{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Contenido bajo licencia Creative Commons BY 4.0 y código bajo licencia MIT. © Manuela Bastidas Olivares y Nicolás Guarín-Zapata 2024."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Método de colocación"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problema a resolver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consideremos la siguiente ecuación diferencial\n",
    "\n",
    "$$\\frac{d^2 u(x)}{dx^2} = -4 \\pi^2 \\sin(2 \\pi x) \\, , $$\n",
    "\n",
    "con condiciones de frontera $u(0)=u(1)=0$.\n",
    "\n",
    "La solución a este problema de valores de la frontera es\n",
    "\n",
    "$$u_e(x) = \\sin (2 \\pi x)\\, .$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Aproximación propuesta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Propongamos una aproximación a la solución de la siguiente forma\n",
    "\n",
    "$$u_N(x) = \\sum_{i=0}^N c_i \\phi_i(x) = x (1-x) \\sum_{i=0}^N c_i x^i\\, ,$$\n",
    "\n",
    "en donde vemos que esta función satisface las condiciones de frontera.\n",
    "\n",
    "Y el residual estaría dado por\n",
    "\n",
    "$$R(x) = \\frac{d^2 u_N(x)}{dx^2} + 4 \\pi^2 \\sin(2 \\pi x)\\, .$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Método de solución"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El método de colocación consiste en forzar que el residual sea cero en un conjunto de puntos.\n",
    "Este método se puede escribir como un método de residuos ponderados si se elige\n",
    "como función de ponderación el delta de Dirac, es decir,\n",
    "\n",
    "$$\\int\\limits_0^1 R(x) w_i(x)\\, \\mathrm{d}x = 0\\quad \\forall w_i\\, ,$$\n",
    "\n",
    "con $w_i(x) = \\delta(x - x_i)$. O, equivalentemente,\n",
    "\n",
    "$$R (x_i) = 0\\quad \\forall x_i\\, .$$\n",
    "\n",
    "La motivación detrás de esto es que si la función debe hacerse 0 en varios puntos, se\n",
    "acerca a 0 a medida que le número de puntos de colocación aumente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Funciones auxiliares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Esto permite tener gráficos interactivos en\n",
    "# el caso de correrse en Google Colab\n",
    "if 'google.colab' in str(get_ipython()):\n",
    "    %pip install ipympl\n",
    "    from google.colab import output\n",
    "    output.enable_custom_widget_manager()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "if 'google.colab' in str(get_ipython()):\n",
    "    style = \"https://raw.githubusercontent.com/nicoguaro/pinns_mapi-3/main/notebooks/clean.mplstyle\"\n",
    "else:\n",
    "    style = \"./clean.mplstyle\"\n",
    "plt.style.use(style)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = symbols('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "u_e = sin(2*pi*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_expr(expr, x, rango=(0, 1), ax=None, linestyle=\"solid\"):\n",
    "    \"\"\"Grafica expresiones de SymPy que dependen de una variable\"\"\"\n",
    "    expr_num = lambdify(x, expr, \"numpy\")\n",
    "    x0 = rango[0]\n",
    "    x1 = rango[1]\n",
    "    x_num = np.linspace(0, 1, 301)\n",
    "    if ax is None:\n",
    "        plt.figure()\n",
    "        ax = plt.gca()\n",
    "    ax.plot(x_num, expr_num(x_num), linestyle=linestyle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creemos algunas funciones que nos serán útiles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def funcion_base(x, k):\n",
