path: root/PVCM/cama/fr/ma41 Convergence de Jacobi avec inertie.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as lin\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n",
    "plt.style.use(['seaborn-v0_8-whitegrid','data/cours.mplstyle'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Dans ce cours on regarde 2 points :\n",
    "    \n",
    "* comment améliorer Jacobi\n",
    "* la convergence des algorithmes itératifs (comment la comprendre et bien l'exploiter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "## Ajouter de l'inertie à Jacobi\n",
    "\n",
    "La méthode de Jacobi mène au système itératif suivant\n",
    "\n",
    "$$\n",
    "{\\bf x}^{k+1} = M^{-1} \\, ( N\\; {\\bf x}^k + {\\bf b})\n",
    "$$\n",
    "\n",
    "On a vu que cette méthode ne converge que si la matrice B a son rayon spectral inférieur à 1, $\\rho(M^{-1}\\,N) < 1$.\n",
    "\n",
    "On peut modifier cette méthode pour qu'elle ait un plus grand rayon de convergence\n",
    "et donc converge pour plus de matrices. Pour cela on ajoute de l'inertie :\n",
    "\n",
    "$$\n",
    "{\\bf x}^{k+1} =  w \\, M^{-1} \\, (N\\; {\\bf x}^k + {\\bf b}) + (1-w) \\, {\\bf x}^k\n",
    "$$\n",
    "\n",
    "avec $0 < w \\le 1$.\n",
    "\n",
    "Si $w = 1$ alors on a Jacobi classique et si $w = 0$ alors on ne bouge pas, ${\\bf x}^{k+1} = {\\bf x}^k$.\n",
    "\n",
    "On parle d'inertie car on voit qu'on avance moins vite puisque la nouvelle valeur de ${\\bf x}^{k+1}$\n",
    "est comprise entre l'ancienne  valeur de ${\\bf x}^{k+1}$ et ${\\bf x}^k$.\n",
    "\n",
    "\n",
    "Note : $w \\, {\\bf a} + (1-w) \\, {\\bf b}$ représente le segment $[{\\bf b}, {\\bf a}]$ lorsque $w$ varie entre 0 et 1.\n",
    "\n",
    "L'idée est qu'avec l'intertie on va peut-être entre dans la zone de convergence alors que sans on aurait sauté\n",
    "par dessus.\n",
    "\n",
    "Cette méthode s'appelle la **surrelaxation** (*over-relaxation* en anglais), je ne sais pas pourquoi."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "### Programmons l'inertie pour Jacobi\n",
    "\n",
    "On commence par un Jacobi simple pour vérifier qu'on diverge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A:\n",
      " [[5 7 6 0]\n",
      " [1 7 2 5]\n",
      " [5 6 5 1]\n",
      " [0 6 3 7]] \n",
      "b:\n",
      " [18 15 17 16] \n",
      "\n",
      "M:\n",
      " [[5 0 0 0]\n",
      " [0 7 0 0]\n",
      " [0 0 5 0]\n",
      " [0 0 0 7]]\n",
      "N:\n",
      " [[ 0 -7 -6  0]\n",
      " [-1  0 -2 -5]\n",
      " [-5 -6  0 -1]\n",
      " [ 0 -6 -3  0]]\n",
      "\n",
      "x_0 = [0.062 0.652 0.185 0.852]\n",
      "x_1 = [2.465 1.472 2.384 1.647]\n",
      "x_2 = [-1.322 -0.067 -1.161  0.002]\n",
      "x_3 = [5.088 2.662 4.803 2.841]\n",
      "x_4 = [-5.89  -1.986 -5.451 -2.055]\n",
      "x_5 = [12.921  6.009 12.084  6.324]\n",
      "x_6 = [-19.314  -7.672 -17.997  -8.044]\n",
      "x_7 = [35.937 15.79  33.53  16.575]\n",
      "x_8 = [-58.741 -24.41  -54.8   -25.618]\n",
      "x_9 = [103.534  44.49   96.557  46.694]\n",
      "x_10 = [-174.554  -73.588 -162.861  -77.23 ]\n",
      "x_11 = [302.056 128.775 281.706 135.159]\n",
      "x_12 = [-514.732 -218.038 -480.218 -228.824]\n",
      "x_13 = [885.114 376.327 825.542 394.983]\n",
      "x_14 = [-1513.908  -642.302 -1412.303  -674.084]\n",
      "x_15 = [2597.587 1103.419 2422.887 1158.103]\n",
      "x_16 = [-4448.651 -1888.411 -4149.91  -1981.882]\n",
      "x_17 = [7627.267 3238.983 7114.521 3399.456]\n",
      "x_18 = [-13068.402  -5548.37  -12190.539  -5823.066]\n",
      "x_19 = [22399.965  9511.401 20894.459  9982.548]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(799)\n",
    "\n",
    "A = np.random.randint(10, size=(4,4))\n",
    "b = A.sum(axis=1)                     # ainsi la solution est [1,1,1,1]\n",
    "print('A:\\n', A, \"\\nb:\\n\", b, \"\\n\")\n",
    "\n",
    "M = np.diag(A)        # attention, c'est un vecteur\n",
    "N = np.diag(M) - A    # np.diag d'une matrice donne un vecteur, np.diag d'un vecteur donne une matrice\n",
    "print(f\"M:\\n {np.diag(M)}\\nN:\\n {N}\\n\")\n",
    "\n",
    "x0 = np.random.random(4)\n",
    "x = x0\n",
    "for i in range(20):\n",
    "    print(f\"x_{i} = {x}\")\n",
    "    x = (N @ x + b) / M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Ajoutons maintenant l'inertie à Jacobi :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_0 = [0.062 0.652 0.185 0.852]\n",
      "x_1 = [1.264 1.062 1.284 1.25 ]\n",
      "x_2 = [0.918 0.882 0.948 1.037]\n",
      "x_3 = [1.072 0.941 1.082 1.08 ]\n",
      "x_4 = [1.028 0.925 1.032 1.048]\n",
      "x_5 = [1.047 0.939 1.042 1.049]\n",
      "x_6 = [1.041 0.943 1.029 1.042]\n",
      "x_7 = [1.043 0.949 1.024 1.039]\n",
      "x_8 = [1.042 0.954 1.017 1.036]\n",
      "x_9 = [1.043 0.959 1.011 1.034]\n",
      "x_10 = [1.044 0.962 1.005 1.032]\n",
      "x_11 = [1.045 0.966 1.    1.031]\n",
      "x_12 = [1.046 0.969 0.995 1.03 ]\n",
      "x_13 = [1.048 0.971 0.99  1.03 ]\n",
      "x_14 = [1.05  0.973 0.986 1.029]\n",
      "x_15 = [1.053 0.974 0.981 1.029]\n",
      "x_16 = [1.056 0.976 0.977 1.03 ]\n",
      "x_17 = [1.059 0.977 0.972 1.03 ]\n",
      "x_18 = [1.063 0.977 0.968 1.031]\n",
      "x_19 = [1.067 0.978 0.963 1.032]\n"
     ]
    }
   ],
   "source": [
    "x = x0    # on reprend la même valeur initiale sinon la comparaison serait faussée\n",
    "w = 0.5   # on choisit w \n",
    "for i in range(20):\n",
    "    print(f\"x_{i} = {x}\")\n",
    "    x = w * (N @ x + b) / M + (1-w) * x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "La solution recherchée étant [1,1,1,1] ca semble bien marcher !\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "### Étudions la convergence\n",
    "\n",
    "Pour bien comprendre une méthode itérative il faut étudier sa convergence et donc tracer une courbe\n",
    "de l'erreur absolue (lorsqu'on connait la solution), ou de l'erreur relative (entre 2 ${\\bf x}^i$ successifs)\n",
    "ou du résidu ($||A \\, {\\bf x}^i - {\\bf b}||$) ou de toute autre mesure qui a du sens.\n",
    "\n",
    "Regardons :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 427,
       "width": 832
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = x0    # on reprend la même valeur initiale sinon la comparaison serait faussée\n",
