CoursMagistral_9.ipynb

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   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#ALGO1-:-Introduction-à-l'algorithmique\" data-toc-modified-id=\"ALGO1-:-Introduction-à-l'algorithmique-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span><a href=\"https://perso.crans.org/besson/teach/info1_algo1_2019/\" target=\"_blank\">ALGO1 : Introduction à l'algorithmique</a></a></div><div class=\"lev1 toc-item\"><a href=\"#Cours-Magistral-9\" data-toc-modified-id=\"Cours-Magistral-9-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Cours Magistral 9</a></div><div class=\"lev2 toc-item\"><a href=\"#Documentation-de-scipy.opt.linprog\" data-toc-modified-id=\"Documentation-de-scipy.opt.linprog-21\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Documentation de <code>scipy.opt.linprog</code></a></div><div class=\"lev2 toc-item\"><a href=\"#Fonction-de-débogage\" data-toc-modified-id=\"Fonction-de-débogage-22\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Fonction de débogage</a></div><div class=\"lev2 toc-item\"><a href=\"#Premier-exemple\" data-toc-modified-id=\"Premier-exemple-23\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span>Premier exemple</a></div><div class=\"lev2 toc-item\"><a href=\"#Second-exemple\" data-toc-modified-id=\"Second-exemple-24\"><span class=\"toc-item-num\">2.4&nbsp;&nbsp;</span>Second exemple</a></div><div class=\"lev3 toc-item\"><a href=\"#Essayons-avec-différentes-méthodes-de-résolution-:\" data-toc-modified-id=\"Essayons-avec-différentes-méthodes-de-résolution-:-241\"><span class=\"toc-item-num\">2.4.1&nbsp;&nbsp;</span>Essayons avec différentes méthodes de résolution :</a></div><div class=\"lev4 toc-item\"><a href=\"#Avec-la-méthode-du-simplexe\" data-toc-modified-id=\"Avec-la-méthode-du-simplexe-2411\"><span class=\"toc-item-num\">2.4.1.1&nbsp;&nbsp;</span>Avec la méthode du simplexe</a></div><div class=\"lev4 toc-item\"><a href=\"#Avec-la-méthode-du-point-intérieur-(un-autre-algorithme)\" data-toc-modified-id=\"Avec-la-méthode-du-point-intérieur-(un-autre-algorithme)-2412\"><span class=\"toc-item-num\">2.4.1.2&nbsp;&nbsp;</span>Avec la méthode du point intérieur (un autre algorithme)</a></div><div class=\"lev2 toc-item\"><a href=\"#Bonus-:-implémentation-manuelle-de-l'algorithme-du-simplexe\" data-toc-modified-id=\"Bonus-:-implémentation-manuelle-de-l'algorithme-du-simplexe-25\"><span class=\"toc-item-num\">2.5&nbsp;&nbsp;</span>Bonus : implémentation manuelle de l'algorithme du simplexe</a></div><div class=\"lev3 toc-item\"><a href=\"#Algorithme\" data-toc-modified-id=\"Algorithme-251\"><span class=\"toc-item-num\">2.5.1&nbsp;&nbsp;</span>Algorithme</a></div><div class=\"lev3 toc-item\"><a href=\"#Conversion-en-forme-standard\" data-toc-modified-id=\"Conversion-en-forme-standard-252\"><span class=\"toc-item-num\">2.5.2&nbsp;&nbsp;</span>Conversion en forme standard</a></div><div class=\"lev3 toc-item\"><a href=\"#Utilitaires-pour-les-matrices\" data-toc-modified-id=\"Utilitaires-pour-les-matrices-253\"><span class=\"toc-item-num\">2.5.3&nbsp;&nbsp;</span>Utilitaires pour les matrices</a></div><div class=\"lev3 toc-item\"><a href=\"#L'algorithme-du-simplexe\" data-toc-modified-id=\"L'algorithme-du-simplexe-254\"><span class=\"toc-item-num\">2.5.4&nbsp;&nbsp;</span>L'algorithme du simplexe</a></div><div class=\"lev3 toc-item\"><a href=\"#Un-premier-exemple\" data-toc-modified-id=\"Un-premier-exemple-255\"><span class=\"toc-item-num\">2.5.5&nbsp;&nbsp;</span>Un premier exemple</a></div><div class=\"lev3 toc-item\"><a href=\"#Tests\" data-toc-modified-id=\"Tests-256\"><span class=\"toc-item-num\">2.5.6&nbsp;&nbsp;</span>Tests</a></div><div class=\"lev2 toc-item\"><a href=\"#Conclusion\" data-toc-modified-id=\"Conclusion-26\"><span class=\"toc-item-num\">2.6&nbsp;&nbsp;</span>Conclusion</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# [ALGO1 : Introduction à l'algorithmique](https://perso.crans.org/besson/teach/info1_algo1_2019/)\n",
    "\n",
    "- [Page du cours](https://perso.crans.org/besson/teach/info1_algo1_2019/) : https://perso.crans.org/besson/teach/info1_algo1_2019/\n",
    "- Magistère d'Informatique de Rennes - ENS Rennes - Année 2019/2020\n",
    "- Intervenants :\n",
    "  + Cours : [Lilian Besson](https://perso.crans.org/besson/)\n",
    "  + Travaux dirigés : [Raphaël Truffet](http://perso.eleves.ens-rennes.fr/people/Raphael.Truffet/)\n",
    "- Références :\n",
    "  + [Open Data Structures](http://opendatastructures.org/ods-python.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cours Magistral 9\n",
    "\n",
    "- Ce cours traite de programmation linéaire.\n",
    "\n",
    "- On va illustrer deux programmes linéaires résolus avec la fonction `scipy.optimize.linprog`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import scipy.optimize as opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Documentation de `scipy.opt.linprog`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "    Linear programming: minimize a linear objective function subject to linear\n",
      "    equality and inequality constraints.\n",
      "\n",
      "    Linear programming solves problems of the following form:\n",
      "\n",
      "    .. math::\n",
      "\n",
      "        \\min_x \\ & c^T x \\\\\n",
      "        \\mbox{such that} \\ & A_{ub} x \\leq b_{ub},\\\\\n",
      "        & A_{eq} x = b_{eq},\\\\\n",
      "        & l \\leq x \\leq u ,\n",
      "\n",
      "    where :math:`x` is a vector of decision variables; :math:`c`,\n",
      "    :math:`b_{ub}`, :math:`b_{eq}`, :math:`l`, and :math:`u` are vectors; and\n",
      "    :math:`A_{ub}` and :math:`A_{eq}` are matrices.\n",
      "\n",
      "    Informally, that's:\n",
      "\n",
      "    minimize::\n",
      "\n",
      "        c @ x\n",
      "\n",
      "    such that::\n",
      "\n",
      "        A_ub @ x <= b_ub\n",
      "        A_eq @ x == b_eq\n",
      "        lb <= x <= ub\n",
      "\n",
      "    Note that by default ``lb = 0`` and ``ub = None`` unless specified with\n",
      "    ``bounds``.\n"
     ]
    }
   ],
   "source": [
    "print(\"\\n\".join(opt.linprog.__doc__.split(\"\\n\")[:31]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La programmation linéaire résout des problèmes de la forme suivante :\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\min_x \\ & c^T x \\\\\n",
    "\\mbox{such that} \\ & A_{ub} x \\leq b_{ub},\\\\\n",
    "& A_{eq} x = b_{eq},\\\\\n",
    "& l \\leq x \\leq u ,\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "avec $x$ un vecteur de variables de décisions ; $c$, $b_{ub}$, $b_{eq}$, $l$, et $u$ sont des vecteurs ; $A_{ub}$ et $A_{eq}$ sont des matrices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fonction de débogage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "code_folding": [
     2
    ]
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   "outputs": [],
   "source": [
    "def make_callback():\n",
    "    list_of_x, list_of_fun = [], []\n",
    "    def debug_callback(opt_res):\n",
    "        print(\"\\nA new optimization step gave:\")\n",
    "        print(f\"Current solution x = {opt_res.x}\")\n",
    "        list_of_x.append(opt_res.x)\n",
    "        print(f\"Current value of c @ x = {opt_res.fun}\")\n",
    "        list_of_fun.append(opt_res.fun)\n",
    "        print(f\"Success? = {opt_res.success}\")\n",
    "        print(f\"The (nominally positive) values of the slack, b_ub - A_ub @ x. = {opt_res.slack}\")\n",
    "        print(f\"The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = {opt_res.con}\")\n",
    "        print(f\"Algorithm in phase {opt_res.phase}\")\n",
    "        print(f\"Algorithm in iteration number {opt_res.nit}\")\n",
    "        status = {\n",
    "            0: \"Optimization proceeding nominally.\",\n",
    "            1: \"Iteration limit reached.\",\n",
    "            2: \"Problem appears to be infeasible.\",\n",
    "            3: \"Problem appears to be unbounded.\",\n",
    "            4: \"Numerical difficulties encountered.\",\n",
    "        }\n",
    "        print(f\"Algorithm status {status[opt_res.status]}\")\n",
    "        if opt_res.message: print(f\"Algorithm message: {opt_res.message}\")\n",