    "    \"\"\"Elemento k de la base\"\"\"\n",
    "    return x*(1 - x)*x**k\n",
    "\n",
    "\n",
    "def funcion_aprox(x, num):\n",
    "    \"\"\"Función de aproximación\n",
    "    \n",
    "    Parametros\n",
    "    ----------\n",
    "    num : int\n",
    "        Número de términos en la expansión.\n",
    "        \n",
    "    Devuelve\n",
    "    -------_\n",
    "    u_n : expresión de SymPy\n",
    "        Función de aproximación.\n",
    "    c : lista\n",
    "        Lista de coeficientes.\n",
    "        \n",
    "    \"\"\"    \n",
    "    c = symbols('c0:%d'%num)\n",
    "    u_n = sum([c[k]*funcion_base(x, k) for k in range(num)])\n",
    "    return u_n, c\n",
    "\n",
    "\n",
    "def residual(u, x):\n",
    "    \"\"\"Residual para el problema de interés\"\"\"\n",
    "    return diff(u, x, 2) + 4*pi**2*sin(2*pi*x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos resolver el problema usando 4 funciones en la base"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "nterms = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle c_{0} x \\left(1 - x\\right) + c_{1} x^{2} \\cdot \\left(1 - x\\right) + c_{2} x^{3} \\cdot \\left(1 - x\\right) + c_{3} x^{4} \\cdot \\left(1 - x\\right)$"
      ],
      "text/plain": [
       "                   2               3               4        \n",
       "c₀⋅x⋅(1 - x) + c₁⋅x ⋅(1 - x) + c₂⋅x ⋅(1 - x) + c₃⋅x ⋅(1 - x)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u, c = funcion_aprox(x, nterms)\n",
    "u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso, el residual sería"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - 2 \\left(c_{0} + 3 c_{1} x - c_{1} + 6 c_{2} x^{2} - 3 c_{2} x + 10 c_{3} x^{3} - 6 c_{3} x^{2} - 2 \\pi^{2} \\sin{\\left(2 \\pi x \\right)}\\right)$"
      ],
      "text/plain": [
       "   ⎛                         2                   3         2      2           \n",
       "-2⋅⎝c₀ + 3⋅c₁⋅x - c₁ + 6⋅c₂⋅x  - 3⋅c₂⋅x + 10⋅c₃⋅x  - 6⋅c₃⋅x  - 2⋅π ⋅sin(2⋅π⋅x)\n",
       "\n",
       "⎞\n",
       "⎠"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = expand(residual(u, x))\n",
    "factor(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solución\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para solucionar el sistema debemos utilizar $n$ puntos de colocación\n",
    "en los que el residual se fuerza a ser exactamente cero. De allí,\n",
    "obtenemos un sistema lineal de $n$ ecuaciones en $n$ incógnitas.\n",
    "\n",
    "El sistema es lineal ya que la ecuación diferencial original es lineal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ \\frac{1}{5}, \\  \\frac{2}{5}, \\  \\frac{3}{5}, \\  \\frac{4}{5}\\right]$"
      ],
      "text/plain": [
       "[1/5, 2/5, 3/5, 4/5]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_colo = [(cont + 1)*S(1)/(nterms + 1) for cont in range(nterms)]\n",
    "x_colo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle - 2 c_{0} + \\frac{4 c_{1}}{5} + \\frac{18 c_{2}}{25} + \\frac{8 c_{3}}{25} + 4 \\pi^{2} \\sqrt{\\frac{\\sqrt{5}}{8} + \\frac{5}{8}} = 0$"
      ],
      "text/plain": [
       "                                       ________    \n",
       "        4⋅c₁   18⋅c₂   8⋅c₃      2    ╱ √5   5     \n",
       "-2⋅c₀ + ──── + ───── + ──── + 4⋅π ⋅  ╱  ── + ─  = 0\n",