    "w = 0.5   # on choisit w \n",
    "error = [np.square(x - np.ones(4)).sum()]\n",
    "for i in range(20):\n",
    "    x = w * (N @ x + b) / M + (1-w) * x\n",
    "    error.append(np.square(x - np.ones(4)).sum())\n",
    "plt.plot(range(len(error)), error);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "A priori cela semble bien, sauf qu'en fait on ne voit rien car l'échelle empêche de voir ce qui se passe à\n",
    "la fin.\n",
    "\n",
    "Regardons en échelle logarithmique :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 425,
       "width": 832
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(len(error)), error)\n",
    "plt.semilogy();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Oula, la fin fait peur...\n",
    "\n",
    "Moralité : **Il faut toujours regarder une erreur en échelle logarithmique.** \n",
    "\n",
    "Puiqu'on mesure quelque chose \n",
    "qui doit tendre vers 0, avec une echelle normale on est vite écrasé et donc on ne voit pas si on est à \n",
    "$10^{-3}$ ou $10^{-6}$ alors que c'est très très différent.\n",
    "\n",
    "De même si on diverge on ne verra pas le début car un échelle linéraire s'ajustera sur les dernières valeurs qui \n",
    "peuvent être très grandes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Reprenons notre calcul sur plus d'itérations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 449,
       "width": 832
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = x0    # on reprend la même valeur initiale sinon la comparaison serait faussée\n",
    "w = 0.5   # on choisit w \n",
    "error = [np.square(x - np.ones(4)).sum()]\n",
    "for i in range(200):\n",
    "    x = w * (N @ x + b) / M + (1-w) * x\n",
    "    error.append(np.square(x - np.ones(4)).sum())\n",
    "plt.plot(range(len(error)), error)\n",
    "plt.title('Erreur absolue')\n",
    "plt.semilogy();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Donc on s'est approché de la solution puis on a divergé ce qui est mieux que de diverger directement.\n",
    "\n",
    "#### Erreur relative \n",
    "\n",
    "Aurait-on pu le voir si on n'avait pas connu la solution ? Regardons l'écart entre 2 ${\\bf x}^k$ successifs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "lang": "fr"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HCzoEAABARSEAKoPffvtNX375pf78809lZGQoKChIV199tYYPH64bbrihotsDAAAAAFQjG/alaPKSOO05nmG31tvDqOFdm+nRnuGqFeDtgu4AAABQ0QiAHDRr1iy98847MhgM6ty5s5o0aaIDBw5o3bp1WrdunSZMmKARI0ZUdJsAAAAAADf317GzenNpnDbsO2231mCQbm8XqrH9I9W4lr8LugMAAEBlQQDkgB07dujdd9+Vl5eXPvnkE3Xp0sX63KJFizRx4kS9/fbbGjBggBo1alSBnQIAAAAA3NWR1By9tTxei/887lD9jZF1NSEmWq0b1XByZwAAAKiMjBXdQFXw3XffyWKx6M4777QJfyTpjjvuUKtWrVRYWKj169dXUIcAAAAAAHeVml2gV376W33eXudQ+NM2NFhzH7hec+67jvAHAACgGuMOIAfcfvvtatu2rTp06FDq882bN9fevXt16tQpF3cGAAAAAHBXuQVF+mxTkmau3a/MfJPd+qYh/ho3IEq3tG0oo9Hggg4BAABQmREAOaBTp07q1KnTRZ8/H/yEhIS4qiUAAAAAgJsyFZm1YPtRvbsyQckZ+XbrQwK89XjvcP3r+mby9mSgDwAAAJxTZQKgP/74Q08//bSOHDkiSZo0aZLuuOMOh7dPTEzUokWLtHHjRiUnJysnJ0e1a9dWRESEYmJiNHDgQHl5eZW5r6SkJO3YsUNGo1E9evQo8/YAAAAAAEiSxWLRir+TNWVZvBJPZdmt9/Py0APdw/TQjS0U5Fv2/z8LAAAA91bpA6DCwkJNnz5dn3zyiYqKii5rHzNmzNBHH32kwsJCm/UnTpzQiRMntH79es2ZM0fvv/++mjdv7vB+CwoKNGHCBJnNZg0aNEhNmjS5rP4AAAAAANXb9kOpmvRLnLYdSrNb62E06O5OTfRknwjVq+Hrgu4AAABQFVXqAGj//v166qmntGfPHkmSh4dHmUOgmTNnatq0aZKkwMBADR06VJ07d1ZgYKCOHDmiBQsWaNOmTYqLi9P999+v+fPnq3bt2nb3m5eXp9GjR+vPP/9UeHi4nnnmmbK/QQDA/2Pvz+OjrO/9//85M5nsISsJkI0ESAKCbC6IoiIgYD16tLTHU/Voq1VcaKsHReqvx8/nc35HUFDQYiu19VhrrbUuR2tlR9ncAQWRLEAISYCQfZsss33/8BiJSbgGyExmedxvt946XvO6Jk/0bZzMM9f1BgAACGkHTrRo2bpCrdtX5dH87HPS9MDsAo1MjfVyMgAAAAQ6vy2AXnnlFT366KPq6OhQWFiY7rrrLpWVlentt9/2+DUOHTrUVf4kJCTolVdeUU5OTtfz48aN01VXXaUlS5bohRdeUEVFhZYvX64lS5ac8nWbmpo0f/587dy5U7m5uXr++ecVExNzZn9QAAAAAEDIOdHUrhUbS/TqZ+VyutyG8+dlJ2rxVQWanM3eswAAAPCM3+4O+dJLL6mjo0Pp6el66aWXdO+998pisZzWazz77LNdVwwtWrSoW/lzsoULFyo7O1uS9NZbb3XtM9Sbqqoq3Xjjjdq5c6fOPfdc/fnPf1ZaWtpp5QIAAAAAhKbmdruWryvSZcve118+OWJY/oxMjdVz/3ae/jb/IsofAAAAnBa/LYAk6eqrr9Zbb72liRMnnva5nZ2d2rRpkyRp0KBBuvrqq/uctVqtmjdvniTJ6XRq/fr1vc5VV1frRz/6kYqLizV9+nS9+OKLSkriDTgAAAAA4NQ6HS79945SXbbsfa1674Da7Ke+vXnaoAgtvX6c1v58mmaNSZPJZPJRUgAAAAQLv70F3MMPP6yLLrrojM/ftWuXWlpaJEmTJk1SeHj4KeenTJnS9XjLli267bbbuj3f0tKiO+64QxUVFbruuuv0X//1X6d9RRIAAAAAILS4XG69s/eYlq8r0pE6m+F8XESY5l8+Qj+5OEdR4fzMCQAAgDPntwXQ2ZQ/klRSUtL1ePTo0YbzBQUFMplMcrvdKi4u7vH8L3/5S3311VeaO3euHn30UZnNfn3xFAAAAABggO04UKOlawq1t7LRcNZqMenmKcN17xUjlRRz6l9gBAAAADzhtwXQ2SotLe16PGzYMMP58PBwpaSkqLq6WvX19aqvr1diYqKkr68IWrdunbKzs/u9/HG73ers7Oy31wtkdru918dAoGANI9CxhhEMWMcIdKzh4LD/eLOWry/RtgO1Hs1fc+4Q/XzGSGUmRklSQP+MyBpGoGMNI9CxhhHoQn0Nu92n3h/ydAVtAVRXV9f12NN9epKSklRdXd11/jcF0HPPPdf1/IoVK/o8Pzs7WzfddNNp5XQ4HNq7d+9pnRMKCgsLBzoCcFZYwwh0rGEEA9YxAh1rOPCcaHXoL1+2aNuRdnnyo/v4tHDdNC5OuYlSQ8UBNVR4PaJPsYYR6FjDCHSsYQQ61vDZC9oCyGb79t7KERERHp1z8tzJ5x89elSStHv3bu3evbvP8y+44ILTLoAAAAAAAIGtucOl1wtbtOaATQ6X8XxOQphuPjdO49M8+1kVAAAAOBNBWwB1dHR0PbZarR6dEx7+7X2WTz5/8+bN/RfsO8LCwjzaoygU2O32rla3oKDA439ugL9gDSPQsYYRDFjHCHSs4cDSbnfqjx8e0e+2H1Zzu8NwPiMhUvfNHKnvjR0is9nkg4S+xxpGoGMNI9CxhhHoQn0N79+/Xw6H8ftKTwVtAXTy1Tye3j/55LnIyMh+z9Qbk8nUrXjC16xWK39fENBYwwh0rGEEA9YxAh1r2H85XW69vrNCT24o1vGmdsP5xGir7r1ilG6akqWIMIsPEvoH1jACHWsYgY41jEAXimvYZOrfXxIK2gIoOjq66/HJV/OcSnv7t2/cY2Ji+j0TAAAAACBwud1ubdp/Qo+tLVTJiRbD+UirWbddkqM7LxuhQZGh9durAAAAGHhBWwClpKR0Pa6pqfHonBMnTvR6PgAAAAAgtO06Uq+l7xbqk8N1hrNmk/TD8zL1i5l5GhLvm7tLAAAAAN8VtAVQbm5u1+OjR48azttsNjU0NEiSUlNTFRcX561oAAAAAIAAcbC6RcvWFmntvuMezc8ak6ZFc/I1MpWfKQEAADCwgrYAGj16dNfjffv2Gc7v2bOn6/GYMWO8kgkAAAAAEBhONLfrqY0leuXTcjldbsP5ydmJemhugc4fnuSDdAAAAICxoC2Axo8fr6SkJNXV1Wn37t1qbW095b4+27Zt63o8Y8YMX0QEAAAAAPiZlg6HfrfloJ7bVqo2u9NwPndwjBbNKdCVY9L6fdNeAAAA4GyYBzqAt5jNZs2dO1fS17d3e/PNN/ucbWlp6Xo+OjpaM2fO9ElGAAAAAIB/6HS49McPDuuyx9/T05sPGJY/g+Mi9Oh147T+F5dq9jlDKH8AAADgd4L2CiBJuvPOO/X666+rvb1dK1as0Pnnn6/8/PxuM06nU4888ohqa2slSbfccouSkrhkHwAAAABCgdvt1jt7jmn5+iKV1doM52MjwjT/slz95JIcRYcH9Y/UAAAACHB++W61tra2q5A5WVNTU9fjqqoqFRcXd3vearUqJyen66/T0tL0q1/9Sg8//LBaWlp0ww036Oabb9bUqVMVHR2t0tJSvfzyy/r8888lSRMmTND8+fO984cCAAAAAPiVDw7WaOmaQu2paDSctVpMuvHCbC24YqSSYyN8kA4AAAA4O35ZAL388statWrVKWdWrlyplStXdjuWnp6uzZs3dzs2b948dXR06PHHH5fNZtPq1au1evXqHq93ySWXaNmyZYqMjDzr/AAAAAAA/7X/WJOWrinUluJqj+avGT9MC6/MV1ZytJeTAQAAAP3HLwug/nbjjTdq2rRpevXVV7V161YdP35c7e3tSklJ0dixY3XNNdew7w8AAAAABLnKhjY9sb5Ib+6ulNttPH/xyGQ9NGe0xmXEez8cAAAA0M/8sgBasGCBFixY0K+vmZWVpYULF2rhwoX9+roAAAAAAP/WYOvUb94/qBc+OKxOh8twfvTQQVo8t0DTRqXIZDL5ICEAAADQ//yyAAIAAAAA4Gy125164YPD+s17B9TU7jCcT0+I0sLZebp2fLrMZoofAAAABDYKIAAAAABAUHG63HpjV4We3FCsY43thvMJ0VbdO32kbpqSrUirxQcJAQAAAO+jAAIAAAAABAW32633ik7osTVFKqpqNpyPCDPrJ5fkaP5lIxQfZfVBQgAAAMB3KIAAAAAAAAFv95F6LV1TqI9L6wxnzSZp3uQM3TcrT0Pjo3yQDgAAAPA9CiAAAAAAQMAqrWnVsnWFenfvcY/mZ45O1YNzCpSXFuflZAAAAMDAogACAAAAAASc6uYOPb2pRH/55IgcLrfh/MSsBC2eO1oX5CT5IB0AAAAw8CiAAAAAAAABo6XDoee2HtJz2w7J1uk0nM9NidGDc/I1+5whMplMPkgIAAAA+AcKIAAAAACA37M7XXrlkyN6alOJalo6DedTYiP0i5mj9C/nZ8pqMfsgIQAAAOBfKIAAAAAAAH7L7Xbr3b3HtWxdoQ7X2gznY8ItuvOyEbrtkhzFRPAjLwAAAEIX74YBAAAAAH7po0O1WrKmUF+UNxjOhplNuvHCLC2YMUopsRHeDwcAAAD4OQogAAAAAIBfKTzepMfXFmlz4QmP5q8+d6gWXpmv4SkxXk4GAAAABA4KIAAAAACAXzja0KYnNxTr9V0VcruN5y/KTdZDcws0PjPB69kAAACAQEMBBAAAAAAYUI02u37z/gH99weH1elwGc4XDInTorkFujxvsEwmkw8SAgAAAIGHAggAAAAAMCDa7U69+OFhPfPeQTW22Q3n0xOidP+sPP3zxHRZzBQ/AAAAwKlQAAEAAAAAfMrpcut/dlfqyQ3FqmxoM5yPj7Lq3ukjdfNF2Yq0WnyQEAAAAAh8FEAAAAAAAJ9wu916v7haj60pVOHxZsP58DCzfnzxcN192UjFR1t9kBAAAAAIHhRAAAAAAACv21PRoCXvFurDQ7WGsyaTNG9Shu6bladhCVE+SAcAAAAEHwogAAAAAIDXHK5p1bL1RfrHnmMezV9RkKpFcwqUPyTOy8kAAACA4EYBBAAAAADodzUtHfr1phL9+eMjcrjchvPjMxO0eG6BpuQm+yAdAAAAEPwogAAAAAAA/aa1w6HfbyvV77YeVGun03A+JyVGD8zO19yxQ2QymXyQEAAAAAgNFEAAAAAAgLNmd7r010/LtXJjiWpaOgznU2LD9fMZo3TDBVmyWsw+SAgAAACEFgogAAAAAMAZc7vdWvvlcS1bV6RDNa2G89HhFt1xaa5un5ar2Ah+JAUAAAC8hXfbAAAAAIAz8klpnZas2a/dRxoMZ8PMJv3rBVn62YxRGhwX4f1wAAAAQIijAAIAAAAAnJbiqmY9vrZQG/ef8Gj+e+OGauHsfOWkxHg5GQAAAIBvUAABAAAAADxyrLFNKzYU67WdFXK5jecvzEnS4qtGa0JmgtezAQAAAOiOAggAAAAAcEqNbXY9u+Wgnt9eqg6Hy3A+Py1OD80t0OX5g2UymXyQEAAAAMB3UQABAAAAAHrV4XDqTx+WadV7B9RgsxvOD42P1P2z8nT9pAxZzBQ/AAAAwECiAAIAAAAAdONyufU/n1fqifXFqmxoM5wfFBmmu6eP1K1ThyvSavFBQgAAAABGKIAAAAAAAJIkt9utrSU1WrqmUPuPNRnOh4eZdevU4br78hFKiA73QUIAAAAAnqIAAgAAAABob0Wjlq7drx0Hag1nTSbp+okZuv/KPKUnRPkgHQAAAIDTRQEEAAAAACHsSK1Ny9YX6e9fHPVo/vL8wVo0p0Cjhw7ycjIAAAAAZ4MCCAAAAABCUG1Lh369+YD+/HGZ7E634fy5GfF6aG6Bpo5I8UE6AAAAAGeLAggAAAAAQoit06E/bCvV6q2H1NLhMJzPTo7WA7Pz9b1xQ2UymXyQEAAAAEB/oAACAAAAgBDgcLr06mcVWrmxWCeaOwznk2PC9bMZo/SvF2QpPMzsg4QAAAAA+hMFEAAAAAAEMbfbrXX7qvT4ukIdqm41nI8Ot+j2abn66bQcxUVafZAQAAAAgDdQAAEAAABAkPrscJ2WrCnUzrJ6w1mL2aQbzs/Uz2eOUmpcpA/SAQAAAPAmCiAAAAAACDIHTjRr6Zoibdxf5dH83LFDtHB2vkYMjvVyMgAAAAC+QgEEAAAAAEGiqqldKzYU69XPyuVyG89fMDxJD11VoElZid4PBwAAAMCnKIAAAAAAIMA1tdu1estB/WF7qdrtLsP5vLRYLZpToCsKUmUymXyQEAAAAICvUQABAAAAQIDqcDj10kdHtGpzieptdsP5IYMidf+sPH1/coYsZoofAAAAIJhRAAEAAABAgHG53Pr7nqNatq5IFfVthvNxkWG6+/KRunXqcEWFW3yQEAAAAMBAowACAAAAgACyraRaS9cUat/RJsPZcItZ/3ZRtu6ZPlKJMeE+SAcAAADAX1AAAQAAAEAA+LKyUY+tLdS2khrDWZNJ+ucJ6bp/Vp4yk6J9kA4AAACAv6EAAgAAAAA/Vl5n0/L1RXrr86MezV+aN1iL5uTrnGHxXk4GAAAAwJ9RAAEAAACAH6pr7dTv1h3QSx+VqdPpMpwfmz5Ii+eO1sUjU3yQDgAAAIC/owACAAAAAD/S4XDrnZJWvf32DrV0OAznM5Oi9MDsAl09bqjMZpMPEgIAAAAIBBRAAAAAAOAHHE6XXt1ZoSfXVauu3fiKn6SYcC24YqRuvDBb4WFmHyQEAAAAEEgogAAAAABgALndbm34qkqPryvSgRMthvNRVotun5ajOy7NVVyk1QcJAQAAAAQiCiAAAAAAGCA7y+q05N1CfVZWbzhrMZv0w/Mydd/MUUodFOmDdAAAAAACGQUQAAAAAPjYgRMtWrauUOv2VXk0P/ucND0wu0AjU2O9nAwAAABAsKAAAgAAAAAfOdHUrhUbS/TqZ+VyutyG8+dlJ2rxVQWanJ3kg3QAAAAAggkFEAAAAAB4WXO7Xau3HNIftpeqze40nE+Ps+jhq8dq7rnpMplMPkgIAAAAINhQAAEAAACAl3Q6XPrzx2X69eYDqmvtNJxPjYvQ9/MiNH14lCaMTqX8AQAAAHDGKIAAAAAAoJ+5XG69s/eYlq8r0pE6m+F8XESY5l8+Qjedn64DRV/5ICEAAACAYEcBBAAAAAD9aMeBGi1dU6i9lY2Gs1aLSTdPGa57rxippJhwdXYaXyUEAAAAAJ6gAAIAAACAfvDV0SYtXVuorcXVHs3/84Rh+vcr85WZFO3lZAAAAABCEQUQAAAAAJyF8jqbntxQrP/5vFJut/H8tFEpWjSnQGPT470fDgAAAEDIogACAAAAgDNQ39qpZ947oBc/LFOn02U4f86wQXpoboGmjRrsg3QAAAAAQh0FEAAAAACchna7U8/vKNVv3z+o5naH4XxGYpQemJ2vfzp3mMxmkw8SAgAAAAAFEAAAAAB4xOly6/WdFXpyQ7GON7UbzidGW3XvFaN005QsRYRZfJAQAAAAAL5FAQQAAAAAp+B2u7Vp/wk9trZQJSdaDOcjrWbddkmO7rxshAZFWn2QEAAAAAB6ogACAAAAgD7sOlKvpe8W6pPDdYazZpP0w/My9YuZeRoSH+mDdAAAAADQNwogAAAAAPiOg9UtWra2SGv3HfdoftaYNC2ak6+RqXFeTgYAAAAAnqEAAgAAAID/daK5XU9tLNErn5bL6XIbzk/KStDiq0br/OFJPkgHAAAAAJ6jAAIAAAAQ8lo6HPrdloN6blup2uxOw/ncwTFaNKdAV45Jk8lk8kFCAAAAADg9FEAAAAAAQlanw6W/fHJET28qUW1rp+H84LgI3TczTz88L0NhFrMPEgIAAADAmaEAAgAAABBy3G633tlzTMvXF6ms1mY4HxsRpjsvzdVt03IUHc6PUQAAAAD8Hz+5AAAAAAgpHxys0dI1hdpT0Wg4a7WYdOOF2VpwxUglx0b4IB0AAAAA9A8KIAAAAAAhYf+xJi1dU6gtxdUezV8zfpgWXpmvrORoLycDAAAAgP5HAQQAAAAgqFU2tOmJ9UV6c3el3G7j+YtHJuuhOaM1LiPe++EAAAAAwEsogAAAAAAEpQZbp37z/kG98MFhdTpchvOjhw7SQ3MLdOmoFJlMJh8kBAAAAADvoQACAAAAEFTa7U698MFh/ea9A2pqdxjOpydEaeHsPF07Pl1mM8UPAAAAgOBAAQS/4/LkvhwAAADAdzhdbr2xq0JPbijWscZ2w/mEaKvunT5SN03JVqTV4oOEAAAAAOA7FEDwG7uPNOiXG2tU1ujQuI8/0ZP/MlE5KTEDHQsAAAB+zu12672iE3psTZGKqpoN5yPCzPrJJTmaf9kIxUdZfZAQAAAAAHyPAgh+oandrnte+UI1LV/fomN3eaNu++On2nT/Zdx/HQAAAH3afaReS9cU6uPSOsNZs0maNzlD983K09D4KB+kAwAAAICBQwEEv1B0vFk1LZ3djh2qbtWXlU0alxE/QKkAAADgr0prWrVsXaHe3Xvco/mZo1P14JwC5aXFeTkZAAAAAPgHCiD4hU6Hq9fjh2tbKYAAAADQpbq5Q09vKtFfPjkih8t478iJWQl6aE6BLsxN9kE6AAAAAPAfFEDwCxmJvd+Co7KhzcdJAAAA4I9aOhx6bushPbftkGydTsP53JQYPTgnX7PPGcIthQEAAACEJAog+IWh8VEymST3d36Js6LeNjCBAAAA4BfsTpde+eSIntpU0uOWwb1JiY3QL2aO0r+cnymrxeyDhAAAAADgnyiA4BfCw8xKjYtQVVNHt+OV9VwBBAAAEIrcbrfe3Xtcy9YV6nCt8S8FxYRbdOdlI3TbJTmKieDHHAAAAADgJyP4jfT4yB4FUAUFEAAAQMj56FCtlqwp1BflDYazYWaTbrwwSwtmjFJKbIT3wwEAAABAgKAAgt8YlhClXeWN3Y5VNrTJ7XZz33YAAIAQUHi8SY+vLdLmwhMezX/v3KF64Mp8DU+J8XIyAAAAAAg8FEDwG+kJkT2O2TqdqrfZlRQTPgCJAAAA4AtHG9r05IZivb6roseekL25KDdZD80t0PjMBK9nAwAAAIBARQEEv5GeENXr8cr6NgogAACAINRos+s37x/Qf39wWJ0Ol+F8wZA4LZpboMvzBnOFOAAAAAAYoACC3+jtCiBJqqi3aVxGvI/TAAAAwFva7U69+OFhPfPeQTW22Q3nh8VH6t+vzNc/T0yXxUzxAwAAAACeoACC3xjW1xVADW0+TgIAAABvcLrc+p/dlXpyQ7FH7/Hio6y6Z/oI/dtFwxVptfggIQAAAAAEDwog+I2+rwCiAAIAAAhkbrdb7xdX67E1hSo83mw4Hx5m1o8vHq67Lxup+GirDxICAAAAQPChAILfiLRaFB9hVmNH9/u/UwABAAAErj0VDVrybqE+PFRrOGsySd+flKH7Z+X1eXU4AAAAAMAzFECnoaioSKtXr9Ynn3yihoYGJScna+rUqbr77ruVmZk50PGCQmqMpZcCyDZAaQAAAHCmDte0atn6Iv1jzzGP5q8oSNWDc/JVMGSQl5MBAAAAQGigAPLQ9u3bNX/+fDkcDk2ZMkVZWVk6ePCg3njjDa1fv15//vOfVVBQMNAxA15KtEUldd03AmYPIAAAgMBR09KhX28q0Z8/PiKHy204Pz4zQYvnFmhKbrIP0gEAAABA6KAA8oDNZtMDDzwgu92up556SnPmzOl67oUXXtCSJUt0//3365133pHZbB7ApIEvNabn5r7N7Q41ttkVH8X93wEAAPxVa4dDv99Wqt9tPajWTqfh/PDkaD0wu0BXjRsik8nkg4QAAAAAEFoogDzw5ptvqq6uTtOnT+9W/kjSrbfeqtdff13FxcXasmWLpk+fPkApg8Pg6N4LtMr6NgogAAAAP2R3uvTXT8u1cmOJalo6DOdTYsP18xmjdMMFWbJa+OUpAAAAAPAWCiAPbNmyRZJ05ZVX9vr8zJkzVVxcrPfee48C6Cz1dgWQ9PVt4MYM437wAAAA/sLtdmvtl8e1bF2RDtW0Gs5Hh1t0x6W5un1armIj+DEEAAAAALyNn7w88NVXX0mSRo8e3evzY8aMkSTt27fPZ5mC1eDo3guginqbj5MAAACgL5+U1mnJmv3afaTBcDbMbNK/XpCln80YpcFxEd4PBwAAAACQFEAF0K5du/Tggw+qvLxckrRkyRJdf/31Hp9/4MABvfHGG9q+fbuqqqpks9mUnJysUaNGac6cObrmmmtktfa8xVhHR4eqq6slSWlpab2+9jfHKyoqTvePhe/oqwCqrG/zcRIAAAB8V3FVsx5fW6iN+094NP+9cUO1cHa+clJivJwMAAAAAPBdfl8A2e12rVq1Ss8995ycTuPNZHvzzDPP6Le//a3sdnu348eOHdOxY8e0detWvfjii3rqqac0fPjwbjMtLS1dj2NjY3t9/ZiYr3+gbW5uPqN8+FaU1azYcJNaOt3djldQAAEAAAyYY41tWrGhWK/trJDLbTx/YU6SFl81WhMyE7yeDQAAAADQO78ugA4ePKgHHnig69ZqFovltEugZ599Vk8//bSkrwucm266SVOmTFFsbKzKy8v12muvaceOHSosLNRtt92mV199VcnJyV3nd3Z2dj3u7QohSQoPD5ckOZ1O2e32PufgmcHRFrV0Orodq2ygAAIAAPC1xja7nt1yUM9vL1WHw2U4n58Wp0Vz8zU9P1Umk8kHCQEAAAAAffHbAuiVV17Ro48+qo6ODoWFhemuu+5SWVmZ3n77bY9f49ChQ13lT0JCgl555RXl5OR0PT9u3DhdddVVWrJkiV544QVVVFRo+fLlWrJkSddMRMS39ym32+1dZc/JvimJwsLCKH/6QWqMRaUN3Qsg9gACAADwnQ6HU3/6sEyr3jugBpvdcH5ofKTun5Wn6ydlyGKm+AEAAAAAf2Ae6AB9eemll9TR0aH09HS99NJLuvfee2Wx9L4/TF+effbZriuGFi1a1K38OdnChQuVnZ0tSXrrrbe69hmSvr5q6JvfXjz5dnAn++Z4X7eIw+npbR+geptdrR2OXqYBAADQX1wut97YVaErlm/R//8f+w3Ln0GRYXpoboHeW3i5fnBeJuUPAAAAAPgRvy2AJOnqq6/WW2+9pYkTJ572uZ2dndq0aZMkadCgQbr66qv7nLVarZo3b56kr2/jtn79+q7nwsPDNXToUElf7xnUm6NHj0pSj/2DcGYGx/Re9HEbOAAAAO9wu93aUlyt7/16u+5/9QvD913hYWbdcWmutj44XfMvG6FI6+n9ohYAAAAAwPv89hZwDz/8sC666KIzPn/Xrl1dV+ZMmjSp11u3nWzKlCldj7ds2aLbbrut66/Hjh2ro0eP6quvvtI555zT49wvv/xS0te3lMPZ6+0KIEmqrG9TXlqcj9MAAAAEt70VjVq6dr92HKg1nDWZpOsmpuv+WXnKSIz2QToAAAAAwJny2yuAzqb8kaSSkpKux6NHjzacLygo6LrVW3FxcbfnZsyYIUlau3Ztj/OcTqfWrVsnSbryyivPOC++ldrHFUDsAwQAANB/jtTatOAvu/VPq7Z7VP5cnj9Y7/5smp784QTKHwAAAAAIAH57BdDZKi0t7Xo8bNgww/nw8HClpKSourpa9fX1qq+vV2JioiTpqquu0tNPP63t27frnXfe6XY7uWeeeUbl5eWaOHGiLrjggtPO6Xa71dnZedrnBSO7/et7zPd1BdCR2lb+XsGvfbOGv/sYCBSsYQQD1rGxutZO/WbLIf3l0wrZnW7D+bHDBunBK0dpSm6SJPF+zMtYwwh0rGEEOtYwAh1rGIEu1New2238M9rpCNoCqK6urutxUlKSR+ckJSWpurq66/xvCqDw8HA9+eSTuvXWW7Vw4UK9/vrrysrK0v79+/XFF19o8ODBWrZs2RnldDgc2rt37xmdG6xirCZFh5lkc3Rf7PsOH9feve0DlAo4PYWFhQMdATgrrGEEA9Zxd+0Ol94ptul/ilrV5jD+oWJIjEU/GherizIiZW6t1N69lT5IiZOxhhHoWMMIdKxhBDrWMAIda/jsBW0BZLN9e7uwiIgIj845ee7k8yVpwoQJeuONN/Sb3/xGH330kT799FMNHjxYN954o+655x4lJyf3T3DIZDIpJcaiI42Obserbc4BSgQAABC4nC63Nh1u06v7WlTf7jKcHxRh1g/GxGhWbrSsZpMPEgIAAAAAvCFoC6COjo6ux1ar1aNzwsPDez3/G7m5uVq+fPnZhztJWFiYR3sUhQK73d7V6uamxutIY/d70Td0mjRu3LiBiAZ45OQ1XFBQ4PH3HsBfsIYRDFjH33K73dqwv1pPvFei0hrjvRSjrGb9ZGq2brt4uGIjg/bHBL/HGkagYw0j0LGGEehYwwh0ob6G9+/fL4fDYTzooaD9ye7kq3k8vU/5yXORkZH9nqk3JpOpW/GEr2UkRUvqXgBVt3TKZbIo0tr7HkGAP7Farfy7jYDGGkYwCOV1/NnhOi1ZU6idZfWGsxazSTecn6mfzxyl1DjfvAeGZ0J5DSM4sIYR6FjDCHSsYQS6UFzDJlP/3oUhaAug6Ojorse9Xc3Tm/b2b/eXiYmJ6fdM8Fx6Qu8fPhxtaFPu4FgfpwEAAAgMB040a+maIm3cX+XR/NyxQ7Rwdr5G8P4KAAAAAIJO0BZAKSkpXY9ramo8OufEiRO9ng/fS0+I6vV4RT0FEAAAwHdVNbVrxYZivfpZuVxu4/kLhifpoasKNCkr0fvhAAAAAAADImgLoNzc3K7HR48eNZy32WxqaGiQJKWmpiouLs5b0eCBYX1cAVTZ0ObjJAAAAP6rqd2u1VsO6g/bS9VudxnOj0qN1aI5BZoxOrXfby0AAAAAAPAvQVsAjR49uuvxvn37DOf37NnT9XjMmDFeyQTPZfR5BZDxBsYAAADBrsPh1EsfHdGqzSWqt9kN54cMitT9s/L0/ckZspgpfgAAAAAgFARtATR+/HglJSWprq5Ou3fvVmtr6yn39dm2bVvX4xkzZvgiIk4hMdqqSKu5x2+yVtZzBRAAAAhdLpdbf99zVMvWFanCg/dFcZFhuuvyEfrx1BxFhVt8kBAAAAAA4C/MAx3AW8xms+bOnSvp69u7vfnmm33OtrS0dD0fHR2tmTNn+iQj+mYymZSRGN3juCcfdAAAAASjbSXV+qdV2/XzVz43fE8UbjHr9ktytPWB6br78pGUPwAAAAAQgoK2AJKkO++8U5GRX+8ls2LFChUVFfWYcTqdeuSRR1RbWytJuuWWW5SUlOTTnOhdei+3gWMPIAAAEGq+rGzUzX/4WDf/4RPtO9p0ylmTSbpuYro2/ftl+v9dPUaJMeE+SgkAAAAA8Dd+eQu42trarkLmZE1N3/7AW1VVpeLi4m7PW61W5eTkdP11WlqafvWrX+nhhx9WS0uLbrjhBt18882aOnWqoqOjVVpaqpdfflmff/65JGnChAmaP3++d/5QOG0ZiT0LoONN7ep0uBQeFtTdJQAAgMrrbFq+vkhvfX7Uo/lL8wZr0Zx8nTMs3svJAAAAAACBwC8LoJdfflmrVq065czKlSu1cuXKbsfS09O1efPmbsfmzZunjo4OPf7447LZbFq9erVWr17d4/UuueQSLVu2rOuKIQy89F4KILdbOt7YrqzknreHAwAACAZ1rZ1atfmAXvqoTJ1Ol+H82PRBWjx3tC4emeKDdAAAAACAQOGXBVB/u/HGGzVt2jS9+uqr2rp1q44fP6729nalpKRo7Nixuuaaa9j3xw/1tgeQJFXU2yiAAABA0GnrdOr5HaV69v2Dau5wGM5nJkXpgdkFunrcUJnNJh8kBAAAAAAEEr8sgBYsWKAFCxb062tmZWVp4cKFWrhwYb++Lryntz2AJKmCfYAAAEAQcThdem1nhVZsLFZVU4fhfFJMuBZcMVI3XpjNbXEBAAAAAH3yywIIkKTMXm4BJ0mV9RRAAAAg8Lndbm34qkqPryvSgRMthvNRVotun5ajOy7NVVyk1QcJAQAAAACBjAIIfislNkLhFnOPe99XUAABAIAAt7OsXkve3a/PyuoNZy1mk354XqbumzlKqYPYrxIAAAAA4BkKIPgts9mk9MQolda0djte2WAboEQAAABn58CJFi1bV6h1+6o8mr9yTJoenFOgkamxXk4GAAAAAAg2FEDwa+kJPQsgrgACAACB5kRTu1ZsLNGrn5XL6XIbzp+XnajFVxVocnaSD9IBAAAAAIIRBRD8WnpCz32Ajje2y+F0KczCpscAAMC/Nbfb9buth/T7baVqszsN50cMjtGiOQWaNSZNJpPJBwkBAAAAAMGKAgh+LSOxZwHkcLlV1dzRazkEAADgDzodLr38cZme3nxAda2dhvNpgyJ038w8zZucwS+5AAAAAAD6BQUQ/Fp6LwWQJFXWt1EAAQAAv+NyufXO3mNavq5IR+qM9y2MiwjT/MtH6CcX5ygq3OKDhAAAAACAUEEBBL+WkRjd6/GKepsuyOGe+AAAwH98cKBGS9YUam9lo+Gs1WLSTVOyteCKUUqKCfdBOgAAAABAqKEAgl871RVAAAAA/mD/sSYtXVOoLcXVHs1fO2GY/n1WvrKSe/9FFwAAAAAA+gMFEPxaWlyEwswmOVzubscrKIAAAMAAq6i36ckNxXpzd6XcbuP5S0am6KG5BRqbHu/9cAAAAACAkEcBBL8WZjFrSHxkj8KnsoECCAAADIwGW6eeee+A/vhhmTodLsP5MUMH6aG5Bbo0b7AP0gEAAAAA8DUKIPi9jMSoHgVQRb3xpsoAAAD9qd3u1AsfHNZv3jugpnaH4Xx6QpQWzs7TtePTZTabfJAQAAAAAIBvUQDB76UnREuq63bsaEO7XC43H6YAAACvc7rcemNXhZ7cUKxjje2G8wnRVt07faRuvihbEWEWHyQEAAAAAKAnCiD4vYzEqB7HOp0uVbd0KG1Q5AAkAgAAocDtduu9ohN6bE2RiqqaDecjwsz6ySU5mn/ZCMVHWX2QEAAAAACAvlEAwe+l91IASVJFfRsFEAAA8IrPyxu05N39+ri0znDWbJLmTc7QfbPyNDS+9/ctAAAAAAD4GgUQ/F5vVwBJ0pG6Vk3OTvRxGgAAEMwO17Rq2boi/WPvMY/mZ45O1YNzCpSXFuflZAAAAAAAnB4KIPi94ckxvR4vrbH5OAkAAAhW1c0d+vXmEr388RE5XG7D+QmZCVo8t0AX5ib7IB0AAAAAAKePAgh+b8igSEVazWq3u7odL61pHaBEAAAgWLR2OPTctkN6bushtXY6DedzUmL04Ox8zRk7RCaTyQcJAQAAAAA4MxRA8Htms0nDk2NUeLz75sulNS0DlAgAAAQ6u9OlVz4t11MbS1TT0mE4nxIboZ/PHKUbzs+U1WL2QUIAAAAAAM4OBRACQk5KLwVQdavcbje/fQsAADzmdru19svjWrauSIc8uJo4JtyiOy4dodun5SgmgrfOAAAAAIDAwU+xCAg5KT33AWrtdKq6pUOpcZEDkAgAAASajw/VasmaQn1e3mA4G2Y26UcXZmnBFaM0OC7C++EAAAAAAOhnFEAICL0VQNLXVwFRAAEAgFMprmrWY2sKtanwhEfz3xs3VAtn5/f5/gMAAAAAgEBAAYSAkDu4jwKoplUX5ib7OA0AAAgExxvbtWrLfr22s0Iut/H8hTlJWnzVaE3ITPB6NgAAAAAAvI0CCAFheHLfBRAAAMDJWjtderOoVe++uUMdDpfhfH5anB6aW6DL8weztyAAAAAAIGhQACEgJMWEa1BkmJraHd2OUwABAIBvdDiceuGDMv16c7VaOo0v+RkaH6n7Z+Xp+kkZspgpfgAAAAAAwYUCCAHBZDIpZ3CsvvjOps0UQAAAwOVy6+0vjmr5+iJV1LcZzg+KDNPd00fq1qnDFWm1+CAhAAAAAAC+RwGEgJGbEtOjACqrtcnpcvNbuwAAhKitxdVauqZQXx1rMpwNDzPr1qnDdfflI5QQHe6DdAAAAAAADBwKIASM3vYB6nS6dLShTZlJ0QOQCAAADJQvKxu1dE2hth+oMZw1maTrJqbr/ll5ykjkPQMAAAAAIDRQACFg5AzuWQBJX98GjgIIAIDQUF5n0/L1RXrr86MezV+WN1iL5hRozLBBXk4GAAAAAIB/oQBCwMhN6bsAujRvsI/TAAAAX6pr7dSvN5fopY/KZHe6DedHJIbpP64dr8sKhvggHQAAAAAA/ocCCAFj+CkKIAAAEJzaOp16fkepnn3/oJo7HIbzmYlR+kF+uC7KiNT43CQfJAQAAAAAwD9RACFgxEaEaXBchKqbO7odP0QBBABA0HE4XXptZ4VWbCxWVVOH4XxSTLh+dsVIzZs4VEX79/kgIQAAAAAA/o0CCAElJyWmRwF0mAIIAICg4Xa7tXH/CT22tlAHTrQYzkdZLbp9Wo7uuDRXcZFWdXZ2+iAlAAAAAAD+jwIIASU3JUaflNZ1O1ZRb1OHw6mIMMsApQIAAP1hZ1m9lq7Zr08P1xvOWswm/cv5mfrFjFFKHRTpg3QAAAAAAAQWCiAElJxe9gFyuaXyOptGpsYNQCIAAHC2Dla36PG1hVq3r8qj+dnnpOmB2QUamRrr5WQAAAAAAAQuCiAElOG9FECSdKi6lQIIAIAAc6KpXSs3leivn5bL6XIbzp+XnajFVxVocnaSD9IBAAAAABDYKIAQUHL7KIAO17IPEAAAgaK53a7fbT2k328rVZvdaTg/YnCMFs0p0KwxaTKZTD5ICAAAAABA4KMAQkDJSo6WySS5v/NLwqU1FEAAAPi7TodLL39cpl9vPqDa1k7D+bRBEbpvZp7mTc5QmMXsg4QAAAAAAAQPCiAElIgwizISo1Re19bt+KFqCiAAAPyVy+XWP/Ye0/L1RSqrtRnOx0WEaf7lI/STi3MUFW7xQUIAAAAAAIIPBRACzvDkmB4FEFcAAQDgnz44WKOlawq1p6LRcNZqMemmKdlacMUoJcWE+yAdAAAAAADBiwIIASc3JUbbSmq6HTvR3KHWDodiIljSAAD4g/3HmrR0TaG2FFd7NH/thGH691n5ykqO9nIyAAAAAABCA5+WI+DkpMT0ery0plVj0+N9nAYAAJyssqFNT6wv0pu7K3vs2debS0am6KG5Bfw3HAAAAACAfkYBhICTMzi21+MUQAAADJwGW6d+8/5BvfDBYXU6XIbzY4YO0kNzC3Rp3mAfpAMAAAAAIPRQACHg5CT3fQUQAADwrXa7Uy98cFi/ee+AmtodhvPpCVFaODtP145Pl9ls8kFCAAAAAABCEwUQAk56YpSsFpPszu73lTlMAQQAgM84XW69satCKzYU62hju+F8QrRV904fqZsvylZEmMUHCQEAAAAACG0UQAg4FrNJ2ckxOnCipdvxQxRAAAB4ndvt1vtF1XpsbaEKjzcbzkeEmfWTS3I0/7IRio+y+iAhAAAAAACQKIAQoHJSehZA3AIOAADv+qK8QUvW7NdHh+oMZ80mad7kDN03K09D46N8kA4AAAAAAJyMAggBKSel5z5AjW121bd2KjEmfAASAQAQvA7XtGrZuiL9Y+8xj+Znjk7Vg3MKlJcW5+VkAAAAAACgLxRACEi9FUDS17eBm0wBBABAv6hp6dDTm0r08sdH5HC5DecnZCZo8dwCXZib7IN0AAAAAADgVCiAEJD6KoBKa1o1OTvRx2kAAAgurR0O/X5bqX639aBaO52G8zkpMXpwdr7mjB0ik8nkg4QAAAAAAMAIBRACUm6fBVBLr8cBAIAxu9OlVz4t11MbS1TT0mE4nxIboZ/PHKUbzs+U1WL2QUIAAAAAAOApCiAEpMFxEYoJt/T4reTDNbYBSgQAQOByu91a++VxLVtXpEM1rYbzMeEW3XHpCN0+LUcxEbydBAAAAADAH/ETOwKSyWTS8JQY7Tva1O24Jx9aAQCAb31SWqcla/Zr95EGw9kws0k/ujBLC64YpcFxEd4PBwAAAAAAzhgFEAJWTi8F0OGaVrlcbpnN7D8AAMCplFQ167G1hdq4/4RH898bN1QLZ+f3uQ8fAAAAAADwLxRACFi97QPUZneqqrldQ+OjBiARAAD+71hjm1ZsKNZrOyvkchvPX5iTpMVXjdaEzASvZwMAAAAAAP2HAggBa3gfv4FcWtNKAQQAwHc0ttn17JaDen57qTocLsP5/LQ4PTS3QJfnD5bJxJW1AAAAAAAEGgogBKy+bkFTWtOqqSNSfJwGAAD/1OFw6k8flmnVewfUYLMbzg+Nj9T9s/J0/aQMWbilKgAAAAAAAYsCCAGrzwKoutXHSQAA8D8ul1tvf3FUy9cXqaK+zXB+UGSY7p4+UrdOHa5Iq8UHCQEAAAAAgDdRACFgJUSHKykmXHWtnd2Ol9ZQAAEAQtvW4motXVOor441Gc6Gh5l169ThuvvyEUqIDvdBOgAAAAAA4AsUQAhow5OjexZAtRRAAIDQ9GVlo5auKdT2AzWGsyaTdN3EdN0/K08ZidE+SAcAAAAAAHyJAggBLSclVruONHQ7dqTWJofTpTCLeWBCAQDgY+V1Ni1fX6S3Pj/q0fxleYO1aE6Bxgwb5OVkAAAAAABgoFAAIaDlDu65D5DD5VZFfZuG97FHEAAAwaKutVO/3lyilz4qk93pNpwflx6vxXMLNHVkig/SAQAAAACAgUQBhIA2PLn3kqe0ppUCCAAQtNo6nXp+R6meff+gmjschvNZSdF6YHa+vjduqMxmkw8SAgAAAACAgUYBhICW00fJU8Y+QACAIORwuvTazgqt2FisqqYOw/mkmHD97IqR+tGF2QoP49aoAAAAAACEEgogBLSs5N43rT5S1+bjJAAAeI/b7dbG/Sf02NpCHTjRYjgfZbXo9mk5uuPSXMVFWn2QEAAAAAAA+BsKIAS02IgwJceEq7a1s9vxI3W2AUoEAED/2llWr6Vr9uvTw/WGsxazSf9yfqZ+MWOUUgdF+iAdAAAAAADwVxRACHiZSdE9CqByCiAAQIA7WN2iZWuLtHbfcY/mZ5+TpgdmF2hkaqyXkwEAAAAAgEBAAYSAl5kUrc/LG7odK6+3ye12y2Rio2sAQGA50dSulZtK9NdPy+V0uQ3nz8tO1OKrCjQ5O8kH6QAAAAAAQKCgAELAy0qK6nHM1ulUbWunUmIjBiARAACnr6XDod9tOajntpWqze40nB8xOEaL5hRo1pg0fuEBAAAAAAD0QAGEgJeVFN3r8SN1NgogAIDf63S49JdPjujpTSU9bmnam7RBEbpvZp7mTc5QmMXsg4QAAAAAACAQUQAh4GX2UQCV19k0KSvRx2kAAPCM2+3WO3uOafn6IpXVGu9dFxcRpvmXj9BPLs5RVLjFBwkBAAAAAEAgowBCwOvzCiAPPkwDAGAgfHCwRkvXFGpPRaPhrNVi0k1TsrXgilFKign3QToAAAAAABAMKIAQ8IbGRynMbJLjOxtll9dTAAEA/Mv+Y016bG2h3i+q9mj+2gnD9O+z8pWV3PsvOwAAAAAAAPSFAggBz2I2KT0xqsftc47UUQABAPxDZUObnlxfrDd2V8jtNp6/ZGSKHppboLHp8d4PBwAAAAAAghIFEIJCVlJ0jwKovK5tgNIAAPC1Rptdz7x/QC98cFidDpfh/Jihg/TQ3AJdmjfYB+kAAAAAAEAwowBCUMjsZR+go41t6nS4FB5mHoBEAIBQ1m536o8fHNYz7x1QU7vDcD49IUoLZ+fp2vHpMptNPkgIAAAAAACCHQUQgkJWLwWQ2/31LXdyUmIGIBEAIBQ5XW69ubtST64v0tHGdsP5hGir7p0+UjdflK2IMIsPEgIAAAAAgFBBAYSg0FsBJEnldTYKIACA17ndbr1fVK3H1haq8Hiz4XxEmFk/uSRH8y8bofgoqw8SAgAAAACAUEMBhKCQmdh7AXSkztbrcQAA+ssX5Q1asma/PjpUZzhrNkn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      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 449,
       "width": 832
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = x0    # on reprend la même valeur initiale sinon la comparaison serait faussée\n",
    "w = 0.5   # on choisit w \n",
    "error2 = []\n",
    "for i in range(200):\n",
    "    old_x = x\n",
    "    x = w * (N @ x + b) / M + (1-w) * x\n",
    "    error2.append(np.square(x - old_x).sum())\n",
    "plt.plot(range(len(error2)), error2)\n",
    "plt.title('Ecart entre 2 x successifs')\n",
    "plt.semilogy();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Il semble bien qu'il y ait une relation forte entre l'écart entre deux **x** successif et l'erreur absolue.\n",
    "Vérifions :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itération présentant le minimum :  12 14\n",
      "Erreur absolue minimum                                        :  0.0040626765429533146\n",
      "Erreur absolue minimum devinée à partir du minimum de l'écart :  0.004333899458826035\n"
     ]
    }
   ],
   "source": [
    "k_min = np.argmin(error)\n",
    "k2_min = np.argmin(error2)\n",
    "print('Itération présentant le minimum : ', k_min, k2_min)\n",
    "print('Erreur absolue minimum                                        : ', min(error))\n",
    "print(\"Erreur absolue minimum devinée à partir du minimum de l'écart : \", error[k2_min])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "L'écart entre 2 **x** successifs est une facon simple et relativement efficace de savoir quand arrêter un algorithme\n",
    "itératif."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "#### Résidu\n",
    "\n",
    "Enfin on peut calculer le résidu à savoir $||A \\, {\\bf x} - {\\bf b}||$ mais c'est $n^2$ opérations :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 449,
       "width": 832
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = x0    # on reprend la même valeur initiale sinon la comparaison serait faussée\n",
    "w = 0.5   # on choisit w \n",
    "residu = []\n",
    "for i in range(200):\n",
    "    old_x = x\n",
    "    x = w * (N @ x + b) / M + (1-w) * x\n",
    "    residu.append(np.square(A @ x - b).sum())\n",
    "plt.plot(range(len(residu)), residu)\n",
    "plt.title('Résidu')\n",
    "plt.semilogy();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "### Testons d'autres matrices avec cet algorithme\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mk_A(seed):\n",
    "    np.random.seed(seed)\n",
    "    return np.random.randint(10, size=(4,4))\n",
    "\n",
    "A = mk_A(234)\n",
    "b = A.sum(axis=1)                    \n",
    "\n",
    "M = np.diag(A)    \n",
    "N = np.diag(M) - A \n",
    "\n",
    "x0 = np.random.random(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_error(M, N, b, x0, w, n=200):\n",
    "    x = x0 \n",
    "    error = [np.square(x - np.ones(4)).sum()]\n",
    "    error2 = []\n",
    "    for i in range(n):\n",
    "        old_x = x\n",
    "        x = w * (N @ x + b) / M + (1-w) * x\n",