    "    return list_of_x, list_of_fun, debug_callback"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Premier exemple\n",
    "\n",
    "On va suivre l'exemple détaillé en cours :\n",
    "\n",
    "- Variables\n",
    "  + $x$ nombre de tables fabriquées par semaine,\n",
    "  + $y$ nombre de chaises fabriquées par semaine.\n",
    "\n",
    "- Objectif :\n",
    "  + maximiser $30x + 10y$.\n",
    "\n",
    "- Contraintes :\n",
    "  + heures de travail : $6x+3y \\leq 36$,\n",
    "  + demande : $y \\geq 3x$,\n",
    "  + stockage : $x + y/4 \\leq 4$,\n",
    "  + positivité : $x \\geq 0$,\n",
    "  + positivité : $y \\geq 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mise sous la forme requise par la fonction `linprog`, cela va donner :\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\min_{[x, y]} \\ & [-30, -10]^T [x, y] \\\\\n",
    "\\mbox{such that} \\ & \n",
    "    [\n",
    "        [6, 3], [3, -1], [1, 1/4]\n",
    "    ]\n",
    "    [x, y]\n",
    "= [6x + 3y, 3x - y, x + y/4] \\leq [36, 0, 4],\\\\\n",
    "& [0, 0] \\leq [x, y] \\leq [+\\infty,+\\infty] ,\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et donc avec Python cela sera :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = np.array([-30, -10])\n",
    "\n",
    "A_ub = np.array([[6, 3], [3, -1], [1, 1/4]])\n",
    "b_ub = np.array([36, 0, 4])\n",
    "\n",
    "A_eq = None\n",
    "b_eq = None\n",
    "\n",
    "# all variables are bound to be in (0, +inf)\n",
    "bounds = (0, None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Objectif :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy\n",
    "x, y = sympy.var('x y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 30 x - 10 y$"
      ],
      "text/plain": [
       "-30*x - 10*y"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.T @ [x, y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Contraintes d'inéqualités :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.0*x + 3.0*y, 3.0*x - 1.0*y, 1.0*x + 0.25*y], dtype=object)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_ub @ [x, y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([36,  0,  4])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_ub"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Essayons avec différentes méthodes de résolution :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [0. 0.]\n",
      "Current value of c @ x = 0.0\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [36.  0.  4.]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 0\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [0. 0.]\n",
      "Current value of c @ x = 0.0\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [36.  0.  4.]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 1\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [2.28571429 6.85714286]\n",
      "Current value of c @ x = -137.14285714285717\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [1.71428571e+00 8.88178420e-16 0.00000000e+00]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 2\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [2.28571429 6.85714286]\n",
      "Current value of c @ x = -137.14285714285717\n",
      "Success? = True\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [1.71428571e+00 8.88178420e-16 0.00000000e+00]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 3\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [2.28571429 6.85714286]\n",
      "Current value of c @ x = -137.14285714285717\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [1.71428571e+00 8.88178420e-16 0.00000000e+00]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 2\n",
      "Algorithm in iteration number 3\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [2. 8.]\n",
      "Current value of c @ x = -140.0\n",
      "Success? = True\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [7.10542736e-15 2.00000000e+00 0.00000000e+00]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 2\n",
      "Algorithm in iteration number 4\n",
      "Algorithm status Optimization proceeding nominally.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "     con: array([], dtype=float64)\n",
       "     fun: -140.0\n",
       " message: 'Optimization terminated successfully.'\n",
       "     nit: 4\n",
       "   slack: array([7.10542736e-15, 2.00000000e+00, 0.00000000e+00])\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([2., 8.])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list_of_x, list_of_fun, debug_callback = make_callback()\n",
    "\n",
    "opt.linprog(c,\n",
    "            A_ub=A_ub, b_ub=b_ub,\n",
    "            A_eq=A_eq, b_eq=b_eq,\n",
    "            bounds=bounds,\n",
    "            method=\"simplex\",\n",
    "            callback=debug_callback,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_opt, y_opt = _.x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La solution obtenue est donc $x = 2$ et $y = 8$, qui donnerait un profit maximal de $+140 €$ par semaine en respectant toutes les contraintes.\n",
    "\n",
    "Pour obtenir une solution entière, on a rien à faire ici.\n",
    "\n",
    "Si la solution optimale était par exemple $2.23$ et $6.43$, on pourrait essayer $x = 2, 3$ et $y = 6, 7$, ie. on arrondit en dessous et au dessus, et on prend la solution qui satisfait les contraintes et maximise l'objectif :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.000000000000001, 7.9999999999999964)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_opt, y_opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour (x, y) = (2, 7), l'objectif vaut -130, la contrainte vaut [ True  True  True]\n",
      "Pour (x, y) = (2, 8), l'objectif vaut -140, la contrainte vaut [ True  True  True]\n",
      "Pour (x, y) = (3, 7), l'objectif vaut -160, la contrainte vaut [False False False]\n",
      "Pour (x, y) = (3, 8), l'objectif vaut -170, la contrainte vaut [False False False]\n",
      "==> Donc on utilise la solution entière optimale = [2, 8]\n"
     ]
    }
   ],
   "source": [
    "sol = None\n",
    "min_obj = float(\"+inf\")\n",
    "\n",
    "for (x, y) in itertools.product(\n",
    "        [int(np.floor(x_opt)), int(np.ceil(x_opt))],\n",
    "        [int(np.floor(y_opt)), int(np.ceil(y_opt))],\n",
    "    ):\n",
    "    obj = c.T @ [x, y]\n",
    "    ctr = (A_ub @ [x, y]) <= b_ub\n",
    "    print(f\"Pour (x, y) = {x, y}, l'objectif vaut {obj}, la contrainte vaut {ctr}\")\n",
    "    if np.all(ctr) and obj < min_obj:\n",
    "        min_obj = obj\n",
    "        sol = [x, y]\n",
    "\n",
    "print(f\"==> Donc on utilise la solution entière optimale = {sol}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La solution entière optimale à ce premier problème est donc de fabriquer $x=2$ tables et $y=8$ chaises chaque semaine."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Second exemple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"figures/CM9_ensemble_admissible.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mise sous la forme requise par la fonction `linprog`, cela va donner :\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\min_{[x, y]} \\ & [4, 3]^T [x, y] \\\\\n",
    "\\mbox{such that} \\ & \n",
    "    [\n",
    "        [-1, 4], [1, 1], [3, -1]\n",
    "    ]\n",
    "    [x, y]\n",
    "= [-x + 4y, x + y, 3x - y] \\leq [16, 9, 15],\\\\\n",
    "& [0, 0] \\leq [x, y] \\leq [+\\infty,+\\infty] ,\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et donc avec Python cela sera :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = np.array([-4, -3])\n",
    "\n",
    "A_ub = np.array([[-1, 4], [1, 1], [3, -1]])\n",
    "b_ub = np.array([16, 9, 15])\n",
    "\n",
    "A_eq = None\n",
    "b_eq = None\n",
    "\n",
    "# all variables are bound to be in (0, +inf)\n",
    "bounds = (0, None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Objectif :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy\n",
    "x, y = sympy.var('x y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 4 x - 3 y$"
      ],
      "text/plain": [
