sin(theta)\n",
|
|
"plt.plot(x,y)\n",
|
|
"\n",
|
|
"# tracé droite\n",
|
|
"x = np.linspace(-5, 5, 40)\n",
|
|
"y=x+1\n",
|
|
"plt.plot(x,y)\n",
|
|
"\n",
|
|
"plt.plot([x[0] for x in l], [x[1] for x in l], 'or')\n",
|
|
"\n",
|
|
"plt.xlabel('x1')\n",
|
|
"plt.ylabel('x2')\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 47,
|
|
"id": "95ad5b3c-ad20-42d8-9db3-8cbfe0e12e96",
|
|
"metadata": {
|
|
"tags": []
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"[[ 0 0]\n",
|
|
" [-1 1]] det= 0.0 Pas inversable :(\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# x0 posant problème?\n",
|
|
"# (0,0)\n",
|
|
"x0 = np.array([0,0])\n",
|
|
"fx, J = fexamen(x0)\n",
|
|
"print(J, \"det=\", np.linalg.det(J), \"Pas inversable :(\")\n",
|
|
"\n",
|
|
"# l = NewtonRnRelax(fexamen, np.array([0,0]))\n",
|
|
"\n",
|
|
"# print(l[-1])\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "ac961713-f133-4254-8065-226906413cc0",
|
|
"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": "3.11.5"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|