    "        error.append(np.square(x - np.ones(4)).sum())\n",
    "        error2.append(np.square(x - old_x).sum())\n",
    "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,4))\n",
    "    ax1.plot(range(len(error)), error)\n",
    "    ax1.set_title('Erreur absolue')\n",
    "    ax1.semilogy();\n",
    "    ax2.plot(range(len(error2)), error2)\n",
    "    ax2.set_title('Erreur relative')\n",
    "    ax2.semilogy()\n",
    "    print(\"Itération du minimum :\",np.argmin(error), np.argmin(error2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itération du minimum : 17 40\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1008x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 264,
       "width": 822
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_error(M, N, b, x0, w=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "On retrouve le même comportement (convergence puis divergence) mais en nettement plus cahotique.\n",
    "\n",
    "On peut réduire les oscillation en augmentant l'inertie c.a.d. en diminuant $w$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itération du minimum : 81 209\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 372,
       "width": 1142
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "error2 = plot_error(M, N, b, x0, w=0.1, n=1000) \n",
    "# w 5 fois plus petit donc je fais 5 fois plus d'itération pour \"avancer\" d'autant (grosso modo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Les oscillations ont disparu ! Mais on a payé le prix fort puisqu'on a du faire 5 fois plus d'itérations.\n",
    "\n",
    "On constate que dans les 2 cas l'erreur relative (entre 2 x successifs) ne donne pas le bon minumum.\n",
    "Donc arrêter un algorithme itératif en fonction de l'erreur relative n'est pas toujours le plus efficace.\n",
    "\n",
    "Regardons ce que donne le résidu :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itération du minimum : 218\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 449,
       "width": 832
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = x0 \n",
    "w = 0.1\n",
    "residu = []\n",
    "for i in range(1000):\n",
    "    x = w * (N @ x + b) / M + (1-w) * x\n",
    "    residu.append(np.square(A @ x - b).sum())\n",
    "plt.plot(range(len(residu)), residu)\n",
    "plt.title('Résidu')\n",
    "plt.semilogy();\n",
    "print(\"Itération du minimum :\", np.argmin(residu))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "### Exercice 20.1\n",
    "\n",
    "Comment se fait-il que la courbe du résidu ait la même forme que celle de l'erreur relative ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Réponse**\n",
    "\n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "#### Nouvelle matrice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itération du minimum : 154 154\n"
     ]
    },
    {
     "data": {
      "image/png": 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nz5Yk+fv7a/jw4QoLC5O/v79iYmK0du1abdu2TUeOHNHo0aO1evVqBQcH5zrHyJEjFRsba9X7jRkzRgMHDsyzPDU1VRMmTNDevXtVt25dTZ482VQ2cOBArVq1Sr/88ot+++033X777aay7777Tt99950kKTubP4gAAADAud3Toor2nErQot//Miv7/US8Xl7/p94e2Iw90wEAAAAAAJBL/UoBWje+oxZt+0uf7zilvy+lWN122vdHVL9SgG5vULEYIwQA11PsST4rV67U1KlTlZaWJg8PDz3++OM6deqUvvrqK6vPcfLkSVOCT2BgoFauXKlatWqZyps1a6a7775b06ZN06JFi3T69Gm9++67mjZtWq7zxMTEWL1FVmJiYp5lV65c0bhx47Rnzx7Vrl1bn376qfz8/EzlLVq00JgxY7Rw4UI9/vjj6ty5s6pUqaKoqCjt27dPY8eO1bx581SmTBmr/w0AAAAAR5l8dyPtO52oyL8TzcpW7Y5R7Qp+eqxrHfsHBgBACfTzzz9rxYoV+vPPP5WUlKSyZcuqadOmGjZsWK4HyW44evSoFixYoJ07dyoxMVHBwcHq2LGjxo8fb1p1GgAAAHAUT3c3jbmttsbcVluJKemKik3S0dirOnLuir47cE4JKRkW2xmN0oQVkdrwRCfVruBv56gBwHkVe5LP0qVLlZaWptDQUL333ntq1aqVJk2aVKBzzJ8/37Tyz0svvZQrwSeniRMn6tdff9WpU6e0YcMGs8mMTZs2Ff4X+f9iY2P16KOPKioqSs2bN9eCBQsUFBRkMZa6devq888/186dO+Xj46MWLVpo8eLF8vDw0Lx588xWGgIAAACckZeHm+YPb6N752zT+SupZuVv/3BENYJ91atpZQdEBwBAyfHmm29q6dKl8vT0VOfOnVWhQgVFR0crPDxc4eHhGj9+vJ5++mlT/a1bt2rcuHHKzMxUWFiYqlevrhMnTmjdunXauHGjli1bpoYNGzrwNwIAAAD+EejrpXa1gtSu1vW/rb7cp7HWR57Rx1tP6mRcsln9q6mZGvv5Hq0f31EBPp72DhcAnJKbPd6kb9++2rBhg1q1alXgtunp6frll18kSWXLllXfvn3zrOvp6alBgwZJkrKysrRx48bCBZyHuLg4DR06VFFRUerWrZuWLFliMcHnhvvuu09ffPGF9u3bpz/++EMfffSR2rZtq1OnTkmSateubdP4AAAAgOJSqayPPnn4Vvl6uZuVGY3SM6v2am9Mov0DAwCghNi0aZOWLl2qcuXK6csvv9T8+fNNST/vvvuuJGnevHk6duyYJCklJUUvvPCCMjIyNHPmTC1atEhvvPGGli1bpv/85z9KSkrSc889x3bxAAAAcFplvNw1tH11/fxsV73Qs4HFOscvJOnZVXuVnW20c3QA4JyKPclnypQpeu+99xQQEFCo9hEREUpKSpIktW7dWl5eXvnWDwsLMx1v3ry5UO9pSVJSksaOHavTp0+rf//+mjt3bqG329q5c6ckqW3btjaLDwAAAChuTaqU0wcPtpKbwbwsNSNbj3y2U8cvXLV/YAAAlADr1q2TJD366KOqW7durrJ77rlHTZo0kdFo1NatWyVJ69ev16VLl9StWzf16tUrV/2HH35Y9evX14kTJ2w6PwYAAAAUBzc3g8bfXkf9W4VaLP/58AW9/cMRGY0k+gBAsSf5dOjQoUjtbzydJEmNGjW6af2GDRvKYLj+V4eoqKgivXdOkydP1qFDh9S7d29NnTpV7u7mTzDfsH//fr322mv6+OOPzcouX76sH374QQEBAercubPN4gMAAADsoXujSnq5T2OLZQkpGRr+8U7FXEqxc1QAALi+8ePHa86cObr33nstlletWlXS9RV8pH8ebrvrrrss1u/Ro4ck6ddff7V1qAAAAIDNGQwGTRvQTM1Cy1ks/yj8pJ5bvU9pmVl2jgwAnIuHowO4mejoaNNxlSpVblrfy8tLISEhiouLU0JCghISElS+fPkixbB582b9+OOPqlGjhqZOnSo3t/xzo/z9/bVy5Ur5+Pioc+fOpr3P09PTNWnSJCUnJ+u5556Tn59foeIxGo1KT08vVFt7ysjIsHgM10D/uTb6z7XRf66N/nNt9J91hrWtouMXrmj5ztNmZeevpGr4xzu0fHRbVQjwtmtc9J9ro/9cm6v2H0+Bwpk0btxYjRtbTqSVpJMnT0qSaZWfQ4cOScr7obgb5zp48KAtwwQAAACKjY+nuxaMaKN+c7bqYpL530LXR57R6YQULRhxq4L88t/9BQBKKqdP8rl06ZLpOCgoyKo2QUFBiouLM7UvapLPwoULTeedMWNGnvVq1Kih4cOHq3bt2nrkkUf06aefavDgwerWrZvKli2r33//XWfOnFH37t316KOPFjqezMxMHThwoNDtHeHIkSOODgFFQP+5NvrPtdF/ro3+c230X/7uq2bU0Rhv7TmXZlZ26tI1Df3od715e5D8vIp98VCL6D/XRv+5NvoPziAiIkIvvviiYmJiJEnTpk3TgAEDrG5//PhxrVu3Tlu3blVsbKxSUlIUHBysevXqqVevXurXr588PT2LK/xcsrOztXDhQh07dkz16tVT9+7dlZaWZpr7qlSpksV2N14/fdo8KRcAAABwVlUCy+jDYW00dOEOZWabP5ix668E3Td3mz59uK3qVvR3QIQA4FhOn+RzYwliSfL2tu5J4Jz1crYvrLNnz0qSIiMjFRkZmWe9du3aafjw4ZKkF198UXXr1tWqVau0Y8cOpaenq3bt2ho9erQefPDBm64GBAAAADgzdzeDnu8QqLfCL+nQRfNVO05dztTUrQl6tWuQvNwNDogQAFAaZWRkaM6cOVq4cKGysgq3jP/cuXM1b948s1Wpzp07p3Pnzik8PFxLlizRrFmzVLNmTRtEbe7UqVNaunSpEhISdODAAZ09e1Z9+/bVyy+/LA8PD12+fNlU19/f8h82bqwgffXq1WKJEQAAACgu7WoFafrg5pq4Zr+yLCT6/H0pRffN3abn7qyvhzrUkIc7f3cFUHo4fZJPWto/TwZb+4SUl9c/y7PlbF9YmzZtKnAbg8GggQMHauDAgUV+/3/z8PDIcylmZ5KRkWF6grNhw4Z2e8INtkH/uTb6z7XRf66N/nNt9F/Bfd4wQw99tkcHz5n/AfFIfIZWn3TT2/2byGAo/kQf+s+10X+uzVX77/Dhw8rMzHR0GLCREydO6IUXXjBtT+Xu7l7gRJ/58+dr9uzZkq4nzwwfPlxhYWHy9/dXTEyM1q5dq23btunIkSMaPXq0Vq9ereDg4FznGDlypGJjY616vzFjxlicOzp//ryWLFli+rlt27Zq3bq1KaEn5zbueY23G/NjWVlZysjIcJlxCQAAAEhS/1ZVFeznrSeWRehqmvn3tqS0TL3xzSGt2XNab93XVG1qFG1nFwBwFU6f5JNzVZ6cExj5yVnPx8fH5jE5msFgyJXI5Ao8PT1dLmb8g/5zbfSfa6P/XBv959roP+sEe3lpyej2Grxgu07GJZuVr997Tk1CA/Vol9p2jYv+c230n2tzpf6zRwIi7GPlypWaOnWq0tLS5OHhoccff1ynTp3SV199ZfU5Tp48aUrwCQwM1MqVK1WrVi1TebNmzXT33Xdr2rRpWrRokU6fPq13331X06ZNy3WemJgYnTlzxqr3TExMtPh6+/btdfToUSUkJOjEiRNauHCh3njjDa1bt06ff/55rvmyjIwMi2PuxvyYh4cHCT4AAABwSbfVr6B14zvqkUW7dDrhmsU6h89d0cB5v2tI22qa3KeRyvrw2RdAyeb0a5f5+vqajq1dlSc1NdV0fGNpYgAAAADFI9jfW5+Pbq8q5Swn2E/97rDCo+LsHBUAoDRZunSp0tLSFBoaqqVLl+rJJ5+Uu7t7gc4xf/5808o/L730Uq4En5wmTpyoGjVqSJI2bNigmJiYXOWbNm3S0aNHrfpv9OjR+cZUvnx53XrrrZo/f746deqkP//8U/PmzZO/v78pSS0pKcli2xuv57WdFwAAAOAK6lUK0JdPdFLr6oH51lu5K0YjPv5DmVnZ9gkMABzE6ZN8QkJCTMcXL160qs2FCxcstgcAAABQPEIDy2jxqHby9zZfLDTbKD25PELRF81X+gEAwFb69u2rDRs2qFWrVgVum56erl9++UWSVLZsWfXt2zfPup6enho0aJCk61thbdy4sXABF4DBYFC/fv0kSdu2bZOXl5cqV64sSTp37pzFNmfPnpUk1axZs9jjAwAAAIpTiL+3lo8J0wO3Vsu33r7Tl/XtAcufjwGgpHD6JJ/atf9Z1v/G5ER+UlJSTEsdV6xYUQEBAcUVGgAAAIAc6lUK0KwhLWVp95srqZkavXiXtp+Il9FotH9wAIASbcqUKXrvvfcKPQ8UERFhWvmmdevWN91yLiwszHS8efPmQr1nThkZGZo6daqefvppXbp0yWKdGyvy3Jj3atq0qSTp0KFDFuv/+eefkq5vMwYAAAC4Oh9Pd/1vUHOtGBOmuhXzXq3y063RzD0BKNHMH7N1Mo0aNTIdHzx48Kb19+/fbzpu3LhxscQEAAAAwLLujSrphZ4N9M4PR83KTsYl68GFO1Q7xE8PtquugW2qKsgv/z+iAgBgjQ4dOhSp/bFjx0zHOeei8tKwYUMZDAYZjUZFRUUV6b2l66sD/fTTTzp79qzuuOMO3XvvvWZ1biTtVK9eXZLUvXt3bdy4UT/88IMGDx6cq25WVpZ+/PFHSdJdd91V4HiMRqPS09ML3M7eMjIyLB7DddCHro8+dG30n+ujD10b/Vc4baoF6Mtx7bVo+ynN/e2krmXk3p5r3+nL2nkiTq1usr2XLdCHro8+dG2u0n+2Tjx0+iSfFi1aKCgoSJcuXVJkZKSSk5Pl5+eXZ/0tW7aYjrt3726PEAEAAADk8HjXOjpy7qq+2md5Jc6TF5P13+8Oa/rGoxp/ex092a2uPNydfpFRAEA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      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 372,
       "width": 1148
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = mk_A(123)\n",
    "b = A.sum(axis=1)                    \n",
    "\n",
    "M = np.diag(A)    \n",
    "N = np.diag(M) - A \n",
    "\n",
    "x0 = np.random.random(4)\n",
    "\n",
    "plot_error(M, N, b, x0, w=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Voici un cas avec une convergence parfaite. Notons qu'on s'est arrêté à l'itération 150 lorsqu'on est passé\n",
    "en dessous de la précision de la machine (les valeurs suivantes devant être 0 et comme log(0) = $-\\infty$,\n",
    "matplolib ne les affiche pas).\n",
    "\n",
    "Vérifions quand même que la méthode de Jacobi de base n'aurait \n",
    "pas marché :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_0 = [0.398 0.738 0.182 0.175]\n",
      "x_1 = [4.127 1.837 1.029 2.203]\n",
      "x_2 = [-0.526 -0.195  0.907 -0.906]\n",
      "x_3 = [3.427 1.782 1.133 3.759]\n",
      "x_4 = [-1.56  -0.204  0.913 -0.86 ]\n",
      "x_5 = [3.395 2.118 1.134 3.775]\n",
      "x_6 = [-1.907 -0.196  0.876 -1.616]\n",
      "x_7 = [3.877 2.342 1.133 3.784]\n",
      "x_8 = [-2.133 -0.357  0.851 -2.12 ]\n",
      "x_9 = [4.364 2.49  1.151 4.165]\n",
      "x_10 = [-2.525 -0.574  0.834 -2.467]\n",
      "x_11 = [4.804 2.671 1.175 4.665]\n",
      "x_12 = [-3.027 -0.792  0.814 -2.89 ]\n",
      "x_13 = [5.293 2.898 1.199 5.17 ]\n",
      "x_14 = [-3.581 -1.027  0.789 -3.421]\n",
      "x_15 = [5.87  3.159 1.225 5.719]\n",
      "x_16 = [-4.194 -1.298  0.76  -4.026]\n",
      "x_17 = [6.531 3.45  1.255 6.35 ]\n",
      "x_18 = [-4.891 -1.608  0.728 -4.704]\n",
      "x_19 = [7.277 3.779 1.29  7.073]\n"
     ]
    }
   ],
   "source": [
    "x = x0\n",
    "for i in range(20):\n",
    "    print(f\"x_{i} = {x}\")\n",
    "    x = (N @ x + b) / M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Jacobi de base diverge, donc c'est bien l'inertie qui a permis de converger."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "#### Nouvelle matrice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itération du minimum : 0 0\n"
     ]
    },
    {
     "data": {
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Pnrzo/qh827dv1/Dhw7V9+3ZJUocOHTR//ny1atXKaT+j+JfFI0eOOO24MNaoUSOFhIRIkgoKCnTy5EmFh4c7Xk9JSSnVcZKTkx3bxfeHc3z99dey2WySpL59+zr9+Mw/13Dm3OI66h5sNpuef/55TZkyRTabTT4+Pnruuef05JNPymKxOO3nXOxcjcp3qXMj8899FBQUOO6CCgoKUvfu3Z3+M5h/F1fW7wdcAwFUFc4Z5kL9ybNRgzIP6lCegc/gnolalGejFmUO1KOqDvWoiqPJBxXSvHlzx/bRo0dLjM/OzlZaWpokqU6dOgoODq6s1PAnv/zyi0aOHKkTJ05IOrtM3Jw5c1S7dm2n/pwaNWo4tku7zBmco/gScXl5eQoNDXVcuFJSUkrVkVr8A2fLli2dn2Q1t3TpUsd2r169nH585p9rOHNucR2tevn5+frHP/7hWMI8NDRUH3zwQamW4C2PP5+rUfkudW5k/rmPn3/+2fH/tkePHqV+HnZZMf/OV57vB1wDAVQVzhnmQf2peqAGZQ7UoTwDn8E9D7Uoz0ctyhyoR1UN6lHOQZMPKqT4M/ESExNLjN+6datjOzo6ulJywoXWr1+v++67T9nZ2ZKkhx56SC+99NJ5zzB0luJdj6GhoU4/Pi7OZrM5LjKSVKtWLUn/m6N2u71UczQhIcGx/ednXqJiUlNTHefAyMhIp97BeA7zz3WcNbe4jlYtm82mhx9+WMuXL5ckNW3aVPPnz1fXrl0r7edd7FyNynWpcyPzz32sXr3asX3ttddWys9g/p2vIt8PuAYCqAqcM8yB+lP1QA3KHKhDeRY+g3sOalHVA7Uoc6Ae5XrUo5zHOQ91RLXVoUMHhYWF6fTp09q0aZOysrIMn0X3448/OrZ79+7tihSrvX379umBBx5Qbm6uLBaLnn322VJ3hOfl5Wnu3Lk6evSoTp8+rX/9618ldrJu3LjRsc0X9PJbt26d1q5dq6NHj+qaa67RwIEDDeO3bdvm6AivXbu2o+O1Z8+ejme+/vTTT+rcufMlj5Genq4tW7ZIOvvc2JiYGGe8Ffxh/fr1stvtks4+B70kzD/35qy5xXW0ak2ZMkXff/+9JCkqKkr//e9/FRYWVur9nXWuRuk589zI/HMfv/32m2O7ffv2pdqH+Vd+Ffl+IHENBFA1OGe4P+pP5kUNyjNRh/IsfAb3HNSizIdalOeiHuVa1KOci5V8UCFWq1UDBgyQdHa5qvj4+EvGZmZmOl4PCAhQnz59XJJjdZafn69HHnlE6enpkqRJkyaV6YTp5+en2bNn66OPPtJXX32l7777zjB+7969+umnnyRJ3t7e6tmzZ/mTr+YOHDigt956S4sWLdJbb72loqIiw/gPP/zQsX3dddc5tvv16+f4wPn5558bLmH36aefOj5sDB482KnP/oW0adMmx3br1q1LjGf+uTdnzS2uo1Xn66+/1rx58yRJzZo106xZs8pUVJGcd65G6Tnz3Mj8cw9ZWVnavXu3JMnHx0dNmzYt1X7Mv/Kp6PcDiWsggKrBOcO9UX8yN2pQnok6lGfhM7hnoBZlTtSiPBP1KNeiHuV8NPmgwu677z7H8wSnT5+uXbt2XRBjs9k0efJkpaSkSJJGjx5d5g8vKLt3331XO3fulCQNHTpUI0eOLPMxiu/z7LPPau/evReNO3XqlB5++GHHBW3o0KFq0KBBObKGJA0cONCxbN+ePXs0ZcqUS8bOnTtXX331lSTJ19dXf/vb3xyv1a1bVyNGjJAkHT9+XM8999xFP3QkJCTorbfekiQFBwefdww4x759+xzbbdq0KdU+zD/35cy5xXXU9dLT0/Xss89KOvtM5DfffLNcS6U661yNsnHmuZH5V/X279/vGKMWLVrI27t0i80y/8rHGd8PuAYCqCqcM9wX9SdzowblmahDeRY+g5sftShzoxbleahHuRb1KOez2M+t2QhUwOeff66JEydKOtvJdscdd6h79+4KCAjQ/v37NW/ePG3evFmS1LFjR3344YeOyYPKkZaWpuuuu05ZWVny8fHR+++/X+oPjT4+PmrWrJmks92Vd9xxh2P8/P39NXz4cHXr1k316tVTVlaW1q1bpzlz5ig1NVXS2S+OH3/8seHyZijZ8uXL9eCDDzqW1m3Xrp1GjBihpk2bqkaNGjp48KCWLFmiVatWOfb517/+pZtuuum842RmZur2229XUlKSJOmyyy7T7bffrqZNmyozM1Nr1qzR3LlzlZOTI6vVqhkzZqhfv34ue5/VRb9+/XTgwAFJ0vz589WhQ4cS92H+VY6UlBTHB7PiZsyY4Vgu9+GHH75g6cXi50bJuXOL62jpOWP8pk+frpkzZ0o628l/7733lvrn16tXTyEhIY4/O+tcXV04Y/ycfW5k/pWes86fxX355Zd67LHHJElXX321/vOf/5Q6H+Zf2Tjr+4HENRBA1eGc4X6oP3kGalCehzqU+6AOZX7UosyNWpT5UY