       "-4*x - 3*y"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.T @ [x, y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Contraintes d'inéqualités :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-x + 4*y, x + y, 3*x - y], dtype=object)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_ub @ [x, y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16,  9, 15])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_ub"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Essayons avec différentes méthodes de résolution :"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Avec la méthode du simplexe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [0. 0.]\n",
      "Current value of c @ x = 0.0\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [16.  9. 15.]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 0\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [0. 4.]\n",
      "Current value of c @ x = -12.0\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [ 0.  5. 19.]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 1\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [4. 5.]\n",
      "Current value of c @ x = -31.0\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [0. 0. 8.]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 2\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [4. 5.]\n",
      "Current value of c @ x = -31.0\n",
      "Success? = True\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [0. 0. 8.]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 3\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [4. 5.]\n",
      "Current value of c @ x = -31.0\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [0. 0. 8.]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 2\n",
      "Algorithm in iteration number 3\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [6. 3.]\n",
      "Current value of c @ x = -33.0\n",
      "Success? = True\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [10.  0.  0.]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 2\n",
      "Algorithm in iteration number 4\n",
      "Algorithm status Optimization proceeding nominally.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "     con: array([], dtype=float64)\n",
       "     fun: -33.0\n",
       " message: 'Optimization terminated successfully.'\n",
       "     nit: 4\n",
       "   slack: array([10.,  0.,  0.])\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([6., 3.])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list_of_x, list_of_fun, debug_callback = make_callback()\n",
    "\n",
    "opt.linprog(c,\n",
    "            A_ub=A_ub, b_ub=b_ub,\n",
    "            A_eq=A_eq, b_eq=b_eq,\n",
    "            bounds=bounds,\n",
    "            method=\"simplex\",\n",
    "            callback=debug_callback,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, \"Valeur de l'objectif étape par étape (méthode simplexe)\")"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8253230dd0>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 7))\n",
    "plt.title(\"Valeur de l'objectif étape par étape (méthode simplexe)\")\n",
    "plt.plot(list_of_fun, \"ro-\", lw=3, ms=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Position des points étape par étape (méthode simplexe)')"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f82531b0bd0>]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8253217e10>]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8253164c10>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 7))\n",
    "plt.title(\"Position des points étape par étape (méthode simplexe)\")\n",
    "list_of_X, list_of_Y = [x for (x,y) in list_of_x], [y for (x,y) in list_of_x]\n",
    "# plt.plot(list_of_X, list_of_Y, 'bo-')\n",
    "plt.plot(list_of_X, 'bo-', label=\"Valeur de x\", lw=3, ms=14)\n",
    "plt.plot(list_of_Y, 'gd-', label=\"Valeur de y\", lw=3, ms=14)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Avec la méthode du point intérieur (un autre algorithme)\n",
    "\n",
    "Cet autre algorithme est plus récent, plus technique, et il fonctionne généralement mieux : plus rapide, plus stable numérique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [1. 1.]\n",
      "Current value of c @ x = -7.0\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [13.  7. 13.]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 0\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [4.01262108 3.38515509]\n",
      "Current value of c @ x = -26.205949599949\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [6.47200073 1.60222383 6.34729184]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 1\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [5.9137431  2.95777926]\n",
      "Current value of c @ x = -32.52831014613114\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [10.08262607  0.12847765  0.21654997]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 2\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [5.9999917  2.99999607]\n",
      "Current value of c @ x = -32.999954993936036\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [1.00000074e+01 1.22338576e-05 2.09841077e-05]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 3\n",
      "Algorithm status Optimization proceeding nominally.\n",
      "\n",
      "A new optimization step gave:\n",
      "Current solution x = [6. 3.]\n",
      "Current value of c @ x = -32.9999999977497\n",
      "Success? = False\n",
      "The (nominally positive) values of the slack, b_ub - A_ub @ x. = [1.00000000e+01 6.11692030e-10 1.04921938e-09]\n",
      "The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x. = []\n",
      "Algorithm in phase 1\n",
      "Algorithm in iteration number 4\n",
      "Algorithm status Optimization proceeding nominally.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "     con: array([], dtype=float64)\n",
       "     fun: -32.9999999977497\n",
       " message: 'Optimization terminated successfully.'\n",
       "     nit: 4\n",
       "   slack: array([1.00000000e+01, 6.11692030e-10, 1.04921938e-09])\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([6., 3.])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list_of_x, list_of_fun, debug_callback = make_callback()\n",
    "\n",
    "opt.linprog(c,\n",
    "            A_ub=A_ub, b_ub=b_ub,\n",
    "            A_eq=A_eq, b_eq=b_eq,\n",
    "            bounds=bounds,\n",
    "            method=\"interior-point\",\n",
    "            callback=debug_callback,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, \"Valeur de l'objectif étape par étape (méthode point intérieur)\")"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f825314e550>]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 7))\n",
    "plt.title(\"Valeur de l'objectif étape par étape (méthode point intérieur)\")\n",
    "plt.plot(list_of_fun, \"ro-\", lw=3, ms=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Position des points étape par étape (méthode point intérieur)')"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f82530fec50>]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8253164c90>]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f82533984d0>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Pdu+G1NSc+YcOwZIl8NVX0KABLF4MJ50U5GArOF2tExERKZuw6bj9yy/QuTMkJ+dNkHJLTYXNm91yv/xSvvGJiIhI1RIWSVJ2NiQmwv79UNyj5Kx1yyUmlqzprVevXixatCjPvEmTJnHTTTcVuV5cXJz/GymD+Ph4du3aVS7bEhERkeKFRZK0eLFrYvP3WbvWuuU/+sj/bQwZMoQ5c+bkmTdnzhyGDBlSgkhLLzMzs1y2IyJS0alvatUVbuc+LJKkiRPhwIGSrXPgAEyY4P/yAwcO5P333ycjIwOAjRs38scff3DWWWeRmppKnz59OP3002nfvj1vv/12gXU88cQTnHHGGXTo0IExY8b46jnllFN8yzz55JOMHTsWgJ49ezJy5EgSEhKYPHlynrpSUlJITEykXbt2XH/99dhcGeLMmTPp3Lkzp512GiNGjCArKyvPuvv27ePkk09m3bp1gEsAp02b5v/BEBEJU7/8AscdB4MGub6ohw65f4y9fVMHDYLjj1eXi8ooHM99SJIkY/L+LFlSunqWLDm6rsLUr1+fzp07s3DhQsBdRRo8eDDGGGJiYnjzzTdZs2YNS5Ys4c4778yTtAAsXryY9evXs2rVKr755huSkpJYunRpsTFmZGSwevVq7rzzzjzzH374YXr06MGPP/7IgAED2Lx5MwBr165l7ty5LF++nG+++YZq1aoxa9asPOvWqVOHZ555hmuuuYY5c+awZ88ehg8f7s8hExEJW+qbWnWF67n36+42Y0xd4CXgFMAC11prVwYzsGDwNrn179+fOXPm8PLLLwNuXKH77ruPpUuXEhERwdatW9m+fTuNGzf2rbt48WIWL15Mx44dAUhNTWX9+vW0bNmyyG1efvnlBc5funQpb7zxBgAXXXQR9erVA+CTTz4hKSmJM844A4BDhw7RqFGjo9Y/77zzmD9/Pv/4xz/49ttvS3gkRETCS2n7pm7Y4JpkpOIK53Pv7xAAk4EPrbUDjTHVgdggxhQ0/fv354477mDNmjWkpaXRqVMnAGbNmsXOnTtJSkoiKiqK+Pj4o8YYstYyevRoRowYkWf+li1byM7VSJp/vZo1a5YoRmstV199NePHjy9yuezsbNauXUtsbCx79uyhefPmJdqOiEg4KUvf1PPPD25sElzhfO6LTZKMMXWAs4FrXHA2A8goy0bzH4jevUvX5NarF3z6qf/Lx8XF0atXL6699to8Hbb37dtHo0aNiIqKYsmSJWzatOmodc8//3wefPBBhg4dSlxcHFu3biUqKopjjz2WHTt2kJKSQlxcHO+99x4XXHBBsbGcffbZzJ49mwceeICFCxeyZ88eAPr06eNL5ho1asTu3bs5cOAArVq1yrP+v//9b