EqnSolvers_Semana4.ipynb

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   "source": [
    "# Resolvendo Equações Não-lineares (Achando raízes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "826be527-2e2b-4d36-9f40-8df618b1186c",
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   "source": [
    "Nosso problema aqui é resolver equações da forma $$f(x) = 0, $$ isto é, achar uma solução (raiz) $\\bar{x}$ tal que $f(\\bar{x})=0$ (note que podemos ter mais de uma solução). A hipótese mínima que pediremos de $f$ é que ela seja contínua no intervalo considerado. Nesse caso, as vezes é importante fazermos uma análise inicial para localizar possíveis intervalos que contém a solução (raiz).\n",
    "\n",
    "Por exemplo, considerando da função $f(x) = x^3 - 12x + 5$, calculando sua derivada, achando os pontos críticos e os intervalos de crescimento e descrescimento, podemos chegar a conclusão que as estão em $[-4,-3]$, $[0,1]$ e $[3,4]$.\n",
    "\n",
    "Outra opção interessante é transformar o problema $f(x)=0$, em $F(x) = G(x)$, e encontrar os pontos onde os gráficos de $F$ e $G$ (possivelmente mais simples de se esboçar) se cruzam. No exemplo anterior podemos tomar $F(x) = x^3$ e $G(x) = 12x-5$."
   ]
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   "source": [
    "## Método da Bissecção "
   ]
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    "A ideia é construir uma sequência de pontos $x_0$, $x_1$, $x_2$, $\\ldots$ de tal forma que $\\lim_{k \\to \\infty} x_k = \\bar{x}$, onde $\\bar{x}$ é uma solução de $f(x) = 0$. Uma explicação das etapas utilizadas na construção da sequência é a seguinte:\n",
    "\n",
    "- **Passo 0**: Para começar, é necessário encontrar $a_0$ e $b_0$ de modo que $f(a_0)f(b_0) < 0$. Os dois pontos são rotulados de modo que $a_0 < b_0$. Com isso, você considera $x_0$ como o ponto médio do intervalo. Então, $x_0 = (a_0 + b_0)/2$. (Achar $a_0$ e $b_0$ é na inspeção, a garantia da existência da raiz vem do TVI).\n",
    "\n",
    "- **Passo 1**: Se $f(x_0) \\neq 0$, então determine qual metade do intervalo contém uma solução. Portanto, se $f(a_0)f(x_0) < 0$, então o novo intervalo contendo a raiz é $a_1 = a_0$ e $b_1 = x_0$. Caso contrário, considere $a_1 = x_0$ e $b_1 = b_0$. Com isso, tome $x_1 = (b_1 + a_1)/2$.\n",
    "\n",
    "- **Passo 2**: Se $f(x_1) \\neq 0$, basta refazer o procedimento de subdivisão usado no **passo 1**.\n",
    "\n",
    "- Os próximos passos repetem o procedimento acima.\n",
    "\n",
    "Consideremos como ilustração o exemplo $f(x) = (x - 0.1)(x - 2.1)(x + 1.1)$."
   ]
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
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   "source": [
    "f = lambda x:  (x - 0.1)*(x - 2.1)*(x + 1.1)\n",
    "\n",
    "nplot = 200\n",
    "a = -2\n",
    "b = 3\n",
    " \n",
    "x = np.linspace(a,b,nplot)\n",
    "y = f(x)\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.xticks(np.arange(a, b+1, 1.0))\n",
    "plt.xlim(a,b)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
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   "source": [
    "Porém ainda não falamos como interromper o procedimento acima. Para isso precisamos de um **critério de parada**. Podemos usar o erro entre iterações sucessivas $|x_k - x_{k-1}|$ ou o erro **relativo** entre iterações sucessivas $\\dfrac{|x_k - x_{k-1}|}{|x_k|}$ (assumindo $x_k \\neq 0$), ou ainda verificar se $|f(x_k)|$ é pequeno. Em termos de pseudo-código temos\n",
    "\n",
    "\n",
    "**Entrada**: $a < b$ com $f(a)f(b) < 0$ e $eps_1 > 0$ (tolerância erro iterativo) e $eps_2 > 0$ (tolerância da raiz).\n",
    "\n",
    "**Inicialização:** $x = (a + b)/2$, $err_1 = 10*eps_1$\n",
    "\n",
    "**Iteração:**\n",
    "    \n",
    "    \n",