       "         5       25     25         ╲╱   8    8     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle - 2 c_{0} - \\frac{2 c_{1}}{5} + \\frac{12 c_{2}}{25} + \\frac{16 c_{3}}{25} + 4 \\pi^{2} \\sqrt{\\frac{5}{8} - \\frac{\\sqrt{5}}{8}} = 0$"
      ],
      "text/plain": [
       "                                        ________    \n",
       "        2⋅c₁   12⋅c₂   16⋅c₃      2    ╱ 5   √5     \n",
       "-2⋅c₀ - ──── + ───── + ───── + 4⋅π ⋅  ╱  ─ - ──  = 0\n",
       "         5       25      25         ╲╱   8   8      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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eGIgGX0ycYLZ5TCZ4PzbJFg2xoq+EPZZ1ZxwsLVz3sUMHw4LdOrQdWy3tzeHXuqbcokl1rJ6HpQC7ol6K1Ew+CQ2+PbN2crmLF/xcpefiYmfhzctuT7Xds1VMjP8TnW3nB2+uQVjWFhciFv7g6ui5qdRe+KaxrpHVGtx1LfAgqOfJFfU8Rktz0GFyyvgxBagTVOX7W8K0eGKKPPhiouJt9rA5TJbgdkweYXun+zkMYyzrKQNh8DiVgZxm910rDYsdhR3kdnBzIREt8LAPlK6o90FrOi9fCcQa2SUsk923yHbzVHctXlEQY19MvI0MbQqTMzYiFjT4Q1jWe1nUarug7HU2ZR8KSn5Q5EXLbAs8JHjPBl1Rz0K0OEP4cmCaW8LE3zJB5vv7eFX5b+zgLB5ilU19MXEzmJy5SYOfOrbDod+gRibD6+Jp3VUmfl/ceOYLT5NLC7fAwyJMfR/1IpiWZYodx/x+TB2xLFmswYJphsRP2C89whCvjHdvzm0FkxEsThItTFGmLOCiqPjkQm4mN/ts3YdV/lKHzYC4p7aPMlXPA6DPkSvqOYQ83REoDIGoYPFL40u+0nVTM7bC4C6iOu76KKIZvBKOwF4ImFuCxVxeo3ZqHAFX1I03sLPXHgKyoMNiYOSsud1E7bXY8Ry5oj4eQy/BEbgEArbTw86XqIM/80wIuKI+E9D+GEdgZQSwpO+idb1y0V5caQi4oi6tRbw+jsAyBNh549b0Mqyqz/Woeg6cAUdgmwj8JrZdUW+k7f8PER2Tn46wSiYAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle - 2 c_{0} - \\frac{8 c_{1}}{5} - \\frac{18 c_{2}}{25} - 4 \\pi^{2} \\sqrt{\\frac{5}{8} - \\frac{\\sqrt{5}}{8}} = 0$"
      ],
      "text/plain": [
       "                                ________    \n",
       "        8⋅c₁   18⋅c₂      2    ╱ 5   √5     \n",
       "-2⋅c₀ - ──── - ───── - 4⋅π ⋅  ╱  ─ - ──  = 0\n",
       "         5       25         ╲╱   8   8      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - 2 c_{0} - \\frac{14 c_{1}}{5} - \\frac{72 c_{2}}{25} - \\frac{64 c_{3}}{25} - 4 \\pi^{2} \\sqrt{\\frac{\\sqrt{5}}{8} + \\frac{5}{8}} = 0$"
      ],
      "text/plain": [
       "                                         ________    \n",
       "        14⋅c₁   72⋅c₂   64⋅c₃      2    ╱ √5   5     \n",
       "-2⋅c₀ - ───── - ───── - ───── - 4⋅π ⋅  ╱  ── + ─  = 0\n",
       "          5       25      25         ╲╱   8    8     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eqs_colo = []\n",
    "for cont in range(nterms):\n",
    "    eqs_colo.append(Eq(res.subs(x, x_colo[cont]), 0))\n",
    "    display(eqs_colo[cont])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\left\\{ c_{0} : - \\frac{5 \\sqrt{2} \\pi^{2} \\sqrt{5 - \\sqrt{5}}}{8} + \\frac{35 \\sqrt{2} \\pi^{2} \\sqrt{\\sqrt{5} + 5}}{72}, \\  c_{1} : - \\frac{145 \\sqrt{2} \\pi^{2} \\sqrt{\\sqrt{5} + 5}}{72} + \\frac{35 \\sqrt{2} \\pi^{2} \\sqrt{5 - \\sqrt{5}}}{8}, \\  c_{2} : - \\frac{75 \\sqrt{2} \\pi^{2} \\sqrt{5 - \\sqrt{5}}}{8} + \\frac{25 \\sqrt{2} \\pi^{2} \\sqrt{\\sqrt{5} + 5}}{8}, \\  c_{3} : - \\frac{25 \\sqrt{2} \\pi^{2} \\sqrt{\\sqrt{5} + 5}}{12} + \\frac{25 \\sqrt{2} \\pi^{2} \\sqrt{5 - \\sqrt{5}}}{4}\\right\\}$"
      ],
      "text/plain": [
       "⎧            2   ________          2   ________                2   ________   \n",
       "⎪      5⋅√2⋅π ⋅╲╱ 5 - √5    35⋅√2⋅π ⋅╲╱ √5 + 5         145⋅√2⋅π ⋅╲╱ √5 + 5    \n",
       "⎨c₀: - ────────────────── + ───────────────────, c₁: - ──────────────────── + \n",
       "⎪              8                     72                         72            \n",