9q0acNjjz3GsGHDWLlypR5BIiJhwVpIT3fNI6mprg+pd7qwnzlzStc39eKLoU6d4OyHlI99+6Ck9zZ5+yWHPEkCjgN2Aq8aY04FkoDbrbUHAxXEqFFuoMjC2iELEhcH99xT8m0NGTKEAQMG5LnTbejQofTr14/27duTkJBA69atj1ovMTGRtWvX0rVrV8/245g5cyaNGjXioYceonPnzjRr1qzAdQsyZswYhgwZQrt27ejWrZuv2a5t27aMGzeOxMREsrOziYqKYurUqXmSpHXr1vHSSy+xatUqatWqxdlnn824ceN4+OGHS35ARMJYdrb7L3PiRPjiC/eHNyYGunRx3xuJiWpqKavsbEhL8z+Z8fenvO5CysyElJTy2ZaEly++CP42TP4OykctYEwC8AXQ3Vr7pTFmMrDfWvtgvuVuAG4AaNmyZaf8V2PWrl1LmzZtCtxGdrbrsb55s3+X24yBli3VFl2coo65SLgrbAR+r7i4qjcCf2YmHDwY2GTmYMD+3RUpXxERkO/m71IzxiRZaxPyz/fnStIWYIu19ktPeQFwb/6FrLUvAi8CJCQk+Nmy6EREuC+6zp3zddyquxEGXg4L5sLeeM+OQO3abnklSCKVk/dOl6I6cnr/wHfuDKtWhV+ilJER2GQmNdVdSasooqOhVi2XzPrzM3o0HDlS8u3ExLg7oqTiatGidO/t6OjAx5JfsUmStfZPY0yyMeZka+06oA/wU6ADOekk90WXmOj+czxwAOg3HJquhotHwMxF1KoF9etXrf8cRaqa8r7TxTsOSyCTmdTU0v3BD5WaNf1PZvz5qVkTStpF8v33S9c3tWtXOOaYkq8n4aNr19Kd+y5dAh9Lfv7e3XYrMMtzZ9sGYFgwgjnpJPdF99FHMGraB3zXYgVEZEPLZXT460ImDu/LeefpCpJIZVaaO1127IAHH4QTTwzv/jNlFRER2GQmLs6NZlytWqj3rHz7pkp4Cedz71eSZK39BjiqrS4YIiLgnD7p7PjhOkhNczOrp7Gz63Wc02cDEREx5RGGiIRIaUbgP3QIHnssOPGUVmRkyZqb/PmpUaPoQXMrssRE18fs4EH/+6Y2aOD6rUnFFs7n3t8rSeVq/P/Gs//w/jzz9h3ex+PLHmdsz7GhCUpEykV53LGSX0xMYJOZWrWgevXy34+KrNC+qQVQ39TKJZzPfdglSRv3buSJFU9wKPNQnvlpR9KYuHwi15x2DfF140MTnIgEXVk6J199dcmTmZo13VUfCb0C+6bmo76plVO4nvuw+2oY/u5wjmQX3OPxSPYRRrw7gkVXLipxvb169eLee+/l/FwjT02aNIl169bx3HPPFbpeXFwcqSVpKC2l+Ph4Vq9ezTHqgShVXEyMaz4rqRo1YPr0gIcj5Sx339QJE9yVxcOH3Z1MXbq4fijqm1o5heO5D6sk6YP1H7AieQWZ2QUPvZmZncmy5GUsXL+Qvn/pW6K6vc9ty50kzZkzh4kTJ5YpZn9lZmYSqX9XRYrVpUv43uki5SMiwo2krMeNVD3hdu7DJhdPz0znuneuI+1IWpHLpR1J47p3riM9s2TX5AcOHMj7779PRoZ7osrGjRv5448/OOuss0hNTaVPnz6cfvrptG/fnrfffrvAOp544gnOOOMMOnTowJgxY3z1nHLKKb5lnnzyScaOHQtAz549GTlyJAkJCUyePDlPXSkpKSQmJtKuXTuuv/56cg/qOXPmTDp37sxpp53GiBEjyMo3Wtann37KpZde6it/9NFHDBgwoETHQyRcnXlmydfRXU4iEgwhubRhHi7b7RnbUrdR4181CnzNjim4x1f9+vXp3LkzCxcupH///syZM4fBgwdjjCEmJoY333yT2rVrs2vXLrp06cIll1yCyXUbyeLFi1m/fj2rVq3CWssll1zC0qVLfY8TKUxGRgarV68+av7DDz9Mjx49eOihh3j//fd5+eWXATdK9ty5c1m+fDlRUVHcfPPNzJo1i6uuusq3bq9evbj55pvZuXMnDRs25NVXX+Xaa68t9riJhLu333Z3t5WE7nISkWCpUu0/3iY3b5LkTUystdx3330sXbqUiIgItm7dyvbt22ncuLFv3cWLF7N48WI6duwIQGpqKuvXry82Sbr88ssLnL906VLeeOMNAC666CLq1asHwCeffEJSUhJnnHEGAIcOHaJRo0Z51jXGcOWVVzJz5kzfw21fe+21UhwRkfDx4YcweHDOmEUREe4ul3C600VEqpYqlST179+fO+64gzVr1pCWlkanTp0AmDVrFjt37iQpKYmoqCji4+NJz3eLjbWW0aNHM2LEiDzzt2zZQnaukejyr1ezZs0SxWit5eqrr2b8+PFFLjds2DD69etHTEwMgwYNUn8nqdA+/RQGDHCP8gA3KOSrr8IVV4TXnS4iUrWE5H8vO8Ye9XPo/kM0jmtc/MpAk7gmHLr/UIH1FCUuLo5evXpx7bXXMmTIEN/8ffv20ahRI6KioliyZAn5H84LcP755/PKK6/47nTbunUrO3bs4Nhjj2XHjh2kpKRw+PBh3nvvPb/24eyzz2b27NkALFy4kD179gDQp08fFixYwI4dOwDYvXt3gfE0bdqUpk2bMm7cOIYNC8oA6CLlYvly6Ncv59b/Vq3gk0+gRw93p8v8+dCrl7t7LSLC/e7Vy83fsEEJkogET9hcfoiJjOGVS15h4PyBRXbejo2K5eVLXiYmsnQjbw8ZMoQBAwYwZ84c37yhQ4fSr18/2rdvT0JCAq1btz5qvcTERNauXUvXrl0Bl3DNnDmTRo0a8dBDD9G5c2eaNWtW4LoFGTNmDEOGDKFdu3Z069bN12zXtm1bxo0bR2JiItnZ2URFRTF16lRatWp1VB1Dhw5l586dtGnTpjSHQiTkvvoK+vaFNM9HvmlTlyB5W7HD7U4XEalajPX3AUklkJCQYPN3Vl67dq1ff8zPm3Een238rMBhACIjIukd37tU4yRVRrfccgsdO3bkuuuuK/B1f4+5SCh8+627IuS5iEqjRvD55+Dn/xkiIgFjjEmy1h71+LWw6+o4rd80oiIKfnx0VEQUL/R7oZwjCk+dOnXiu+++44orrgh1KCIl9tNP7m40b4JUvz58/LESJBEJL2GXJMXXjefubncTGxWbZ35sVCyjuo/SI0k8kpKSWLp0KdHR0aEORaREfv0Vzj0Xdu505Tp13Ai77duHNi4RkfzKNUnyt2lv9FmjqR1dO8+8OtF1uLfHvcEIq1IKRjOqSFlt3Ai9e8O2ba4cF+du/T/99JCGJSJSoHJLkmJiYkhJSfHrj7e3E7f3alJZO2tXNdZaUlJSiInR8ZLwsXUr9OkDycmuXKMGvPeeHiciIuGr3O5ua968OVu2bGGn9xp7MeKJ59T6p/Ll9i85rf5pxGfGs3bt2iBHWXnExMTQvHnzUIchAsD27S5B2rDBlatXh7fegnPOCW1cIiJFKbckKSoqiuOOO65E68xuMpvL51/OrEGz1BdJpIJKSXGdtNetc+XISFiwABITQxuXiEhxwmacpILE143ny+FfhjoMESmlvXtdMvT9964cEQH//a8bPFJEJNyF3d1tIlI5HDjgBopcs8aVjYHXXoOBA0Mbl4iIv5QkiUjApaXBxRfDF1/kzJs2DYYODV1MIiIlpSRJRAIqPR0uvRSWLs2ZN2UKFDIwvIhI2FKSJCIBk5EBgwa5wSG9Jk6EW24JXUwiIqWlJElEAiIz0zWnvfdezryHH4a77w5dTCIiZaEkSUTKLCsLhg1zt/Z73XsvPPhg6GISESkrJUkiUibZ2XDjjTBzZs6822+Hxx5zd7SJiFRUSpJEpNSsdQnRSy/lzBsxAv79byVIIlLxKUkSkVKxFu65B555JmfeVVfBs88qQRKRykFJkoiUysMPwxNP5JQHD4aXX3ajaouIVAb6OhOREpswwSVJXv37uz5JkWH9oCMRkZJRkiQiJTJ5srtzzeuCC2DuXIiKCl1MIiLBoCRJRPz24oswcmROuVcveOMNiI4OXUwiIsGiJElE/PLaa+5Wf6/u3eGdd6BGjdDFJCISTEqSRKRYc+e6wSKtdeWEBHj/fYiLC21cIiLBpCRJRIr09ttwxRVu0EiADh1g0SKoUye0cYmIBJuSJBEp1KJF7tb+zExXbtPGPby2fv3QxiUiUh6UJIlIgZYsgUsvhYwMVz7hBPj4Y2jUKLRxiYiUFyVJInKU5cuhXz9IT3flVq3g00+hadPQxiUiUp6UJIlIHqtXw4UXwsGDrty0KXzyCbRsGdq4RETKm5IkEfH59ltITIT9+125USOXIJ1wQmjjEhEJBSVJIgLA2rVw3nmwZ48r16/v+iC1bh3auEREQkVJkojw66/Qpw/s3OnKderA4sXQvn1o4xIRCSUlSSJV3KZNLkHats2Va9aEhQuhU6fQxiUiEmpKkkSqsK1boXdv2LzZlWvUcCNpd+0a2rhERMKBkiSRKmr7dncFacMGV65eHd56C845J7RxiYiECyVJIlVQSorrpL1unStHRsKCBe7ONhERcZQkiVQxe/e6ZOj77105IgJmz3aDR4qISA4lSSJVyIED0LcvrFnjysbAf/4DgwaFNi4RkXCkJEmkikhLc1eLvvgiZ96LL8IVV4QuJhGRcKYkSaQKSE+HAQPg889z5k2ZAtdfH7qYRETCnZIkkUouIwMGD3aDQ3pNnAi33BK6mEREKgIlSSKVWGYmDB0K776bM+/hh+Huu5s6hucAACAASURBVEMXk4hIRaEkSaSSysqCYcPcrf1e99wDDz4YuphERCoSJUkilZC1cOONMHNmzrzbboPx490dbSIiUjwlSSKVjLVw++3w0ks58264ASZNUoIkIlISSpJEKhFr4d573Z1rXlddBc89pwRJRKSklCSJVCIPP+zuXPMaPBheftmNqi0iIiWjr06RSmLCBJckefXv7/okRUaGLiYRkYpMSZJIJTB5smtm8zr/fJg7F6KiQheTiEhFpyRJpIJ78UUYOTKn3LMnvPEGREeHLCQRkUpBSZJIBTZjhrvV36tbNzdwZGxs6GISEakslCSJVFDz5sE117g72gASEuCDDyAuLqRhiYhUGn516TTGbAQOAFlAprU2IZhBiUjR3n7bPW4kO9uVO3SARYugTp3QxiUiUpmU5L6XXtbaXUGLRET8smiRu7U/M9OVW7eGjz6C+vVDG5eISGWj5jaRCmTJErj0UsjIcOUTToBPPoFGjUIbl4hIZeRvkmSBxcaYJGPMDQUtYIy5wRiz2hizeufOnYGLUEQAWLEC+vWD9HRXbtnSJUhNm4Y2LhGRysrfJKmHtfZ0oC/wD2PM2fkXsNa+aK1NsNYmNGzYMKBBilR1q1dD375w8KArN20Kn34KrVqFNi4RkcrMryTJWrvV83sH8CbQOZhBiUiO776DxETYv9+VGzVyV5BOOCG0cYmIVHbFJknGmJrGmFreaSAR+CHYgYkIrF0L554Le/a4cv36rpN269ahjUtEpCrw5+62Y4E3jXuEeCQw21r7YVCjEhF+/RX69AFvF7/atWHxYne7v4iIBF+xSZK1dgNwajnEIiIemza5BGnbNleuWRMWLoROnUIbl4hIVaIhAETCzNat0Ls3bN7syjEx8N577pEjIiJSfpQkiYSRHTtcH6QNG1y5enU3unbPniENS0SkSlKSJBImUlJcgvTzz64cGQkLFrg720REpPwpSRIJA3v3wvnnw/ffu3JEBMye7QaPFBGR0FCSJBJiBw7AhRdCUpIrGwPTp8OgQSENS0SkylOSJBJCaWnuatHKlTnzXngBrrwydDGJiIijJEkkRNLTYcAA+PzznHlPPw3Dh4cuJhERyaEkSSQEjhyBwYPd4JBeEybArbeGLiYREclLSZJIOcvMhKFD4d13c+aNHQujRoUsJBERKYCSJJFylJ0N114L8+fnzLvnHnjoodDFJCIiBVOSJFJOrIUbb4QZM3Lm3XYbjB/v7mgTEZHwoiRJpBxYC7ffDtOm5cwbPhwmTVKCJCISrpQkiQSZtXDvvTBlSs68K6+E559XgiQiEs6UJIkE2SOPwMSJOeVBg+CVV9yo2iIiEr70NS0SRBMnujvXvC65BGbNcs9lExGR8KYkSSRInn7a3bnmlZgI8+ZBVFToYhIREf8pSRIJghdfdB21vXr2hDffhOjokIUkIiIlpCRJJMBmzHC3+nt17eoGjoyNDV1MIiJSckqSRAJo3jy45hp3RxtAp06wcCHExYU0LBERKQUlSSIB8s477nEj2dmu3L49LFoEdeqENi4RESkdJUkiAbBokbu1PzPTlVu3ho8/hgYNQhuXiIiUnpIkkTL67DO49FLIyHDlE06ATz6BRo1CGpaIiJSRkiSRMlixAi6+GNLTXbllS5cgNW0a2rhERKTslCSJlNLq1dC3Lxw86MpNmrgEqVWr0MYlIiKBoSRJpBS++84NDrl/vys3bOgSpBNPDG1cIiISOEqSREro55/h3HNhzx5Xrl/fddJu0ya0cYmISGApSRIpgd9+gz59YOdOV65dGxYvhg4dQhuXiIgEnpIkET9t2gS9e8Mff7hyzZpuoMhOnUIbl4iIBIeSJBE/bN3qriBt3uzKMTHw3nvQrVto4xIRkeBRkiRSjB07XB+k335z5erV4a233ENrRUSk8lKSJFKElBSXIP38sytHRsL8+XD++aGNS0REgk9Jkkgh9u1zydD337tyRATMng2XXBLauEREpHwoSRIpQGoqXHghJCW5sjEwfbp7PpuIiFQNSpJE8klLg3793CNHvJ5/Hq68MnQxiYhI+VOSJJLL4cMwYIB7aK3X5Mlwww0hC0lEREJESZKIx5EjMHiwGxzS6/HH4bbbQheTiIiEjpIkESAzE4YOhXfeyZk3Zgzcc0/oYhIRkdBSkiRVXnY2XHutu7Xfa9QolySJiEjVpSRJqjRr4cYbYcaMnHm33eaa2YwJXVwiIhJ6SpKkyrIWRo6EadNy5g0fDpMmKUESERElSVJFWQujR8PTT+fMu+IKeO45JUgiIuIoSZIq6ZFHYMKEnPKgQfDqq1CtWuhiEhGR8KIkSaqciRNh7Niccr9+MGuWey6biIiIl5IkqVKefjrvbf2JiTBvHkRFhS4mEREJT0qSpMqYNg1uvz2n3LMnvPkmxMSELCQREQljSpKkSpg5E0aMyCl37eoGjoyNDV1MIiIS3pQkSaU3fz5cfbW7ow3g9NPhgw+gVq3QxiUiIuFNSZJUau+8A3//uxtVG6B9e/dstrp1QxuXiIiEPyVJUmktWuRu7c/MdOXWreGjj6BBg9DGJSIiFYOSJKmUPvsMLr0UMjJc+fjj4eOP4dhjQxqWiIhUIEqSpNJZuRIuvhjS0125RQv49FNo1iy0cYmISMWiJEkqlaQkuOACOHjQlZs0cQlSq1ahjUtERCoeJUlSaXz3nRsccv9+V27YED75BE48MbRxiYhIxaQkSSqFn3+Gc8+F3btduV4910m7TZvQxiUiIhWXkiSp8H77Dfr0gZ07Xbl2bXeb/6mnhjYuERGp2JQkSdjLzoYPP4Tevd0I2RER7nfv3vCf/0CvXvDHH27ZmjVh4UJISAhtzCIiUvHpuecS1n75Bc47zzWjpabmzD90CJYscbf6e0fSjomBd9+Fbt1CEqqIiFQySpIkbP3yC3Tu7DpiexOh/HLPnzLFXVUSEREJBDW3SVjKzs65U62wBCk3Y2DcuJzHj4iIiJSVkiQJS4sXuyY2fxIkcMvt3u3uaBMREQkEv5MkY0w1Y8zXxpj3ghmQCMDEiXDgQMnWOXAAJkwITjwiIlL1lORK0u3A2mAFIpLbF1+U73oiIiL5+ZUkGWOaAxcBLwU3HBHH+9y1kjp8OLBxiIhI1eXvlaRJwCig0G6xxpgbjDGrjTGrd3pH9RMppZiY0q0XHR3YOEREpOoqNkkyxlwM7LDWJhW1nLX2RWttgrU2oWHDhgELUKqmLl3Kdz0REZH8/LmS1B24xBizEZgD9DbGzAxqVFLljRoFcXElWycuDu65JzjxiIhI1VNskmStHW2tbW6tjQf+Bnxqrb0i6JFJlZaYCA0a+L+8MW75884LXkwiIlK1aJwkCUsREf5fFTIm56G2EXpHi4hIgJToT4q19jNr7cXBCkbEKy0t75hHUVEFL1erFrRsCatWwUknlU9sIiJSNej/bglL//oXbNrkpuvXh1mz3HPZatRwV4tq1HDl+fNhwwYlSCIiEnh6wK2EnZ9/hieeyClPnAiDBrkfERGR8qIrSRJWrIVbboEjR1y5a1cYNiy0MYmISNWkJEnCyty58MknbjoiAp57Tp2xRUQkNPTnR8LGvn1wxx055VtvhVNPDV08IiJStSlJkrAxZgz8+aebbtIEHnkktPGIiEjVpiRJwsI338CUKTnl//s/N/aRiIhIqChJkpDLzoabb3a/Afr0gcsvD21MIiIiSpIk5F59FVaudNNRUTB1qhtFW0REJJSUJElI7drlHmbrdffdcPLJoYtHRETES0mShNTo0bB7t5tu1Qruvz+08YiIiHgpSZKQ+eILeOmlnPKUKRAbG7p4REREclOSJCGRmQk33ZRTvuQS6NcvdPGIiIjkpyRJQuLZZ91t/+AeVjt5cmjjERERyU9JkpS7bdvggQdyyg88APHxIQtHRESkQEqSpNzddRccOOCmTz4Z7rwztPGIiIgUREmSlKtPP4XZs3PKU6dCdHTo4hERESmMkiQpNxkZbmRtr7/9zY2uLSIiEo6UJEm5eeopWLfOTdeq5coiIiLhSkmSlItNm+DRR3PKjz4KTZuGLh4REZHiKEmScnH77XDokJs+9VT4xz9CG4+IiEhxlCRJ0L37Lrz9dk75uecgMjJ08YiIiPhDSZIEVVoa3HZbTvm666Br19DFIyIi4i8lSRJU48fDxo1uun59ePzxkIYjIiLiNyVJEjTr1sHEiTnlCRPgmGNCF4+IiEhJKEmSoLAWbrnFjY0E0KULXHttaGMSEREpCSVJEhTz5sHHH7vpiAj3QNuIALzbNu7dyJnTzmTj3o1lr0xERKQISpIk4PbvhzvuyCnfcgt07BiYuoe/O5zV21Yz4t0RgalQRESkEEqSJODGjoVt29x048bwyCOBqfeD9R+wInkF2TabZcnLWLh+YWAqFhERKYCSJAmob7+Fp5/OKf/f/0GdOmWvNz0zneveuY60I2kApB1J47p3riM9M73slYuIiBRASZIETHa2e4BtVpYr9+rlHmIbCOP/N579h/fnmbfv8D4eX6YxBUREJDiUJEnATJ8OK1a46agomDoVjCl7vRv3buSJFU/4riJ5pR1JY+LyierELSIiQaEkSQIiJQVGjcop33UXtGkTmLqHvzucI9lHCnztSPYRdeIWEZGgUJIkAXHffS5RAmjVCh54IDD1ejtrZ2ZnFvh6ZnamOnGLiEhQKEmSMvviC5g2Lac8eTLExpa93vydtQujTtwiIhIMSpKkTLKyXGdta1354ovhkksCU3dBnbULo07cIiISaEqSpEyeew6+/tpNx8S42/8D0Vkb4OlVTxd7Fckr7UgaE5ZPYMnvSziYcTAwAYiISJWmJElK7c8/4f77c8oPPADHHRe4+m/rfBuxUf6326VnptP7td7UnVCXM186k38u+idvrH2D7anbAxeUiIhUGcZ620kCKCEhwa5evTrg9Up4ueIKmDXLTZ90Enz3HURHB67+9Mx0jpt8HH+m/lnmuv5S/y90b9mdHi160KNlD05qcBImUJe8RESkQjPGJFlrE/LPjwxFMFLxLVmSkyABPPNMYBMkgJjIGC488UJe+eaVIperEVmDm8+4mQOHD7A8eTk/7vzxqGXW717P+t3rmf7NdACOiT2G7i2606NlD7q36E6npp2oXq16YHdAREQqNF1JkhLLyIDTToO1a1358sthzpzAb2fppqX0/k9vsmxWoctERkTSO743i65c5Ju3+9BuViSvYPnm5SxLXsaqravIyMooclsxkTF0btbZlzh1a9GNujF1A7YvIiISvgq7kqQkSUpswgS49143XasW/PwzNG0a2G38mfonHV/o6GtqizARZNvso5arEVmDn/7xE/F14wut63DmYZK2JbFs8zKWbV7G8uTl7D60u8jtGwynNDrFlzT1aNmDlnVaqolORKQSUpIkAbFpE7RtC2mem87+7//gjjsCu43M7EzOfe1cPt/0OeCaxoa2H8q0NdPy3O0WGxXL3d3uZmzPsSWqP9tms27XOpc0JS9j+ebl/Lbnt2LXa1armS9h6t6iOx2O7UC1iGol2raIiIQfJUkSEAMGwFtvuekOHSApCSID3LPt3o/vZcLyCYC7orP4ysX0aNnjqE7cTeKasOH2DcRExpR5m9sObGN58nJfE93X274uspkPoFb1WnRt0dV3tenMZmdSs3rNMsciIiLlS0mSlNn777vBIr2WLYPu3QO7jXfWvUP/Of195Ud7PcoDZ7tnnCxcv5CB8weSdiSN2KhYFgxaQN+/9A1sAB6pGams2rrK10S3cstKUjNSi1ynmqlGxyYdfXfQdW/ZncZxjYMSn4iIBI6SJCmTQ4egXTv4/XdXvvZaePnlwG5jw54NnP7C6ew7vA+Avif25b2/v0eEyRnO67wZ5/Hp759y7nHn5umsHWyZ2Zl8v/17X5+m/23+H38c+KPY9U6od0KeJrrWx7RWvyYRkTCjJEnK5KGH4NFH3XS9erBuHTRsGLj60zPT6fZyN77+0w3f3bJOS9bcsIYGsQ3yLLdx70Yun385cwfNLbKzdrBZa9m0b5NLmjxNdD/s+KHY9RrUaED3lt19TXSdmnQiOjLAYyeIiEiJKEmSUvvlF2jf3t36D/DCC3DDDYHdxvB3hvPS1y8BUL1adZYNW8YZzc4I7EaCbM+hPazcstLXRLdq6yoOZx0ucp3oatGc0ewMXxNdtxbdqFejXjlFLCIioCRJSslaOP98+OgjV+7cGVauhIgAPtBm+jfTGfb2MF/52Quf5aYzbgrcBkLkcOZh1mxbk+cuupRDKcWu165huzxNdPF149VEJyISREqSpFTmz4fBg910RAR89RWcfnrg6v/2z2/p8nIX0jPTAfh7+78zc8DMSpkUWGtZl7LO169p2eZl/Lr712LXa1qrqS9h6tGyBx2O7UBkhAbLFxEJFCVJUmIHDkDr1vCHp3/yrbfC008Hrv596ftImJbgSxTaNmzLqutXVanb6P9M/ZMVySt8TXRf//k1mdmZRa4TVz2Ors1zDT3Q/EziqseVU8QiIpWPkiQpsTvvdINFAhx7rOusXadOYOq21jJw/kDeWPsG4P7wfzX8K1of0zowG6igDmYczBl6IHkZK5NXciDjQJHrVDPVOK3xaXma6JrUalJOEYuIVHxKkqREvv8eOnaELM94ijNnwtChgav/qRVPcddHd/nKc/46h8tPuTxwG6gksrKz+H5HrqEHNv2PrQe2Frve8fWOz9NE1/qY1nmGUhARkRxKksRv2dlw9tmwfLkr9+wJn34KgeomtGzzMnpO7+kb0frWzrfydN8AtuNVYtZaNu/b7OvTtGyzG3rAUvTnuH6N+nRr0c13F11C0wQNPSAVQrgM+yHlrzzPvZIk8dv06TDMc7NZZCR89x20aROYurenbqfjCx3ZlroNgC7Nu/D5NZ9TvVr1wGygCtqbvpeVySt9V5u+3PqlryN8YaKrRZPQNMHXRNetRTfq16hfThGL+C9UA8hK6JXnuVeSJH7ZvRtOPhl27XLle+6Bxx8PTN2Z2ZkkzkhkycYlgBtY8esRX9OiTovAbEAAyMjK8A094L3itCttV7HrtW3Ylh4t3ONUerTswXF1j6uUdxlKxfHB+g8YNH9QuTyKSMJLeZ97JUnilxtvdINFArRoAWvXQs0A3Wx23yf3MX7ZeMA9uPbDKz4k8YTEwFQuhbLW8kvKL3ma6NbvXl/sek3imriEydNEd2rjU0M69ICaXaqW9Mz0oD7UWsJXKM69kiQp1qpV0KWLG0AS4M034dJLA1P3e7+8R7//9vOVx54zljE9xwSmcimx7anbc4YeSF7Gmm1rih16oGZUTbo07+Jrojuz2ZnUiq5VThGr2aWqGbNkDE+ufJK0I2m+ebFRsdzd7W7G9hwbusAk6EJx7pUkSZGystxo2mvWuPJFF8G77wams/bve37n9BdPZ2/6XgDOP+F8Phj6ge62CiNpR9J8Qw8sT17OiuQV7D+8v8h1IkyEG3ogVxNd01pNgxKfml2qlo17N9J2alsOZR466rUakTX46R8/6WpiJRWqc68kSYo0dSrccoubjomBH3+E448ve73pmel0f6U7a7a57KtF7RasGbGGY2KPKXvlEjRZ2Vn8sOOHPE10yfuTi13vuLrH5Rl6oE3DNmVOhtXsUvWcN+M8Ptv4WYFXNyMjIukd31tXEyupUJ37wpKkYjsYGGNigKVAtGf5BdZatZNUItu3w/3355Tvuy8wCRLAyA9H+hKkqIgo5g+arwSpAqgWUY1TG5/KqY1P5eYzbgZwQw9sXu5rovt++/dHDT3w+97f+X3v78z4bgYA9WLquaEHWuYMPVDSxGb8/8YfdVVr3+F9PL7scTW7VEIfrP+AFckrCm3+zczOZFnyMhauX6iriZVMOJ77Yq8kGXd7S01rbaoxJgpYBtxurf2isHV0JaliueoqmOH+pvGXv7hb/mMC8A/6jG9ncNVbV/nKU/pO4ZbOt5S9YgkL+9L3sXJLrqEHtnxZ4CXy3KpXq+6GHvA00XVv0Z0GsQ0KXV7NLpVDts3mSNYRMrIyfD9HsvOWM7IyOHD4AIMXDGb3od3F1lk3pi5PnPeEhg+pJDKyMrhr8V3sO7yv2GWDcSU5IM1txphYXJJ0k7X2y8KWU5JUcXz+uRss0mvRIkgMwA1n32//njNfOtP3x+1vp/yN2ZfN1i3llVhGVgZfb/s6TxPdzrSdxa7X5pg2vua5Hi17cHy9433vEzW7FC4rO+uoJKO4JKTA5bL8WC7bz+UK2W5xNwWIlEQwOnGXKUkyxlQDkoATganW2nsKWOYG4AaAli1bdtq0aVOZg5bgyshwjx756SdXHjQI5s0re737D+8n4cUE323mbY5pw6rhq/QQ1irGWsuvu3/1JUzLk5ezLmVdses1jmtM9xbdqV+jPjO+m1HkwJiB7MRtrfX9gS9LQuBXIpJd+oTFu81sm13mfRapqOrF1GP3PcVfcfRXoK4k1QXeBG611v5Q2HK6klQxTJzoBosEiIuDn3+GZs3KVqe1lsELBrPgpwWAu2181fBVtG3YtozRSmWw4+AO39ADy5OXk/RHEkeyj5SpztioWAa3HUw22WW6alLWOKRo1atVJyoiiurVqhf682fqn2w9sNWvBLCaqUa7hu04tfGp5RC9BNs3f37DTzt/8j2uqihhdyUpX0UPAWnW2icLW0ZJUvhLTobWrSHNMwzFU0/BP/9Z9nonfTGJOxbd4SvPvmw2Q9oPKXvFUimlHUnjq61f+ZroViSv8KtPgrgBWaMjo/MkGcUlIb7lqnmWi/BzueLqK2a7kRGRfjW1F3QnY2F0h2PlEupzX5a72xoCR6y1e40xNYDzgAkBi0xCYuTInASpfXu49day17l883Lu/uhuX/kfZ/xDCZIUKTYqlnPiz+Gc+HMA18/mx50/0uWlLsV2Ag+GyIjIMiUDpU5WSlFftYhq5X58gi0mMoZXLnmFgfMH5hlIML/YqFhevuRlJUiVSLiee3+eMdAE+I+nX1IEMM9a+15ww5Jg+uADeOONnPKzz0JUVNnq3HFwB4MXDPZ10OzcrDNPJT5VtkqlyqkWUY0Ox3bg7m53HzXibmGqR1Qn8YREBrYdWKYkJKpalAY4DQN9/9KXbi26Fdlhv0eLHrr9vxIKx3OvwSSrmEOH4JRTYMMGV77mGnj11bLVmZWdxfkzz+eT3z8BoH6N+qy5YQ2t6rYqW8VSZYX60ruEloZ+qLrCbcRt/dtUxTz+eE6CVK+e67xdVmM/G+tLkAyGWZfNUoIkZeK99B4bFVvkcmp2qZzi68Zzd7e7jzr/sVGxjOo+SglSJRZu515JUhWyfj1MyNWbbPx4aNiwbHV+sP4Dxv1vnK/84NkPcsGJF5StUhFyLr1HRhTcK0DNLpXb6LNGUzu6dp55daLrcG+Pe0MUkZSXcDr3SpKqCGtd5+zDh125c2e4/vqy1blx70aueOMKX/m848/joXMeKlulIrlM6zeNqIiCO8xFRUTxQr8XyjkiKS/5rybqqmHVEU7nXklSFfH66240bQBjXGftamW4OeZw5mEGzR/EnvQ9ADSv3ZxZl82qlHfcSOiE26V3KV/eq4kRJkJXDauYcDn3SpKqgAMH3C3/XjffDJ06la3OOxbdweo/XOf8yIhI5g2cR8OaZWy7EylAOF16l/I3rd80Epok6KphFRQO515JUhXwyCOwdaubbtQIxo0revnizPpuFs+tfs5XfirxKbq26Fq2SkUKEU6X3qX8xdeN58vhX+qqYRUUDudeSVIl98MP8O9/55Sfegrq1i19fT/u+JEb3rvBVx7cbjC3dg7ASJQiRQiXS+8iUrUoSarErIWbboIsz6NwzjkHhg4tfX0HDh/gr/P+6hvg7+QGJ/NSv5f8etyASFmFw6V3Eala/BlxWyqo116DZcvcdGQkTJ3qOm2XhrWW69+93vcU99ioWF4f/Dq1omsFKFqRonkvvYuIlBddSaqk9uyBu3Meo8Y//wnt2pW+vimrpjDvx3m+8osXv0i7RmWoUEREJMwpSaqk7r8fdu500y1awIMPlr6ulckruXPxnb7yjZ1uZGiHMrTbiYiIVABKkiqhr76C55/PKU+aBHFxpatr58GdeR5cm9A0gUkXTApAlCIiIuFNSVIlk5XlOmt7n1vcty8MGFDKurKzGPrGULbs3wJAvZh6zB80n+jI6ABFKyIiEr6UJFUyL74ISUluOjoapkwpfWftRz5/hI82fOQrz7xspsYqERGRKkNJUiWyfTuMHp1Tvu8+OOGE0tX14a8f8ujSR33l+8+6nwv/cmEZIxQREak4lCRVIqNGwb59bvqEE1y5NDbv28zQN4ZicW12fY7rw8M9Hw5QlCIiIhWDkqRKYulSNy6S1zPPQEwpntrgfXDt7kO7AWhaqymz/zpbD64VEZEqR0lSJXDkiHtordfAgXDBBaWr687Fd7Jq6yog58G1jWo2CkCUIiIiFYuSpEpg8mT48Uc3XbNm3me1lcR/v/8vU7+a6itPPHci3Vt2D0CEIiIiFY+SpAouORnGjs0pjx0LzZuXvJ6fdv7E8HeH+8oD2w5kZJeRZY5PRESkolKSVMHdcQccPOim27WD228veR2pGakMnDeQg0dcRX+p/xdevuRlPbhWRESqNCVJFdiHH8Lrr+eUn3sOoqJKVoe1luHvDmftrrUA1IisweuDX6d2dO0ARioiIlLxKEmqoNLT4ZZbcspXXw1nnVXyep796lnm/DDHV37+4udpf2z7AEQoIiJSsSlJqqAmTIDffnPTdevCxIklr+PLLV9yx6I7fOUbTr+Bq069KkARioiIVGxKkiqgX3+F8eNzyo89Bo1KeJf+rrRdDJo/iCPZRwA4vcnpTO47OYBRioiIVGxKkioYa+HWW+HwYVdOSIAbbihZHdk2myveuILk/ckA1I2py4JBC4iJDckgrwAAGNpJREFULMXokyIiIpWUkqQK5s03XYdtcA+ufe45qFbCwbDHLR3Hot8W+cozBszguHrHBTBKERGRik9JUgWSmpr3Fv+bbnJXkkpi8W+LGfvZWF95dI/RXHzSxYEJUEREpBJRklSBPPIIbNniphs2hHHjSrZ+8r5k/v76330Pru0V34tHej0S4ChFREQqByVJFcSPP+Z93MiTT0K9ev6vn5GVweAFg0k5lAJAk7gm/Pev/yUyIjLAkYqIiFQOSpIqAGvdA2wzM135rLPgyitLVsfdi+/miy1fAFDNVGPuwLkcG3dsgCMVERGpPJQkVQAzZ8LSpW46MhKefdZ12vbX3B/m8vSqp33lCedO4KxWpRh5UkREpApRkhTm9uyBu+7KKY8cCaec4v/6P+/6mevfvd5XHtB6AP/s+s8ARigiIlI5KUkKcw88ADt2uOlmzWDMGP/XPZhxkL/O+yupGakAnFj/RF7t/6oeXCsiIuIHJUlhLCnJjYPkNXkyxMX5t661lhHvjeCnnT8BEBMZw4JBC6gTUycIkYqIiFQ+SpLCVFaWGwfJurv1ueACuOwy/9d/fvXzzPp+lq/83EXPcWrjUwMcpYiISOWlJClMTZsGX33lpqOjYcoU/ztrf7X1K0YuGukrX9fxOq457ZrABykiIlKJKUkKQzt2wOjROeV774UTT/Rv3ZS0FAbOH0hGVgYApzU+jSl9pwQhShERkcpNSVIYuuce2LvXTZ9wgiv7I9tmc+WbV7J532YA6kTX4fXBr1MjqkaQIhUREam8lCSFmf/9D6ZPzylPmQI1/MxxHvvfYyz8daGv/NqA1zi+3vGBDVBERKSKUJIURo4ccSNre112GfTt69+6H2/4mIeWPOQrj+o2iktOviTAEYqIiFQdSpLCyNNPww8/uOmaNWHSJP/W27J/C0NeH+J7cO05rc7hX33+FaQoRUREqgYlSWFiy5a8A0WOGQMtWhS/3pGsI1y+4HJ2pe0CoHFcY+YMnKMH14qIiJSRkqQw8c9/wsGDbrptW/f4EX+M+mgUK5JXADkPrm0c1zhIUYqIiFQdSpLCwKJFMH9+TvnZZyEqqvj1Fvy0gElf5rTJPdbnMc5udXYQIhQREal6lCSFWHo63HJLTvnKK+Gcc4pf75eUX7j27Wt95f4n9+fubncHIUIREZGqSUlSiE2cCL/+6qbr1IEnnih+He+Daw9kHADg+HrHM/3S6XpwrYiISAApSQqh336Dxx7LKT/2GBx7bNHrWGu56f2b+GGHuw0uulo0CwYtoG5M3SBGKiIiUvUoSQoRa+G22+DwYVfu1AlGjCh+vWlrpjHjuxm+8tQLp9KxSccgRSkiIlJ1KUkKkbfegg8+cNPGwHPPQbVqRa+T9EcSty681Vcedtowrjv9uiBGKSIiUnUpSQqBgwfh9ttzyiNGwBlnFL3O7kO78zy4tsOxHZh64dQgRikiIlK1KUkKgUcfheRkN92wYd5+SQXJttlc9eZVbNy7EYDa0bX14FoREZEgU5JUzn76CZ56Kqf8xBNQr17R60xYNoH317/vK0/vP50T658YpAhFREQElCSVK2vdA2wzM125Rw+46qqi11ny+xIeWPKAr3xX17sY0GZAEKMUERERUJJUrmbNgs8/d9PVqrmRtYsa2mjr/q387fW/kW2zATir5Vk81qeYtjkREREJCCVJ5WTvXrjrrpzyyJHQvn3hy3sfXLvj4A4Ajq15LHMGziGqmh/PKxEREZEyU5JUTh58ELZvd9PNmsGYMUUvP/qT0SxPXg5AhIlgzsA5NK3VNMhRioiIiJeSpHKQlOSa1rz+/W+oVavw5d9Y+wZPrczp3f2v3v+iZ3zP4AUoIiIiR1GSFGRZWXDTTZDtuhWRmAgDBxa+/PqU9Qx7e5iv3O+kfozqPirIUYqIiEh+SpKC7KWX4Kuv3HT16vDMM4V31k47ksZf5/2V/Yf3A3Bc3eP4z6X/IcL8f3v3Hh5Vde5x/PsmJEDAQAU8IrdYhXrvUTlcikepCkoReLiKHBSsd6ABy1NuKlZFrYBXKEqReKwFNIDFgNijRawPpWApglYRFATUgmK5KiQQss4fe5iBMCEDZGbP7Pl9niePa81ek7wvC3de9l6zl6ZJREQk0Sr97WtmTcxssZl9bGYfmdnQyt4jnm3bYPToSH/UKGjePPpY5xyDXh/Eh998CIQ2ru0zhx/UrOQhSiIiIhIX1WIYUwoMd86tNLNTgH+Y2VvOuY/jHFvKGzkSduzw2mee6RVJFZn+/nReXP1iuD+p0yQuaXhJnCMUERGRilR6Jck5t8U5tzLU3gOsARrFO7BUt2QJvPBCpD95MtSsYBeRlVtWMmThkHB/wI8HcOslt8Y5QhERETmW41rsYmZ5wMXA8ijHbjezFWa2Ytu2bVUTXYoqLfWerH1I9+7ws59FH7tj3w56Ffai5GAJABeediFTOk/BjvWUSREREYm7mIskM6sNzAWGOed2lz/unPudc66lc65lgwYNqjLGlDNpEnzoLS0iJweeeir6uDJXxsDXBvL5zs8BOCX7FOb0mUNOVk6CIhUREZGKxFQkmVkWXoE0wzn3anxDSm1ffQVjx0b6Y8dC06bRx0746wSK1haF+y90e4EW9VrEOUIRERGJRSyfbjNgOrDGOfdE/ENKbb/8JXz3ndc+91y4++7o497Z+A5j3h4T7t/d5m56ntczARGKiIhILGK5ktQOuBG40sxWhb4qWGGT3t58EwoLI/0pU7xnI5W3Zc8W+s6JbFzbrkk7Hrv6sQRFKSIiIrGo9BEAzrklgFYRV6KkBIZEPqBG//7Qvv3R40rLSuk7ty9ff+9t5HZardN4pdcr2rhWREQkyehRzlVkwgT49FOvXaeO149mzKIxvLvpXcDbuHZmj5k0ytUTFURERJKNiqQqsGEDPPxwpD9uHJx++tHj5n0yjwlLI9XTg+0f5KofXpWACEVEROR4qUg6Sc5Bfj4UF3v9iy/2NrQtb/329QyYNyDc79y8M6P/e/TRA0VERCQpqEg6SUVF8PrrXtsMnn0WMjOPHLPvwL4jNq7Nq5vH77v/XhvXioiIJDH9lj4J33/vXUU65PbboXXro8cNWTiE1V+vBiA7M5vZvWdzas1TExSliIiInAgVSSdh3DjYvNlr168Pjzxy9JiC9wsoWFUQ7j997dO0PKNlgiIUERGRE6Ui6QStWQMTJ0b648fDqeUuDq3auorBCweH+/0v6s8dl96RoAhFRETkZKhIOgHOweDB3ka2AO3awYABR47ZWbyTXoW9KC71VnSf3+B8nuv8nDauFRERSREqkk7ArFmweLHXzsz0nqydcdifpHOOm1+7mfU71gNQO7s2c/vMpVZ2LR+iFRERkROhIuk47drl7c92SH4+XHTRkWMmLp3IvE/mhfsFXQv4Uf0fJShCERERqQoqko7TfffB196OIpxxBvz610cef3fTu4xeFHn+0dDWQ+l9fu/EBSgiIiJVQkXScVi5En7720j/ySchNzfS3/rdVq6fcz0H3UEA2jZuy/gO4xMcpYiIiFQFFUkxKiuDQYO8/wJ06AC9D7tAVFpWSt85fdn63VYA6ufUp7B3IdmZ2T5EKyIiIidLRVKMpk+H5cu9dnY2TJ7sPWH7kPvevo+/bPoLAIYxs8dMGuc29iFSERERqQoqkmKwbRuMHBnpjxgBLVpE+kVri/jNX38T7j/Q/gE6nNUhgRGKiIhIVVORFINRo2DHDq995pkwZkzk2IYdG7jpjzeF+53O7sQ9l9+T4AhFRESkqqlIqsTSpVAQ2VWEZ56BmjW9dnFpMb0Ke7GrZBcATes05aXuL2njWhERkQDQb/NjKC2Fu+6K9Lt1g+uui/Tz38jn/a3vA5CVkcXs3rOpl1MvwVGKiIhIPKhIOobJk+GDD7x2zZrw9NORYy+uepFpK6eF+09d+xStGrVKcIQiIiISLyqSKvCvf8HYsZH+2LHQrJnX/uDrD7jz9TvDx/pd2I+7Wt6FiIiIBIeKpAoMHw579njtc86JbEWyq3gXPQt7hjeuPbf+uUy9bqo2rhUREQkYFUlR/PnP8PLLkf6UKd6zkZxz/Lzo53y2/TMAamXVYm6fudTOru1TpCIiIhIvKpLKKSmBwYMj/X794Kc/9dpPLnuSV9e8Gj42vet0zm1wboIjFBERkURQkVTOxImwbp3Xzs31+gBLNi9hxFsjwuN+0eoXXH/B9T5EKCIiIomgIukwn38O48ZF+uPGQcOG8PV3X9Nndp/wxrWtG7VmYseJPkUpIiIiiaAi6TBDh0Kxtx6biy/2npF0sOwgN8y9gS3fbQGgXs162rhWREQkDVTzO4BkUVQE8+dH+lOmQLVqcM+isSzeuBjwNq6d0WMGTes09SlKERERSRRdSQL27oX8/Ej/ttugTRtYsG4Bjyx5JPz62CvGcs3Z1/gQoYiIiCSaiiTg4Ydh0yavXa8ePPoofL7jc278443hMR3P6sh9l9/nU4QiIiKSaGl/u+2TT2DChEh//HioVaeYjgW92Fm8E4AmuU2Y0WMGmRmZPkUpIiIiiZbWRZJz3jORDhzw+m3bwsCBMGjhMFZuWQl4G9cW9i6kfk59/wIVERGRhEvr220vvwxvv+21MzLg2WdhxocvMfUfU8NjHu/4OG0at/EpQhEREfFL2hZJu3ZF9mMDb+F2xukfcseCO8Kv9b2gL0NaDfEhOhEREfFb2t5uu/9+2LrVazdsCMPH7OaqV3qxr3QfAOfUP4dpXaZp41oREZE0lZZXklatgkmTIv3HH3fc/c4trPu3tx9JTlaONq4VERFJc2lXJJWVeU/SLivz+lddBVvznmbOx3PCY6Z1mcZ5Dc7zKUIRERFJBml3u62gAJYt89pZWXDLA0u56c+/Ch8f1HIQ/S7s51N0IiIikizS6krSt9/CyJGR/uAR3/Cr5X0oLSsFoFWjVjxxzRM+RSciIiLJJK2KpNGjYft2r9007yCrzurHV3u+AuDUmqdS2KuQ6tWq+xihiIiIJIu0KZL+9jd4/vlIv82oX/PO5kWAt3HtH7r/gWZ1m/kUnYiIiCSbtCiSSku9xdqHtO7/BoVbx4X7915+L52ad/IhMhEREUlWaVEkTZkCq1d77er/sYm15/cPH7v6h1dz/xX3+xSZiIiIJKvAF0lbtsC994Y6mSXUH9SLnSXewqRGpzRiZo+Z2rhWREREjhL4Imn4cNizx2vX7Xs3X7kVAFTLqMbs3rNpUKuBj9GJiIhIsgp0kbRoEcyaFepcOIOdzZ8NH5vYYSJtm7T1JzARERFJeoEtkvbvh8GDQ50GH5HZ/fbwsd7n9Sa/db4/gYmIiEhKCGyR9PjjsHYtkL2HjBt6cjBjLwAt6rXg+a7Pa+NaEREROaZAFkkbN8JDDwE46HorZaeuBSIb1+ZWz/UzPBEREUkBgSyShg6FffuAVpPhgsLw61Ovm8oFp13gX2AiIiKSMgJXJM2fD0VFQONlcM3w8Ot3Xnon/S/qX/EbRURERA4TqCJp717IzwdytkHv3pB5AIBLG17Kk9c+6W9wIiIiklICVSQ98ghs3HQQevSHOl8C8IMaP2BOnznUqFbD5+hEREQklQSmSFq7FsaPB654CM5+M/z6S91fIq9unm9xiYiISGoKRJHknPdMpAPN/gRXPBh+/Z7/vofOLTr7GJmIiIikqpQskjbu3Ejraa3ZuHMjAIWFsGjFZujxP2AOgCvPvJIH2j/gY5QiIiKSylKySLpt/m2s2LKCO+bfwe7dMGz4fm+hdo63ce0Zp5zBrJ6ztHGtiIiInLBqfgdwvBZ+upClXyylzJWx5Isl3PTQG2y9aCE0fg/wNq4t7FXIabVO8zlSERERSWUpUySVlcGCPxXTe8kt7K/ubTGy98BeXsvsB613hseNv3o87Zq28ytMERERCYiUKJLWrYMOHWDLOY9yoOXuIw/WiBRIHRv3ZFibYQmOTkRERIIo6dckrVsHrVrB5t0bOfBfEyB775EDDu1TuyOPZaML+PRTbVwrIiIiJ6/SIsnMCszsGzP7ZyICOlxZGXTsCLt3A11ug4wD0Qc6YE9D9nybS8eO3vtERERETkYsV5L+F7g2znFE9eabsH07uLMXQpOlkFkafaABp6/GnfUG27fDW28lNEwREREJoEqLJOfcu8D2BMRylPHjYc++Yuh6y9G32crL3gvdbmHPvmIeeywx8YmIiEhwJfWapGXLgMseheq7Kx0LQPVdcNlvvPeJiIiInIQqK5LM7HYzW2FmK7Zt21Yl37O4GGj9TOVXkQ7J3gutn6GkpEp+vIiIiKSxKiuSnHO/c861dM61bNCgQZV8zxo1gOX5sD8ntjfsz4Hl+VSvXiU/XkRERNJYUt9ua9MGWDIaSnJje0NJHVgyynufiIiIyEmI5REAs4C/AT8ysy/N7Jb4h+UZMQJq16gBrxVUfjVpfw68Np3aNWowcmRi4hMREZHgqvSJ2865GxIRSDQdO0K9evD9+k64L34Cee9EfwzAwWqw+TJsfSfqNfWezi0iIiJyMpL6dltGhvespNxcYP40KMuKPvBgFiyYSm6uNz4jqbMSERGRVJD05USLFvDee9CsTh7Zf//V0bfd9ueQvWIEzerk8d573ngRERGRk5X0RRJ4hc+GDTBn2Giy3ZGLuLNdHeYMG8WGDSqQREREpOqkRJEE3i20Lp1qMO/mAnKyvKtJOVk5zLt5Ol061dAtNhEREalSKVdadGreiZ80+QkZlsFlTS6jU/NOfockIiIiAZRyRRLAtC7TaNmwJVO7TPU7FBEREQmoSh8BkIzy6uax/LblfochIiIiAZaSV5JERERE4k1FkoiIiEgUKpJEREREolCRJCIiIhKFiiQRERGRKMw5V/Xf1GwbsKnKv/GR6gPfxvlnJKt0zh3SO/90zh3SO3/lnr7SOf9E5d7MOdeg/ItxKZISwcxWOOda+h2HH9I5d0jv/NM5d0jv/JV7euYO6Z2/37nrdpuIiIhIFCqSRERERKJI5SLpd34H4KN0zh3SO/90zh3SO3/lnr7SOX9fc0/ZNUkiIiIi8ZTKV5JERERE4kZFkoiIiEgUSV8kmdm1ZrbWzD4zs1FRjlc3s1dCx5ebWV7io4yPGHIfaGbbzGxV6OtWP+KMBzMrMLNvzOyfFRw3M3sm9GfzgZldkugY4yWG3Nub2a7D5n1somOMFzNrYmaLzexjM/vIzIZGGRPkuY8l/0DOv5nVMLP3zGx1KPcHoowJ8vk+lvwDe84HMLNMM3vfzBZEOebP3DvnkvYLyATWAz8EsoHVwHnlxgwCngu1+wKv+B13AnMfCEz2O9Y45X85cAnwzwqO/wx4AzCgDbDc75gTmHt7YIHfccYp94bAJaH2KcC6KH/vgzz3seQfyPkPzWftUDsLWA60KTcmkOf748g/sOf8UH6/BGZG+/vt19wn+5WkVsBnzrkNzrn9wMtAt3JjugEvhtpzgKvMzBIYY7zEkntgOefeBbYfY0g34PfOswyoa2YNExNdfMWQe2A557Y451aG2nuANUCjcsOCPPex5B9Iofn8LtTNCn2V/2RRUM/3seYfWGbWGOgMPF/BEF/mPtmLpEbAF4f1v+ToE0Z4jHOuFNgF1EtIdPEVS+4APUO3HOaYWZPEhJYUYv3zCaq2ocvyb5jZ+X4HEw+hy+kX4/2L+nBpMffHyB8COv+h2y2rgG+At5xzFc59wM73QEz5Q3DP+U8BI4CyCo77MvfJXiTJsc0H8pxzFwFvEamyJdhW4u0z9GNgEjDP53iqnJnVBuYCw5xzu/2OJ9EqyT+w8++cO+ic+0+gMdDKzC7wO6ZEiiH/QJ7zzew64Bvn3D/8jqW8ZC+SvgIOr5Qbh16LOsbMqgF1gH8nJLr4qjR359y/nXMloe7zwKUJii0ZxPJ3I5Ccc7sPXZZ3zi0Essysvs9hVRkzy8IrEGY4516NMiTQc19Z/kGffwDn3E5gMXBtuUNBPd8foaL8A3zObwd0NbONeEtLrjSzP5Qb48vcJ3uR9HeguZmdaWbZeIu1isqNKQIGhNq9gLddaGVXiqs093LrMLrirV9IF0XATaFPOrUBdjnntvgdVCKY2emH7sWbWSu8/48D8YsilNd0YI1z7okKhgV27mPJP6jzb2YNzKxuqF0T6AB8Um5YUM/3MeUf1HO+c260c66xcy4P73fd2865/uWG+TL31eL9A06Gc67UzIYA/4f3aa8C59xHZvYgsMI5V4R3QnnJzD7DW+za17+Iq06MueebWVegFC/3gb4FXMXMbBbep3jqm9mXwP14Cxlxzj0HLMT7lNNnwF7gZn8irXox5N4LuMvMSoF9QN+g/KLA+xfljcCHobUZAGOAphD8uSe2/IM6/w2BF80sE6/wK3TOLUiH831ILPkH9pwfTTLMvbYlEREREYki2W+3iYiIiPhCRZKIiIhIFCqSRERERKJQkSQiIiIShYokERERkShUJImIiIhEoSJJREREJIr/B90Qpz3LmKFnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 7))\n",
    "plt.title(\"Position des points étape par étape (méthode point intérieur)\")\n",
    "list_of_X, list_of_Y = [x for (x,y) in list_of_x], [y for (x,y) in list_of_x]\n",
    "# plt.plot(list_of_X, list_of_Y, 'bo-')\n",
    "plt.plot(list_of_X, 'bo-', label=\"Valeur de x\", lw=3, ms=14)\n",
    "plt.plot(list_of_Y, 'gd-', label=\"Valeur de y\", lw=3, ms=14)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Bonus : implémentation manuelle de l'algorithme du simplexe\n",
    "\n",
    "- Refs : [ce poste de blogue](http://jeremykun.com/2014/12/01/linear-programming-and-the-simplex-algorithm/), [ces notes de cours](http://jeffe.cs.illinois.edu/teaching/algorithms/notes/I-simplex.pdf), et [cet autre poste de blogue](https://medium.com/@jacob.d.moore1/coding-the-simplex-algorithm-from-scratch-using-python-and-numpy-93e3813e6e70).\n",