8yN+pRlYMmHzjN3Llz9eKLLyo3N/eSMVdddZVeeuklt+p081SLFi3Sk08+Wa59IyMjtWLFCsefMzMz9eSTT2r58uUl7tu7d2+98MIL533oRPktW7ZMkyZNUlpammFczZo1NWXKFPXt2/eirx8/flwPP/zweUv1/llQUJAmT56sIUOGVCRlXMIVV1zhGMevv/5aLVq0KNV+zD/ne/311/XGG2+Ueb8/nxsl584trqOl44zx69Onjw4dOlSunx8XF6dhw4ad93fOOldXB86af84+NzL/SseZ589zPvroI8ddTwMGDNCMGTPKdGzmX+k58/uBxDUQQNXhnOFeqD95DmpQnoU6lPugDmV+1KLMjVqU+VGPMjfqUZWjdGtPAaUwcuRIXX311Zo/f75Wr16t48ePKzc3VxEREYqJidGQIUPc6ll1nq6k50CWRVBQkN58802tX79eS5Ys0aZNm3T06FHl5OQoMDBQ9erVU+fOnTV06FB17NjRaT8XUt++fdWtWzfFx8dr9erVSkpKUlpamiwWi2rWrKmoqChdffXVGjZsmIKCgi55nHr16mnevHn6+uuv9eWXX2rnzp1KSUlRQECAIiMj1atXLw0fPlz16tVz4burXrKyshzbRmP1Z8w/9+bMucV11HWceY2UnHeuRuk5+9zI/Ks65b0+nsP8Kz1nn/u4BgKoKpwz3Av1J89BDcqzUIfyTHwGNy9qUeZHLcqzUI9yHepRlYOVfAAAAAAAAAAAAAAAAAA3Z63qBAAAAAAAAAAAAAAAAAAYo8kHAAAAAAAAAAAAAAAAcHM0+QAAAAAAAAAAAAAAAABujiYfAAAAAAAAAAAAAAAAwM3R5AMAAAAAAAAAAAAAAAC4OZp8AAAAAAAAAAAAAAAAADdHkw8AAAAAAAAAAAAAAADg5mjyAQAAAAAAAAAAAAAAANwcTT4AAAAAAAAAAAAAAACAm6PJBwAAAAAAAAAAAAAAAHBzNPkAAAAAAAAAAAAAAAAAbo4mHwAAAAAAAAAAAAAAAMDN0eQDAAAAAAAAAAAAAAAAuDmafAAAAAAAAAAAAAAAAAA3R5MPAAAAAAAAAAAAAAAA4OZo8gEAAAAAAAAAAAAAAADcHE0+AAAAAAAAAAAAAAAAgJujyQcAAAAAAAAAAAAAAABwczT5AAAAAAAAAAAAAAAAAG6OJh8AAAAAAAAAAAAAAADAzdHkAwAAAAAAAAAAAAAAALg5mnwAAAAAAAAAAAAAAAAAN0eTDwAAAAAAAAAAAAAAAODmaPIBAAAAAAAAAAAAAAAA3BxNPgAAAAAAAAAAAAAAAICbo8kHAAAAAAAAAAAAAAAAcHP/DzJf/awbXsX/AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 372,
       "width": 1148
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = mk_A(16)\n",
    "b = A.sum(axis=1)                    \n",
    "\n",
    "M = np.diag(A)    \n",
    "N = np.diag(M) - A \n",
    "\n",
    "x0 = np.random.random(4)\n",
    "\n",
    "plot_error(M, N, b, x0, w=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Divergence directe mais si on baise $w$ on constate qu'on est dans le 1er cas :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itération du minimum : 32 38\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 372,
       "width": 1135
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_error(M, N, b, x0, w=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Mais ca reste pas terrible. Au mieux on n'est même pas à $10^{-1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "## Normaliser\n",
    "\n",
    "Cette dernière remarque n'a de sens que si on sait à quoi on se compare. \n",
    "\n",
    "* Si la solution cherchée est un milliard, avoir une erreur de 0.1 est très bien.\n",
    "* Si la solution cherchée est 0.01, une erreur de 0.1 est énorme.\n",
    "\n",
    "On ne peut donc juger une erreur qu'en fonction d'une référence. Si on connais la solution exacte, alors \n",
    "elle est la bonne référence.\n",
    "\n",
    "$$\n",
    "\\frac{||{\\bf x}^k - {\\bf x}||}{||{\\bf x}||}\n",
    "$$\n",
    "\n",
    "De même l'erreur entre 2 itérations successives n'a de sens que normalisée.\n",
    "Si $||{\\bf x}^k|| = 1 000 000$ alors $||{\\bf x}^k - {\\bf x}^{k-1}|| = 1$ est bien mais ce n'est pas le cas\n",
    "si $||{\\bf x}^k|| = 1$.\n",
    "\n",
    "Aussi on compare la différence entre 2 itérations avec le **x** courant ou le précédant :\n",
    "\n",
    "$$\n",
    "\\frac{||{\\bf x}^{k+1} - {\\bf x}^k||}{||{\\bf x}^k||}\n",
    "$$\n",
    "\n",
    "Faisons le et regardons nos résultats précédents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_error_normalized(M, N, b, x0, w, n=200):\n",
    "    x = x0 \n",
    "    error = [np.square(x - np.ones(4)).sum()]\n",
    "    error2 = []\n",
    "    for i in range(n):\n",
    "        old_x = x\n",
    "        x = w * (N @ x + b) / M + (1-w) * x\n",
    "        error.append((np.square(x - np.ones(4)).sum())/4)               # normalisé par rapport à la solution\n",
    "        error2.append((np.square(x - old_x).sum())/np.square(x).sum())  # normalisé par rapport à x\n",
    "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,4))\n",
    "    ax1.plot(range(len(error)), error)\n",
    "    ax1.set_title('Erreur absolue normalisée')\n",
    "    ax1.semilogy();\n",
    "    ax2.plot(range(len(error2)), error2)\n",
    "    ax2.set_title('Erreur relative normalisée')\n",
    "    ax2.semilogy()\n",
    "    print(\"Itération du minimum :\",np.argmin(error), np.argmin(error2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itération du minimum : 60 70\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 372,
       "width": 1142
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = mk_A(799)\n",
    "b = A.sum(axis=1)                    \n",
    "\n",
    "M = np.diag(A)    \n",
    "N = np.diag(M) - A \n",
    "\n",
    "x0 = np.random.random(4)\n",
    "plot_error(M, N, b, x0, w=0.1, n=1000) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itération du minimum : 60 70\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 372,
       "width": 1142
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_error_normalized(M, N, b, x0, w=0.1, n=1000) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "Et oui, l'erreur relative normalisée se stabilise dans ce cas alors que non normalisée elle augmentait toujours.\n",
    "\n",
    "Cela étant pour converger l'ecart entre 2 itérations doit tendre vers 0.\n",
    "\n",
    "Parfois on peut avoir une surprise :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Itération du minimum : 500 499\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 372,
       "width": 1142
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = mk_A(308)\n",
    "b = A.sum(axis=1)                    \n",
    "\n",
    "M = np.diag(A)    \n",
    "N = np.diag(M) - A \n",
    "\n",
    "x0 = np.random.random(4)\n",
    "plot_error_normalized(M, N, b, x0, w=0.1, n=500) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.0040626765429533146)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lang": "fr"
   },
   "source": [
    "On converge mais à coté de la valeur cherchée. C'est rare et c'est du au très mauvais conditionnement\n",
    "de la matrice A. Ce mauvais conditionnement génère des erreurs de calcul qui font qu'on ne peut pas arriver\n",
    "à la solution exacte.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.1405202107473442e+17)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.cond(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.13.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}