       "⎩                                                                             \n",
       "\n",
       "       2   ________               2   ________          2   ________          \n",
       "35⋅√2⋅π ⋅╲╱ 5 - √5         75⋅√2⋅π ⋅╲╱ 5 - √5    25⋅√2⋅π ⋅╲╱ √5 + 5         25\n",
       "───────────────────, c₂: - ─────────────────── + ───────────────────, c₃: - ──\n",
       "         8                          8                     8                   \n",
       "                                                                              \n",
       "\n",
       "     2   ________          2   ________⎫\n",
       "⋅√2⋅π ⋅╲╱ √5 + 5    25⋅√2⋅π ⋅╲╱ 5 - √5 ⎪\n",
       "───────────────── + ───────────────────⎬\n",
       "       12                    4         ⎪\n",
       "                                       ⎭"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_col = solve(eqs_colo, c)\n",
    "sol_col"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Luego de encontrar los coeficientes $c_i$ podemos visualizar\n",
    "la solución aproximada y compararla con la solución exacta,\n",
    "que para este caso es conocida."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d164cf8ce044478b84271714b6b7ae90",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "ax = plt.gca()\n",
    "plot_expr(u_e, x, ax=ax)\n",
    "plot_expr(u.subs(sol_col), x, ax=ax)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"u(x)\")\n",
    "plt.legend([\"Exacta\", \"Colocación\"]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualicemos el residual para la solución aproximada. Podemos ver que\n",
    "en los puntos de colocación este es exactamente 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'R(x)')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4ae144b1067f486fb6d6b4f7a00f5275",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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DTscBACAuULASnOXxKGvc7ZKksqnPKPDDaocTAQAQ+yhYkG/gQHkHDpBqalT8t785HQcAgJhHwYIkKeuO2yW3W1XvzZb/o8VOxwEAIKZRsCBJSurUSWnnniNJKho3jouPAgCwHyhYqJNxww2ymjRRYMU3Kn96qtNxAACIWRQs1HE3zVbW2FslSSX33qfg+g0OJwIAIDZRsFBP6hmnK7lnT5nychWP/4vTcQAAiEkULNRjuVxqMnGC5HKp8u23VTVvntORAACIORQs7CLpkK5Ku/ACSVLRzbcoVF7ucCIAAGILBQu7lXnTn+Vu1UrBdetUMmGi03EAAIgpFCzslistTU3uuVuSVP7Mv+RfssThRAAAxA4KFvbId/RRSj37LEnSthv/rFBlpcOJAACIDRQs7FXWbWPlzstTcM1alfyVt9EBAGBfULCwV67MTDWZdK8kqfxfz6pyzvsOJwIAIPpRsPCbfEcfrbRLLpYkFd1wo4KFhQ4nAgAgulGwsE+yxtwsT5cuCm3Zom3X3yBjjNORAACIWhQs7BPL51PTRx+WfF75P5ynsimPOR0JAICoRcHCPks6+GA1GT9eklQy8R/yL+bSDQAA7A4FCw2SevZZShk5UgqFtPWKKxUsKHA6EgAAUYeChQaxLEtN/jFBni6dFdq0SVsvv0KmutrpWAAARBUKFhrMlZKiA554QlZGhqr/s1RFt9zKQe8AAOyEgoVG8bRvp6ZTHpVcLlVMn6Gyxx93OhIAAFGDgoVG8w0cqKw7x0mSSv42QZWzZzucCACA6EDBwn5Ju/ACpZ17jmSMtl1+pfyfLnM6EgAAjqNgYb9YlqWsv/5F3oEDZKqqtOX881Xz7bdOxwIAwFEULOw3KylJTZ94XEm//71MUbE2n3WOAuvWOR0LAADHULBgC1dqqnKefUaeTp0UKijQ5tPPUODn9U7HAgDAERQs2MaVna2cF56Xu20bBdes1ebTTqNkAQASEgULtnLn5ynn5Zd+KVmnnqrAzz87HQsAgIiiYMF2npYtfylZa3/U5pNOVs3KlU7HAgAgYihYCIvakvWyPB06KLhhgzad/Ccu4QAASBgULISNp2W+cl5/TUk9esgUFWnL6WeoctYsp2MBABB2FCyElbtptnJemi7vMQNlqqq09eL/U8n9D/DehQCAuEbBQti5UlN1wNSnlXbRhZKk0nvv07bLr1CorMzhZAAAhAcFCxFheTxq8pfxanL3XZLHo8q33tamYcNV8/Vyp6MBAGA7y4R5X40xRvPnz9fChQu1Zs0aVVRUqFmzZurRo4cGDx6s1q1bh/Pho1qZ3y9JSvd6HU4SWf7//EdbL79SoYICyetV1h23K+3882RZ1n7/7ESdabgwT/sxU3sxT/sxU3uEbQtWZWWlJkyYoNatW2vYsGGaOXOmioqK5Ha7tWrVKo0bN07t2rXTcccdp48//jhcMRCFvL17q/mc9+Q95hjJ71fx2Nu05ayzuSgpACBuhG0LVuvWrdWnTx+NGjVKQ4cOVVJS0i7rrF27VtOmTdNjjz2m2267TZdcckk4okStRP8rwYRCKv/nUyq+6y6pyi8rI0NZt41V6llnynI1rvsn+kztxjztx0ztxTztx0ztEbaC9b///U/dunXbp3Wrq6u1du1adezYMRxRohZP4lo1q77XtuuuV81nn0mSknp0V5O//03Jhx3W4J/FTO3FPO3HTO3FPO3HTO0R9mOwsGc8iX9hgkGVPz1VJffeJ1NWJlmWUk8dqYwbb5CnZct9/jnM1F7M037M1F7M037M1B4ROYvw9ttvVzAY3GV5cXGxzjzzzEhEQJSz3G6lX3KxchfMU8opp0jGqOKll7XxqP4q/stfFdy82emIAADss4hswWrbtq3y8vL0wgsv6KCDDpIkzZs3T+edd55atmypJUuWhDtCVOKvhD2r/uxzFU+YoOol20+A8HmVduaZSr/sUnlatdrt9wRDRktWbdTWsmq1zE5X97bZcrv2/8zERMU87RcPMzXBoExVlUxlpUxFRe3HykoZv18KhaRgSCYUkkzt53K7ZCUny0r2Sl6vLG+yLK9XrqwsWZmZ+3X2cDzMMxrx2mSPiBSs4uJiXXrppZo5c6YmTZqklStX6sEHH9SYMWM0btw4ud3ucEfYo8mTJ+uee+7Rhg0bdMghh+iBBx7QUUcdFZHH5km8d8YY+T+cp5JJk1Tz+Re1C10u+QYPUto558g7oL+s7c+dD5dv1P2zVqiwxF/3/c0zvbpuWBcN7JrrQPrYxjztF00zNYGAQiUlCm0rkikqUqi4WKGiop1uv9yv9/XSUsnv/+0H2Fdut1xNmsiVnV17yzlA7lat5GndWu7WreVp01qedu1k7eZ3ZDTNM97w2mSPiB6DNXbsWE2cOFEej0ezZs3SoEGDIvXQuzVjxgyde+65mjx5so444gg9/vjj+uc//6nly5erTZs2YX98nsT7xhij6o8Wq/SRR+VfuLBuubtVK6WeeYaWdj9GYz/c8yUeJp7enV+4DfDh8o26ZcYXe/w682y4cMzUGCNTXl5XiMyOElRcvFNhKq4tSL8qUaa0dD//RbWslJRfbl6v5HZLLktyuWvPBHa5pGBQprpaxu+XqfbL+KulqiqZqqp9exCPR5727ZXU+WAldemipO7dtTijjW5945s9fgvP0f3Da5M9IlawHn74Yd188806+eSTtWzZMrndbk2bNk2HNeJMMbv06dNHv//97zVlypS6ZV26dNGIESM0ceLEsD8+T+KGq/nuO5U//4IqXn5FprhYQcvS5affpS1p2dIedjXkZvr02nVHs+tgHwRDRiffP7/eVoFfa57q0Usn5MsVCkrVNTKBGqkmIBOokamukQI1Umg3v1b29KvGsiS3S3J7ZHnc2z966i/zeGq3Vrrduy7zeGpf0HdZ5rLl4rX7a59m6rU0raeRq7yitjSVl8ns+LysXKa8bHtBqi1JprhYoZISKRDYr2xWRkbtFqQdt6wsWU2ayNUkS67sJnJlbf98+9etzExZKalypfgkn2+/5muqqmoL39ZtCm2rvQULCxVct06Bn9YpuO4nBdaslSkpqfd9QcvS5WfcpS2p/J8PF16b7OGJxIMMGzZMS5cu1bPPPquRI0eqsrJS119/vQ4//HCNHz9eN910UyRi1FNdXa1ly5ZpzJgx9ZYPGTJEixcv3u33lNm5aVxSRXW1rT8vIbRpI8+ttyjj+utUM2uWlr2zWFvSm+71WzaWVGnJqo3q3jY7QiGdZYyRKitlSkpkiktqP5aUyJQUy5SU/nK/tFSqqKg7jkYVlfoq+QAVHnbWXn9+YUVA88+7St02fBuhf9F+2FHKPB7J7d5e3Nx1tx2FTjt9tFzuX+67t58HZExtaTQ7bqFfPt9puQkEpOpqmZoaqbpaqq7WV03aqHDQVXuNWeg3+mjsPY2baXKSrKwmsrIyZWVl7Xpr0mSnj5m16zbZfvyTZ+8vAUZScPttF/v7+8uypOzs2ttO3Ntv0vatdAUFCn7zrULffqvgim/09Zqt2pLG//lwCtdrU6IVtogUrEAgoC+//FL5+fmSpJSUFE2ZMkXHH3+8Lr74YkcK1ubNmxUMBpWbW38zcm5urgoKCiKeBw1j+XxKPvlkVXbqJ/17xW+uv+Ghx9W5fabc3Q6Ru0sXWc2aRcXWjb0xxkilZTJF27bv6tkms61Iprio9mPRTrdtRdtLU4lMSalUU9Oox9zSvvc+rVfUvKWsUFHtFqOkJCnJI3mSfvnctYfjKnc38pCRQsHag6ODASkQlHZ8DAVldr4fDNaWmFCodutNICDt5gzlOsHa79lRBn69DS0Sm++3Ze/b9f2Ku/xOnvY5UlqqrLQ0WampUlpa3ee1hWl7Qar7PGu/tyRFM8uyZOXlyZWXJw0cIEmq+nrjPv2fL1zwicypA2T5fOENCexBRArWnDlzdrt8+PDh+uqrryIRYY9+/YvJGLPHX1bhat+J1urt1DI7fZ/Wy/x4ofyv/7J1wEpNlefAA+U+8EB5Dmwrd26uXM2ayZ3bXK6cZnJlZcpKT5e1v7tB/H6FyspkSktrP5aUKlRWKlNaplBp7dakUFFR3S6SUFHxTp8X7b08/Ba3u+5MLVdWplxZWXJl1r4wuzIz5crI+OXFOzVFVmqq2lZ6pc9++9iYDo/er/x2e9+KECnGmO1nrwVlgsG64rXjcxMM1RW02gL3y9d2LnUmEJCCgdpCFwr+skyqPZ7IsmpvLuuXz63a5daO+0me2jPmkpIlb7Ks5GS13xKQ3v3pN/8dB/3lduVGyUyj2b7+n0977GGV3nerUk86UWkXjFLSwQeHOVn84bVp/0SkYO1NTk6OpL0Xm3A9rtvt3mVrVWFh4S5btRC9urfNVvNM728e39LnolMV+vp/qvnyKwVWr5apqFDN8uWqWb587w/gctWWkLS02gN53e7aA3ddVu2uJJer9gXaX117IG91tUy1v/Z+Tc1+HyMj1R5IvONMK2vnM66aZP3yefb2Y2gyM+tKlJWa2uD/U71DRs1X7f14odxMX1TterEs65ddfk6H2Y2eIaPmiwtjaqbRbF/+zzezqtXNXSFTUqLy555X+XPPy9v/aKVf+n/yHn103G7xQ3QJ20HuXbp00e23366RI0cqOTl5j+t99913mjRpktq2bbvL8VDh1qdPH/Xs2VOTJ0+uW9a1a1eddNJJHOQeQxp6hpaprlbgx58UXLNGgdWrFfjpJ4UKC2sPsC3cpNCmTbVXk7eRlZYmKyNdrvSM2gOLM9Jlpdd+/KUwNdm1MDVpIislxdYsv4WzCO3HTO21L/Mc0LmZqhcvUdmzz6lq1qzarZySknr0UOaN18vbvz9Faw94bbJH2ArW3LlzdfPNN2vVqlUaMmSIevXqpfz8fPl8Pm3btk3Lly/XokWLtHz5co0ePVq33nqrMjMzwxFlj3ZcpuGxxx5T37599cQTT+jJJ5/U119/rbZt24b98XkS22d318TJzfTp2mGdG/XCZUKh2osnlpXVncVlKivrDmo2weD2CykGa89q2747yEr21h50nLz9fmpq7a5GB6/11hh2zxPM1G4NmWfgxx9V9s+nVfHCC3WXh0ju/Qdl3XG7knv0iGjuWMBrkz3CfpmGxYsXa8aMGVqwYIHWrFmjyspK5eTkqEePHho6dKjOOeccNWnSJJwR9mry5Mm6++67tWHDBnXr1k3333+/jj766Ig8Nk9ie3FVZ3sxT/sxU3s1dJ7BwkKVTp6i8ueek6pqf/+mnHKKsm4ZI3d+XqRiRz1em+zh+Js9//zzz2rZgDfzjSc8ie3HTO3FPO3HTO3VmHkGN2xQyV13q+LlVyTV7sLPvGWM0s47N+a2NocDz1F7ROTNnnenoKBAV111lTp06OBUBABAAnLn5Sn7gfvV7J23ldyzp0x5uYpvu12bRpyimpUrnY6HOBHWglVUVKSzzz5bzZo1U35+vh566CGFQiHdcccdat++vT7++GM9/fTT4YwAAMBuJR92mHLeeE1Zf/+brPR01Xz2mQqHHaeyqc/I4Z07iANh3UV4xRVX6K233tLpp5+ud999VytWrNDQoUNVVVWlcePGqX///uF66JjAZlj7MVN7MU/7MVN72TXP4PoN2nbTTfJ/OE+S5B04QNkP3C/39ksJJRKeo/YI6xasmTNnaurUqbr33nv15ptvyhijTp06ae7cuQlfrgAA0cOdn6cDnntWWX/9i+T1yv/hPBUOHabqZZ85HQ0xKqwFa/369erataskqX379vL5fLr44ovD+ZAAADSKZVlKv/ACNZ81U54OHRQqKNCmP41U+bPPscsQDRbWghUKhZSUlFR33+12Ky0tLZwPCQDAfkk6+GA1e/tN+Y4bJtXUqOiWW1V8x7ja698B+yisx2C5XC4NGzZM3u37cd966y0dc8wxu5Ss1157LVwRohr7ue3HTO3FPO3HTO0VznkaY1T26GSVTPyHJMl37GBlT35UrtRU2x8rmvActUdYC9YFF1ywT+tNnTo1XBGiGk9i+zFTezFP+zFTe0VinpVvva2t11wr+f1KOuxQHfD8c3I3jd835uY5ag/HLzSayHgS24+Z2ot52o+Z2itS8/Qv/VRbL7xIoa1b5enUSTnTp8mdG59vccRz1B6OXWgUAIBY4f1DL+W8/qpcLXIVWLlSm075kwLr1jkdC1GMggUAwD5I6tBBzV57Ve42bRRcs1abTxmpwM8/Ox0LUYqCBQDAPvK0batmr74id7t2Cv78szafdoaCGzc6HQtRiIIFAEADuPPzlDNjutytWyu4Zo02n3GWglu2OB0LUYaCBQBAA3la5itnxotytWihwMqV2nLueQpVVDgdC1GEggUAQCN42ratLVnZ2ar575fadvmVMoGA07EQJShYAAA0UlKHDmr6zFTJ51XV+++r+PY7eFsdSKJgAQCwX7y9eqrpww9LlqXyZ59T2eNPOB0JUYCCBQDAfko5bpiyxt0hSSr5+wRVzZ/vcCI4jYIFAIAN0i6+SKlnnC6FQtp6xZUKrFnjdCQ4iIIFAIANLMtSk7//TUk9esgUFWvLRRcrVF7udCw4hIIFAIBNLJ9PB/zzCbmaN1fgm29VNOYWDnpPUBQsAABs5G7RQk0fnyK53ap87XVVvPSS05HgAAoWAAA28/burcwbb5AkFY+9XTUrVzqcCJFGwQIAIAzSR18p79FHyVRWautll8tUVjodCRFEwQIAIAwsl0vZDz0oV7NmCny7UsX/uMvpSIggChYAAGHibtZM2ffdK0kq/+dT8n+02OFEiBQKFgAAYeQbdIxSzz5LkrTtuusVKi11OBEigYIFAECYZd1xu9xt2ij4888qHnen03EQARQsAADCzJWeruwHJkmWpYoZL/FWOgmAggUAQAR4+/RR2gWjJElFY25ViLMK4xoFCwCACMm8+Sa58/IU/PFHlU663+k4CCMKFgAAEeJKT1fWhL9Lksoef0LV//ufw4kQLhQsAAAiKGXIsUo5/ngpGFTRzWNkQiGnIyEMKFgAAERY1l/Hy8rIUM0X/1XFDN6rMB5RsAAAiDB38+bKuO5aSVLJxH8oVFzsbCDYjoIFAIAD0i+8QJ6OHRXaskUl901yOg5sRsECAMABVlKSsv4yXpJU/sy/VPPNNw4ngp0oWAAAOMR39FHyHTdMCgZVfOdfnI4DG1GwAABwUNbtt0lJSfIvXMgV3uMIBQsAAAd52rRR2qjzJUnFf/27TDDocCLYgYIFAIDDMq+5WlZWlgIrVqji1decjgMbULAAAHCYKztbGVeNliSV3n2PDO9TGPMoWAAARIH0C0bJ3bKlghs2qGzqM07HwX6iYAEAEAUsn08ZN94gSSqbPEWhsjKHE2F/ULAAAIgSqaecLE/79gpt26byp552Og72AwULAIAoYXk8yrjhOklS6eNP8BY6MYyCBQBAFEk54QR5OnWSKS5W2ZP/dDoOGomCBQBAFLHcbmXecL0kqezJfyq4dZvDidAYFCwAAKKM77hhSuraVaasTOVTpzodB41AwQIAIMpYLpcyrrlaklT29NOcURiDKFgAAEQh37A/ynPQQTJFxSp//nmn46CBKFgAAEQhy+1W+pWXS5LKHn9SpqrK4URoiLgrWGvWrNFFF12kdu3aKSUlRQcddJDGjRun6urqeuv9+OOPOuGEE5SWlqacnBxdffXVu6wDAICTUk8+We78fIUKC1Xx0stOx0EDxF3B+uabbxQKhfT444/r66+/1v3336/HHntMt956a906wWBQw4cPV3l5uRYtWqTp06fr1Vdf1Q033OBgcgAA6rOSk5V++WWSpNLJU2QCAYcTYV9ZxhjjdIhwu+eeezRlyhT98MMPkqRZs2bp+OOP108//aT8/HxJ0vTp0zVq1CgVFhYqMzMzIrnK/H5JUrrXG5HHSwTM1F7M037M1F6JMM9QZaU29umr0JYtyp78qFJPOjGsj5cIM40Ej9MBIqG4uFhNmzatu79kyRJ169atrlxJ0tChQ+X3+7Vs2TINHDhwtz9nx5POLhXskrQdM7UX87QfM7VXQszT5VLSOWfL/+BDKnnscQWHDpFlWWF7uHDNNNEKW9ztIvy177//Xg8//LAuu+yyumUFBQXKzc2tt152draSk5NVUFAQ6YgAAOxV8tlnS8nJCn75pYLLPnM6DvZBzGzBuvPOOzV+/Pi9rrN06VL16tWr7v769ev1xz/+Uaeeeqouvvjieuvurv0bY/b6V0G42neitfpIYKb2Yp72Y6b2ivt5tsxXcOSfVDHtRQWnTlWTI/qF/SHjfqZhFjMFa/To0TrjjDP2us6BBx5Y9/n69es1cOBA9e3bV0888US99Vq0aKFPPvmk3rJt27appqZmly1bAABEg/RLLlbFtBdV9e57CqxZI89Or3mIPjFTsHJycpSTk7NP6/78888aOHCgevbsqalTp8rlqr8ntG/fvvr73/+uDRs2KC8vT5I0e/Zseb1e9ezZ0/bsAADsr6ROneQ9ZqD8cz9U2VNPq8lf/+J0JOxF3B2DtX79eg0YMECtW7fWvffeq02bNqmgoKDesVVDhgxR165dde655+rzzz/XBx98oBtvvFGXXHJJxM4gBACgodIvuUSSVDF9hkIlJQ6nwd7EXcGaPXu2Vq1apblz56pVq1bKy8uru+3gdrs1c+ZM+Xw+HXHEETrttNM0YsQI3XvvvQ4mBwBg77xHHSlPp04yFRWqeOVVp+NgLxLiOljRimuN2I+Z2ot52o+Z2isR51n2zDMqHnu7PB06qPm8ubZfsiERZxoOcbcFCwCAeJb6pz/JSktTYNUq+Rd95HQc7AEFCwCAGOLKyFDqyD9Jksr/9S+H02BPKFgAAMSYtPPPkyRVvTdbgZ/XO5wGu0PBAgAgxiQdfLCS+/aVQiFVPP+803GwGxQsAABiUPqo8yVJ5dNnyNTUOJwGv0bBAgAgBvmGHCtXTo5ChYWqmjvX6Tj4FQoWAAAxyEpOVuqpIyVJ5S+86HAa/BoFCwCAGJV65pmSJP+HHyq4foPDabAzChYAADEq6aD2Sj68jxQKqXzGDKfjYCcULAAAYljaWWdJqn1/QhMKOZwGO1CwAACIYSnHDZOVmangunXyL1zodBxsR8ECACCGWSkpSj3lZElSxYvTHU6DHShYAADEuNTTT5MkVc6eo1BxscNpIFGwAACIeUm/+508B3eS/H5Vvj3T6TgQBQsAgJhnWZZSR9ZeE6vi5VccTgOJggUAQFxIPeVkyeVS9dKlCqxZ43SchEfBAgAgDrhbtJD3qCMlSRWvvOpwGlCwAACIEzveOqfilVe5JpbDKFgAAMQJ3x//KCs9XcGfflL1f/7jdJyERsECACBOuFJSlDL8OElSxev/djhNYqNgAQAQR1JGjJAkVc2cKVNT42yYBEbBAgAgjniP6CdXs2YKbdsm/wLeOscpFCwAAOKI5XYr5YTjJUkVb7Cb0CkULAAA4kzKSSdJkqree0+hykqH0yQmChYAAHEmuefv5W7dWqa8XP73P3A6TkKiYAEAEGcsy1LKSSdKkir+zW5CJ1CwAACIQ6k7dhPO/VChkhKH0yQeChYAAHHI06WzPJ06SX6/qua873SchEPBAgAgDlmWpZTjh0uSKmfOdDhN4qFgAQAQp1KOGyZJqpo3X6GyMofTJBYKFgAAccrTubM87dvX7ib8gLMJI4mCBQBAnLIsS77t701Y+fY7DqdJLBQsAADi2I7jsPxz5ypUUeFwmsRBwQIAII4lHXKI3G3byFRVyT/3Q6fjJAwKFgAAccyyLKUM52zCSKNgAQAQ51K2H4dV9f4HMrw3YURQsAAAiHNJhx0md36+TEWFqhZ95HSchEDBAgAgzlmWJd+QYyVJVbNnO5wmMVCwAABIAL6hQyRJVbPnyASDDqeJfxQsAAASgPfww2VlZiq0ebOqP/vc6Thxj4IFAEACsJKT5TtmoCR2E0YCBQsAgAThG7J9N+F7FKxwo2ABAJAgfMcMlJKSFPj+e9WsWuV0nLhGwQIAIEG4MjLkPaKfJLZihRsFCwCABMJuwsigYAEAkEBSjq29Hlb1Z58puGWLw2niFwULAIAE4s7PU1LXrpIx8n84z+k4cYuCBQBAgvEOOkaSVPXBBw4niV8ULAAAEoxv0CBJUtX8BTKBgMNp4hMFCwCABJP8+x5yZWfLFBer+tNPnY4TlyhYAAAkGMvtlnfgAElS1QdzHc0SryhYAAAkIN+O47DmUrDCIa4Llt/vV/fu3WVZlr744ot6X/vxxx91wgknKC0tTTk5Obr66qtVXV3tTFAAACLM17+/5HIp8M23Cvz8s9Nx4k5cF6ybbrpJ+fn5uywPBoMaPny4ysvLtWjRIk2fPl2vvvqqbrjhBgdSAgAQea7sbCX36ilJqnqfswntFrcFa9asWZo9e7buvffeXb42e/ZsLV++XM8//7x69OihwYMH67777tOTTz6pkpISB9ICABB5O84m9M/90OEk8cfjdIBw2Lhxoy655BK98cYbSk1N3eXrS5YsUbdu3ept3Ro6dKj8fr+WLVumgQMH7vbnlvn9tuasYJek7ZipvZin/ZipvZjn/gnteF/CxYtVWloqKzk5bDNN93rD8nOjVdxtwTLGaNSoUbrsssvUq1ev3a5TUFCg3Nzcesuys7OVnJysgoKCSMQEAMBxrs6dZeXkSBUVCi5b5nScuBIzW7DuvPNOjR8/fq/rLF26VIsXL1ZJSYluueWWva5rWdYuy4wxu12+Q7jad6K1+khgpvZinvZjpvZino1X07+/Kl99VdZHi5U+YEDdcma6f2JmC9bo0aO1YsWKvd66deumuXPn6uOPP5bX65XH41GHDh0kSb169dL5558vSWrRosUuW6q2bdummpqaXbZsAQAQz3wD+kuS/PPmO5wkvljGGON0CDv9+OOP9Q5UX79+vYYOHapXXnlFffr0UatWrTRr1iwdf/zxWrdunfLy8iRJM2bM0Pnnn6/CwkJlZmZGJOuOY7r4K8E+zNRezNN+zNRezHP/BTdvVsFhPSRJLT5fpsqsLEnMdH/FzC7CfdWmTZt699PT0yVJBx10kFq1aiVJGjJkiLp27apzzz1X99xzj7Zu3aobb7xRl1xyScTKFQAA0cCdk6Ok3/1ONV99Jf/8BdKJJzgdKS7EzC5CO7ndbs2cOVM+n09HHHGETjvtNI0YMWK3l3QAACDeefsfLUmqms9uQrvE3S7CWMKmbfsxU3sxT/sxU3sxT3v4lyzR5pGnydW0qdL/87Esl4uZ7qeE3IIFAAB+kdyzp6y0NIW2blXo6+VOx4kLFCwAABKclZws7/aLjtYsWOBwmvhAwQIAAHXHYQUWL3Y4SXygYAEAAHmPqi1YwWXLZCorHU4T+yhYAABAnvbt5M7Pl6prFPj0U6fjxDwKFgAAkGVZ8h51pCQp8BG7CfcXBQsAAEjSTgXrI4eTxD4KFgAAkCR5j6wtWGbTZoU4Dmu/xN1b5QAAgMZxN2um9PfnyNXuQLl8PqfjxDQKFgAAqONu387pCHGBXYQAAAA2o2ABAADYjIIFAABgMwoWAACAzShYAAAANqNgAQAA2IyCBQAAYDMKFgAAgM0oWAAAADajYAEAANiMggUAAGAzyxhjnA4BAAAQT9iCBQAAYDMKFgAAgM0oWAAAADajYAEAANiMggUAAGAzClaYTZ48We3atZPP51PPnj21cOHCva4/f/589ezZUz6fT+3bt9djjz0WoaSxoSHzfO2113TssceqWbNmyszMVN++ffXee+9FMG1saOhzdIePPvpIHo9H3bt3D2/AGNTQmfr9fo0dO1Zt27aV1+vVQQcdpKeffjpCaaNfQ+f5wgsv6LDDDlNqaqry8vJ0wQUXaMuWLRFKG90WLFigE044Qfn5+bIsS2+88cZvfg+vS41kEDbTp083SUlJ5sknnzTLly8311xzjUlLSzNr167d7fo//PCDSU1NNddcc41Zvny5efLJJ01SUpJ55ZVXIpw8OjV0ntdcc4256667zH/+8x+zcuVKc8stt5ikpCTz2WefRTh59GroTHcoKioy7du3N0OGDDGHHXZYZMLGiMbM9MQTTzR9+vQxc+bMMatXrzaffPKJ+eijjyKYOno1dJ4LFy40LpfLPPjgg+aHH34wCxcuNIcccogZMWJEhJNHp3feeceMHTvWvPrqq0aSef311/e6Pq9LjUfBCqPevXubyy67rN6yzp07mzFjxux2/Ztuusl07ty53rJLL73UHH744WHLGEsaOs/d6dq1qxk/frzd0WJWY2d6+umnm9tuu82MGzeOgvUrDZ3prFmzTFZWltmyZUsk4sWchs7znnvuMe3bt6+37KGHHjKtWrUKW8ZYtS8Fi9elxmMXYZhUV1dr2bJlGjJkSL3lQ4YM0eLFi3f7PUuWLNll/aFDh+rTTz9VTU1N2LLGgsbM89dCoZBKS0vVtGnTcESMOY2d6dSpU/X9999r3Lhx4Y4Ycxoz0zfffFO9evXS3XffrZYtW6pTp0668cYbVVlZGYnIUa0x8+zXr5/WrVund955R8YYbdy4Ua+88oqGDx8eichxh9elxvM4HSBebd68WcFgULm5ufWW5+bmqqCgYLffU1BQsNv1A4GANm/erLy8vLDljXaNmeev3XfffSovL9dpp50WjogxpzEz/e677zRmzBgtXLhQHg+/Pn6tMTP94YcftGjRIvl8Pr3++uvavHmzrrjiCm3dujXhj8NqzDz79eunF154QaeffrqqqqoUCAR04okn6uGHH45E5LjD61LjsQUrzCzLqnffGLPLst9af3fLE1VD57nDiy++qDvvvFMzZsxQ8+bNwxUvJu3rTIPBoM466yyNHz9enTp1ilS8mNSQ52koFJJlWXrhhRfUu3dvHXfccZo0aZKeeeYZtmJt15B5Ll++XFdffbXuuOMOLVu2TO+++65Wr16tyy67LBJR4xKvS43Dn6BhkpOTI7fbvctfWYWFhbv8NbBDixYtdru+x+PRAQccELassaAx89xhxowZuuiii/Tyyy9r8ODB4YwZUxo609LSUn366af6/PPPNXr0aEm15cAYI4/Ho9mzZ+uYY46JSPZo1ZjnaV5enlq2bKmsrKy6ZV26dJExRuvWrVPHjh3DmjmaNWaeEydO1BFHHKE///nPkqRDDz1UaWlpOuqoo/S3v/2NLS4NxOtS47EFK0ySk5PVs2dPzZkzp97yOXPmqF+/frv9nr59++6y/uzZs9WrVy8lJSWFLWssaMw8pdotV6NGjdK0adM4BuNXGjrTzMxMffXVV/riiy/qbpdddpkOPvhgffHFF+rTp0+koketxjxPjzjiCK1fv15lZWV1y1auXCmXy6VWrVqFNW+0a8w8Kyoq5HLVf2lzu92Sftnygn3H69J+cOjg+oSw4/Tip556yixfvtxce+21Ji0tzaxZs8YYY8yYMWPMueeeW7f+jtNhr7vuOrN8+XLz1FNPcTrsTho6z2nTphmPx2MeffRRs2HDhrpbUVGRU/+EqNPQmf4aZxHuqqEzLS0tNa1atTIjR440X3/9tZk/f77p2LGjufjii536J0SVhs5z6tSpxuPxmMmTJ5vvv//eLFq0yPTq1cv07t3bqX9CVCktLTWff/65+fzzz40kM2nSJPP555/XXfaC1yX7ULDC7NFHHzVt27Y1ycnJ5ve//72ZP39+3dfOP/98079//3rrz5s3z/To0cMkJyebAw880EyZMiXCiaNbQ+bZv39/I2mX2/nnnx/54FGsoc/RnVGwdq+hM12xYoUZPHiwSUlJMa1atTLXX3+9qaioiHDq6NXQeT700EOma9euJiUlxeTl5Zmzzz7brFu3LsKpo9OHH36419+LvC7ZxzKGbaYAAAB24hgsAAAAm1GwAAAAbEbBAgAAsBkFCwAAwGYULAAAAJtRsAAAAGxGwQIAALAZBQsAAMBmFCwAAACbUbAAAABsRsECELM2bdqkFi1aaMKECXXLPvnkEyUnJ2v27NkOJgOQ6HgvQgAx7Z133tGIESO0ePFide7cWT169NDw4cP1wAMPOB0NQAKjYAGIeVdeeaXef/99/eEPf9B///tfLV26VD6fz+lYABIYBQtAzKusrFS3bt30008/6dNPP9Whhx7qdCQACY5jsADEvB9++EHr169XKBTS2rVrnY4DAGzBAhDbqqur1bt3b3Xv3l2dO3fWpEmT9NVXXyk3N9fpaAASGAULQEz785//rFdeeUX//e9/lZ6eroEDByojI0Nvv/2209EAJDB2EQKIWfPmzdMDDzyg5557TpmZmXK5XHruuee0aNEiTZkyxel4ABIYW7AAAABsxhYsAAAAm1GwAAAAbEbBAgAAsBkFCwAAwGYULAAAAJtRsAAAAGxGwQIAALAZBQsAAMBm/w/dGD76kbxa2gAAAABJRU5ErkJggg==",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "ax = plt.gca()\n",
    "plot_expr(residual(u.subs(sol_col), x), x, ax=ax)\n",
    "plt.plot(x_colo, [0]*nterms, \"o\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"R(x)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ya que conocemos la solución exacta, podemos calcular el error\n",
    "relativo en la norma $L^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "El error relativo es 0.80 %\n"
     ]
    }
   ],
   "source": [
    "err_col = integrate((u_e - u.subs(sol_col))**2, (x, 0, 1))/integrate(u_e**2, (x, 0, 1))\n",
    "print(f\"El error relativo es {N(err_col*100, 2)} %\")"
   ]
  },
  {
   "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": "3.12.3"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}