    "- Code source venant de : https://github.com/j2kun/simplex-algorithm/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Algorithme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import heapq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "def identity(numRows, numCols, val=1, rowStart=0):\n",
    "    \"\"\" Return a rectangular identity matrix with the specified diagonal entiries, possibly starting in the middle.\n",
    "    \"\"\"\n",
    "    # return val * np.ones((numRows, numCols))\n",
    "    return [\n",
    "        [\n",
    "            (val if i == j else 0)\n",
    "            for j in range(numCols)\n",
    "        ]\n",
    "        for i in range(rowStart, numRows)\n",
    "    ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conversion en forme standard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "def standardForm(cost,\n",
    "                 greaterThans=None, gtThreshold=None,\n",
    "                 lessThans=None, ltThreshold=None,\n",
    "                 equalities=None, eqThreshold=None,\n",
    "                 maximization=True):\n",
    "    \"\"\"\n",
    "       standardForm: [float], [[float]], [float], [[float]], [float], [[float]], [float] -> [float], [[float]], [float]\n",
    "       Convert a linear program in general form to the standard form for the\n",
    "       simplex algorithm.  The inputs are assumed to have the correct dimensions: cost\n",
    "       is a length n list, greaterThans is an n-by-m matrix, gtThreshold is a vector\n",
    "       of length m, with the same pattern holding for the remaining inputs. No\n",
    "       dimension errors are caught, and we assume there are no unrestricted variables.\n",
    "    \"\"\"\n",
    "    newVars = 0\n",
    "    numRows = 0\n",
    "    if gtThreshold:\n",
    "        newVars += len(gtThreshold)\n",
    "        numRows += len(gtThreshold)\n",
    "    if ltThreshold:\n",
    "        newVars += len(ltThreshold)\n",
    "        numRows += len(ltThreshold)\n",
    "    if eqThreshold:\n",
    "        numRows += len(eqThreshold)\n",
    "\n",
    "    if not maximization:\n",
    "        cost = [-x for x in cost]\n",
    "\n",
    "    if newVars == 0:\n",
    "        return cost, equalities, eqThreshold\n",
    "\n",
    "    newCost = list(cost) + ([0] * newVars)\n",
    "\n",
    "    constraints = [ ]\n",
    "    threshold   = [ ]\n",
    "\n",
    "    oldConstraints = [(greaterThans, gtThreshold, -1), (lessThans, ltThreshold, 1),\n",
    "                     (equalities, eqThreshold, 0)]\n",
    "\n",
    "    offset = 0\n",
    "    for constraintList, oldThreshold, coefficient in oldConstraints:\n",
    "        constraints += [c + r for c, r in zip(constraintList,\n",
    "             identity(numRows, newVars, coefficient, offset))]\n",
    "\n",
    "        threshold += oldThreshold\n",
    "        offset += len(oldThreshold)\n",
    "\n",
    "    return newCost, constraints, threshold"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Utilitaires pour les matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dot(a, b):\n",
    "    return sum(x*y for x, y in zip(a, b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "def column(A, j):\n",
    "    return [row[j] for row in A]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "def transpose(A):\n",
    "    return [column(A, j) for j in range(len(A[0]))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "def isPivotCol(col):\n",
    "    return (len([c for c in col if c == 0]) == len(col) - 1) and sum(col) == 1\n",
    "\n",
    "def variableValueForPivotColumn(tableau, column):\n",
    "    pivotRow = [i for (i, x) in enumerate(column) if x == 1][0]\n",
    "    return tableau[pivotRow][-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "# assume the last m columns of A are the slack variables; the initial basis is\n",
    "# the set of slack variables\n",
    "def initialTableau(c, A, b):\n",
    "    tableau = [row[:] + [x] for row, x in zip(A, b)]\n",
    "    tableau.append([ci for ci in c] + [0])\n",
    "    return tableau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "def primalSolution(tableau):\n",
    "    # the pivot columns denote which variables are used\n",
    "    columns = transpose(tableau)\n",
    "    indices = [j for j, col in enumerate(columns[:-1]) if isPivotCol(col)]\n",
    "    return [(colIndex, variableValueForPivotColumn(tableau, columns[colIndex]))\n",
    "            for colIndex in indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "def objectiveValue(tableau):\n",
    "    return -(tableau[-1][-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "def canImprove(tableau):\n",
    "    lastRow = tableau[-1]\n",
    "    return any(x > 0 for x in lastRow[:-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this can be slightly faster\n",
    "def moreThanOneMin(L):\n",
    "    if len(L) <= 1:\n",
    "        return False\n",
    "\n",
    "    x, y = heapq.nsmallest(2, L, key=lambda x: x[1])\n",
    "    return x == y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "def findPivotIndex(tableau):\n",
    "    # pick minimum positive index of the last row\n",
    "    column_choices = [(i, x) for (i, x) in enumerate(tableau[-1][:-1]) if x > 0]\n",
    "    column = min(column_choices, key=lambda a: a[1])[0]\n",
    "\n",
    "    # check if unbounded\n",
    "    if all(row[column] <= 0 for row in tableau):\n",
    "        raise Exception('Linear program is unbounded.')\n",
    "\n",
    "    # check for degeneracy: more than one minimizer of the quotient\n",
    "    quotients = [\n",
    "        (i, r[-1] / r[column])\n",
    "        for i, r in enumerate(tableau[:-1])\n",
    "        if r[column] > 0\n",
    "    ]\n",
    "\n",
    "    if moreThanOneMin(quotients):\n",
    "        raise Exception('Linear program is degenerate.')\n",
    "\n",
    "    # pick row index minimizing the quotient\n",
    "    row = min(quotients, key=lambda x: x[1])[0]\n",
    "\n",
    "    return row, column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pivotAbout(tableau, pivot):\n",
    "    i, j = pivot\n",
    "\n",
    "    pivotDenom = tableau[i][j]\n",
    "    tableau[i] = [x / pivotDenom for x in tableau[i]]\n",
    "\n",
    "    for k,row in enumerate(tableau):\n",
    "        if k != i:\n",
    "            pivotRowMultiple = [y * tableau[k][j] for y in tableau[i]]\n",
    "            tableau[k] = [x - y for x,y in zip(tableau[k], pivotRowMultiple)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### L'algorithme du simplexe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simplex(c, A, b):\n",
    "    \"\"\"\n",
    "    simplex: c: [float], A: [[float]], b: [float] -> [float], float\n",
    "    Solve the given standard-form linear program:\n",
    "        max <c, x>\n",
    "        s.t. Ax = b\n",
    "             x >= 0\n",
    "    Providing the optimal solution x* and the value of the objective function.\n",
    "    \"\"\"\n",
    "    tableau = initialTableau(c, A, b)\n",
    "    print(\"Initial tableau:\")\n",
    "    for row in tableau:\n",
    "        print(row)\n",
    "    print()\n",
    "\n",
    "    while canImprove(tableau):\n",
    "        pivot = findPivotIndex(tableau)\n",
    "        print(\"Next pivot index is={}\\n\".format(pivot))\n",
    "        pivotAbout(tableau, pivot)\n",
    "        print(\"Tableau after pivot:\")\n",
    "        for row in tableau:\n",
    "            print(row)\n",
    "        print()\n",
    "\n",
    "    return tableau, primalSolution(tableau), objectiveValue(tableau)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Un premier exemple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial tableau:\n",
      "[15, 20, 25, 1, 0, 0, 0, 1200]\n",
      "[35, 60, 60, 0, 1, 0, 0, 3000]\n",
      "[20, 30, 25, 0, 0, 1, 0, 1500]\n",
      "[0, 250, 0, 0, 0, 0, -1, 500]\n",
      "[300, 250, 450, 0, 0, 0, 0, 0]\n",
      "\n",
      "Next pivot index is=(3, 1)\n",
      "\n",
      "Tableau after pivot:\n",
      "[15.0, 0.0, 25.0, 1.0, 0.0, 0.0, 0.08, 1160.0]\n",
      "[35.0, 0.0, 60.0, 0.0, 1.0, 0.0, 0.24, 2880.0]\n",
      "[20.0, 0.0, 25.0, 0.0, 0.0, 1.0, 0.12, 1440.0]\n",
      "[0.0, 1.0, 0.0, 0.0, 0.0, 0.0, -0.004, 2.0]\n",
      "[300.0, 0.0, 450.0, 0.0, 0.0, 0.0, 1.0, -500.0]\n",
      "\n",
      "Next pivot index is=(1, 6)\n",
      "\n",
      "Tableau after pivot:\n",
      "[3.333333333333332, 0.0, 5.0, 1.0, -0.33333333333333337, 0.0, 0.0, 200.0]\n",
      "[145.83333333333334, 0.0, 250.0, 0.0, 4.166666666666667, 0.0, 1.0, 12000.0]\n",
      "[2.5, 0.0, -5.0, 0.0, -0.5, 1.0, 0.0, 0.0]\n",
      "[0.5833333333333334, 1.0, 1.0, 0.0, 0.01666666666666667, 0.0, 0.0, 50.0]\n",
      "[154.16666666666666, 0.0, 200.0, 0.0, -4.166666666666667, 0.0, 0.0, -12500.0]\n",
      "\n",
      "Next pivot index is=(2, 0)\n",
      "\n",
      "Tableau after pivot:\n",
      "[0.0, 0.0, 11.666666666666664, 1.0, 0.33333333333333315, -1.333333333333333, 0.0, 200.0]\n",
      "[0.0, 0.0, 541.6666666666667, 0.0, 33.333333333333336, -58.33333333333334, 1.0, 12000.0]\n",
      "[1.0, 0.0, -2.0, 0.0, -0.2, 0.4, 0.0, 0.0]\n",
      "[0.0, 1.0, 2.166666666666667, 0.0, 0.13333333333333336, -0.23333333333333336, 0.0, 50.0]\n",
      "[0.0, 0.0, 508.3333333333333, 0.0, 26.666666666666664, -61.666666666666664, 0.0, -12500.0]\n",
      "\n",
      "Next pivot index is=(1, 4)\n",
      "\n",
      "Tableau after pivot:\n",
      "[0.0, 0.0, 6.250000000000001, 1.0, 0.0, -0.75, -0.009999999999999993, 80.00000000000007]\n",
      "[0.0, 0.0, 16.25, 0.0, 1.0, -1.7500000000000002, 0.03, 360.0]\n",
      "[1.0, 0.0, 1.25, 0.0, 0.0, 0.04999999999999993, 0.006, 72.0]\n",
      "[0.0, 1.0, 0.0, 0.0, 0.0, 5.551115123125783e-17, -0.004000000000000001, 1.999999999999993]\n",
      "[0.0, 0.0, 75.0, 0.0, 0.0, -14.999999999999993, -0.7999999999999999, -22100.0]\n",
      "\n",
      "Next pivot index is=(0, 2)\n",
      "\n",
      "Tableau after pivot:\n",
      "[0.0, 0.0, 1.0, 0.15999999999999998, 0.0, -0.11999999999999998, -0.0015999999999999988, 12.80000000000001]\n",
      "[0.0, 0.0, 0.0, -2.5999999999999996, 1.0, 0.1999999999999995, 0.05599999999999998, 151.99999999999986]\n",
      "[1.0, 0.0, 0.0, -0.19999999999999996, 0.0, 0.1999999999999999, 0.007999999999999998, 55.999999999999986]\n",
      "[0.0, 1.0, 0.0, 0.0, 0.0, 5.551115123125783e-17, -0.004000000000000001, 1.999999999999993]\n",
      "[0.0, 0.0, 0.0, -11.999999999999998, 0.0, -5.999999999999995, -0.68, -23060.0]\n",
      "\n",
      "[(0, 55.999999999999986), (1, 1.999999999999993), (2, 12.80000000000001), (4, 151.99999999999986)]\n",
      "23060.0\n"
     ]
    }
   ],
   "source": [
    "c = [300, 250, 450]\n",
    "A = [[15, 20, 25], [35, 60, 60], [20, 30, 25], [0, 250, 0]]\n",
    "b = [1200, 3000, 1500, 500]\n",
    "\n",
    "# add slack variables by hand\n",
    "A[0] += [1, 0, 0, 0]\n",
    "A[1] += [0, 1, 0, 0]\n",
    "A[2] += [0, 0, 1, 0]\n",
    "A[3] += [0, 0, 0, -1]\n",
    "c += [0, 0, 0, 0]\n",
    "\n",
    "t, s, v = simplex(c, A, b)\n",
    "print(s)\n",
    "print(v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et pou comparer avec la réponse donnée par `scipy.optimize.linprog` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     con: array([], dtype=float64)\n",
       "     fun: -23400.0\n",
       " message: 'Optimization terminated successfully.'\n",
       "     nit: 5\n",
       "   slack: array([  0.,   0.,   0., 500.])\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([ 60.,   0.,  12.,   0., 180.,   0.,   0.])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt_res = opt.linprog(-np.array(c), A_ub=A, b_ub=b, method=\"simplex\")\n",
    "opt_res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La solution optimale trouvée par `scipy.optimize.linprog` est meilleure que celle trouvée par notre algorithme."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(23060.0, 23400.0)"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v, - opt_res.fun"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notre implémentation donne une solution :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 55.999999999999986),\n",
       " (1, 1.999999999999993),\n",
       " (2, 12.80000000000001),\n",
       " (4, 151.99999999999986)]"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Qui s'interprète comme étant assez proche de la solution trouvée par `scipy.optimize.linprog`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 60.,   0.,  12.,   0., 180.,   0.,   0.])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt_res.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 56,   2,  12,   0, 152,   0,   0])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2 = np.array([56, 2, 12, 0, 152, 0, 0])\n",
    "s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1491454186681393"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(opt_res.x - s2) / np.linalg.norm(opt_res.x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C'est une différence relativement faible…"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test(expected, actual):\n",
    "    e, a = np.array(expected), np.array(actual)\n",
    "    if not np.isclose(np.linalg.norm(e - a), 0):\n",
    "        import sys, traceback\n",
    "        (filename, lineno, container, code) = traceback.extract_stack()[-2]\n",
    "        print(\"Test: {} failed on line {} in file {}.\\nExpected {} but got {}\\n\".format((code, lineno, filename, expected, actual)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "def testFromPost():\n",
    "    cost = [1, 1, 1]\n",
    "    gts = [[0, 1, 4]]\n",
    "    gtB = [10]\n",
    "    lts = [[3, -2, 0]]\n",
    "    ltB = [7]\n",
    "    eqs = [[1, 1, 0]]\n",
    "    eqB = [2]\n",
    "\n",
    "    expectedCost = [1,1,1,0,0]\n",
    "    expectedConstraints = [[0,1,4,-1,0], [3,-2,0,0,1], [1,1,0,0,0]]\n",
    "    expectedThresholds = [10,7,2]\n",
    "    c, cs, ts = standardForm(cost, gts, gtB, lts, ltB, eqs, eqB)\n",
    "    test(expectedCost, c)\n",
    "    test(expectedConstraints, cs)\n",
    "    test(expectedThresholds, ts)\n",
    "    \n",
    "    A_ub = np.array([\n",
    "        [0, 1, 4],\n",
    "        [-3, 2, 0]\n",
    "    ])\n",
    "    b_ub = np.array([10, -7])\n",
    "    opt_res = opt.linprog(-np.array(cost),\n",
    "                          A_eq=np.array(eqs), b_eq=np.array(eqB),\n",
    "                          A_ub=np.array(A_ub), b_ub=np.array(b_ub),\n",
    "                          method=\"simplex\")\n",
    "    print(\"Expected cost\", expectedCost)\n",
    "    print(\"scipy.optimize.linprog gives a solution =\", opt_res.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost [1, 1, 1, 0, 0]\n",
      "scipy.optimize.linprog gives a solution = [2.  0.  2.5]\n"
     ]
    }
   ],
   "source": [
    "testFromPost()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un second test :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test2():\n",
    "    cost = [1, 1, 1]\n",
    "    lts = [[3, -2, 0]]\n",
    "    ltB = [7]\n",
    "    eqs = [[1, 1, 0]]\n",
    "    eqB = [2]\n",
    "\n",
    "    expectedCost = [1, 1, 1, 0]\n",
    "    expectedConstraints = [[3, -2, 0, 1], [1 ,1 ,0 ,0]]\n",
    "    expectedThresholds = [7, 2]\n",
    "    test((expectedCost, expectedConstraints, expectedThresholds),\n",
    "         standardForm(cost, lessThans=lts, ltThreshold=ltB, equalities=eqs, eqThreshold=eqB))"
   ]
  },
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   "outputs": [],
   "source": [
    "test2()"
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  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un dernier test :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test3():\n",
    "    cost = [1, 1, 1]\n",
    "    eqs = [[1, 1, 0], [2, 2, 2]]\n",
    "    eqB = [2, 5]\n",
    "\n",
    "    expectedCost = [1, 1, 1]\n",
    "    expectedConstraints = [[3, -2, 0], [1, 1, 0]]\n",
    "    expectedThresholds = [2, 5]\n",
    "    test((expectedCost, expectedConstraints, expectedThresholds),\n",
    "         standardForm(cost, equalities=eqs, eqThreshold=eqB))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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  {
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   "metadata": {},
   "source": [
    "Ca suffit pour ces exemples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "C'est bon pour aujourd'hui !"
   ]
  }
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