{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "83556834-6ac7-4721-8121-4189de0b13d0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "from matplotlib . colors import ListedColormap\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a151b08e-688f-4a07-95c1-c0ad95232e0e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    y = np.array([\n",
    "        x[0]**5 - 10*x[0]**3 * x[1]**2 + 5 * x[0] * x[1]**4 - 1,\n",
    "        -5 * x[0]**4 * x[1] + 10 * x[0]**2 * x[1]**3 - x[1]**5\n",
    "    ])\n",
    "    \n",
    "    J = np.array([\n",
    "        [5*x[0]**4 - 10*3*x[0]**2 * x[1]**2 + 5 * x[1]**4, -10*x[0]**3 * 2 * x[1] + 5 * x[0] * 4 * x[1]**3 ],\n",
    "        [-5 * 4 * x[0] ** 3  * x[1] + 10 * x[0] * 2 * x[1]**3, -5 * x[0]**4 + 10 * x[0]**2 * x[1] ** 2 * 3 - 5*x[1]**4]\n",
    "    ])\n",
    "    \n",
    "    return y, J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "214d1930-4c0e-4aab-ae5e-bdc44dc3cd90",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def NewtonRn(fct,x0,tol=1e-6):\n",
    "    k = 0\n",
    "    x = x0\n",
    "    f, df =fct(x)\n",
    "    # f, df = fct(x)\n",
    "    # print(\"f=\",f,\"df=\", df, \"|f|=\",np.linalg.norm(f), tol)\n",
    "    while np.linalg.norm(f) > tol:\n",
    "        f, df = fct(x)\n",
    "        dfI = np.linalg.inv(df)\n",
    "        x = x - f@dfI\n",
    "        \n",
    "        k+=1\n",
    "        if k > 10:\n",
    "            break\n",
    "            \n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "59abd31c-26b5-4a71-9668-ecef255d54a4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.30901699 0.95105652]\n"
     ]
    }
   ],
   "source": [
    "p = np.array([1, 1])\n",
    "\n",
    "# print(f(p))\n",
    "\n",
    "x0 = np.array([1,1])\n",
    "xroot = NewtonRn(f, x0)\n",
    "print(xroot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4370d5c6-b098-484b-a577-9ce86ada4f02",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Erreur pour x0 =  [0. 0.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fonction a utiliser si on souhaite tracer les bassins d’attraction d’une fonction f\n",
    "def plot_newton_fractal (f , roots , h =0.007 , domain =( -2 , 2 , -2 , 2) ) :\n",
    "    colors = ['b', 'r', 'g', 'y','m'] # Liste de couleurs\n",
    "    xmin , xmax , ymin , ymax = domain\n",
    "    nbpixelsY = math . ceil (( ymax - ymin ) / h )\n",
    "    nbpixelsX = math . ceil (( xmax - xmin ) / h )\n",
    "    image = np . zeros (( nbpixelsY , nbpixelsX ) )\n",
    "    for j in range ( nbpixelsX ) :\n",
    "        for i in range ( nbpixelsY ) :\n",
    "            x0 = np . array ([ xmin + j *h , ymin + i * h ])\n",
    "            try:\n",
    "                r = NewtonRn (f , x0 ) #On appelle la methode ici !\n",
    "                if r is not False : image [i , j ] = np . argmin ( np . linalg . norm ( roots -r , axis =1) )\n",
    "            except:\n",
    "                print(\"Erreur pour x0 = \", x0)\n",
    "    plt . imshow ( image , cmap = ListedColormap ( colors [: len( roots ) ]) , origin ='lower')\n",
    "    plt . axis ('off')\n",
    "    plt . show ()\n",
    "# Definition des racines et trace des bassins d’attraction\n",
    "roots = np . array([[ -0.809 , -0.587] ,[0.309 , -0.951] ,[1.000 ,0.000] ,[0.309 ,0.951] ,[ -0.809 ,0.587]])\n",
    "x = plot_newton_fractal (f , roots, h=0.05 )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3811318-c08f-4fcc-8e6a-f35d9958548f",
   "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"
  }
 },
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}