    "    while err_1 > eps_1 or |f(x)| > eps_2\n",
    "        if f(a)f(x) < 0, then b = x \n",
    "            else if f(b)f(x) < 0, then a = x \n",
    "            else stop \n",
    "        end \n",
    "        X = x \n",
    "        x = (a + b)/2\n",
    "        f(x)\n",
    "        err_1 = |x − X|/|x| \n",
    "    fim"
   ]
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    "def bisection(f, a, b, eps1=1e-4, eps2=1e-4, debug=False):\n",
    "    \n",
    "    f_a = f(a)\n",
    "    f_b = f(b)\n",
    "    x_M = (a + b)/2.0\n",
    "    f_M = f(x_M)\n",
    "    \n",
    "    err1 = 10.*eps1\n",
    "    iteration_counter = 1\n",
    "\n",
    "    while ((err1 > eps1) and (abs(f_M) > eps2)):\n",
    "        \n",
    "        if debug:\n",
    "            print('Erro rel. iteração {:2d} = {:.8e},  |f(x_M)| = {:.8e}'.format(iteration_counter,err1,abs(f_M)))\n",
    "            \n",
    "        if f_a*f_M < 0:\n",
    "            b = x_M\n",
    "            f_b = f_M\n",
    "        else:\n",
    "            a = x_M\n",
    "            f_a = f_M\n",
    "        \n",
    "        Xprev   = x_M    \n",
    "        x_M = (a + b)/2\n",
    "        f_M = f(x_M)\n",
    "        err1 = abs((x_M - Xprev)/x_M)\n",
    "        iteration_counter = iteration_counter + 1\n",
    "    \n",
    "    if debug:\n",
    "            print('Erro rel. iteração {:2d} = {:.8e},  |f(x_M)| = {:.8e}'.format(iteration_counter,err1,abs(f_M)))\n",
    "            \n",
    "    return x_M, iteration_counter"
   ]
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   "source": [
    "sol, count = bisection(f,-1.5,2.5,eps1=1e-5,eps2=1e-10,debug=True)"
   ]
  },
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   "source": [
    "print('Solução: {:g}'.format(sol))\n",
    "print('Número de Iterações: {:d}'.format(count))"
   ]
  },
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   "source": [
    "raiz = 2.1\n",
    "erro = abs(sol - raiz)\n",
    "erro_rel = erro/abs(raiz)\n",
    "print('Erro absoluto = {:.6e}'.format(erro))\n",
    "print('Erro relativo = {:.6e}'.format(erro_rel))"
   ]
  },
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   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Tanto o erro (absoluto) quanto o erro relativo são usados, mas o erro relativo tem a vantagem de ser baseado em um valor <b>normalizado</b>. Para explicar, considere o requisito de que a solução computada satisfaça $|x_{ex} − x_{ap}| < 0.1$ versus satisfazendo $|x_{ex} − x_{ap}|/|x_{ex}| < 0.1$. Se $x_{ex} = 10^{−8}$, então usando o erro (absoluto) você aceitaria $x_{ap} = 10^{−2}$, mesmo que este seja um fator $10^6$ maior que a solução. Com o erro relativo, você não aceitaria $x_{ap} = 10^{−2}$, mas aceitaria qualquer valor que satisfizesse $0.9 < |x_{ap}/x_{ex}| < 1.1$.\n",
    "    \n",
    "O outro aspecto útil do erro relativo é que ele tem uma conexão com o número de dígitos significativos corretos, e isso será explicado mais tarde.\n",
    "</div>"
   ]
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   "cell_type": "markdown",
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   "source": [
    "### Convergência do Método"
   ]
  },
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   "source": [
    "**Teorema**\n",
    "\n",
    "Se $f \\in C[a_0, b_0]$, com $f(a_0)f(b_0) < 0$, então os pontos médios $x_0, x_1, x_2, \\ldots$ calculados usando o método da bissecção convergem para uma solução $\\bar{x}$ de $f(x) = 0$. Além disso, o erro satisfaz\n",
    "$$\n",
    "|x_k - \\bar{x}| \\leq \\dfrac{1}{2^{k+1}} (b_0 - a_0),\n",
    "$$\n",
    "e o erro da iteração é \n",
    "$$\n",
    "|x_k - x_{k-1}| = \\dfrac{1}{2^{k+1}} (b_0 - a_0).\n",
    "$$\n",
    "\n",
    "**Ou seja, o método da bissecção nos permite saber o número de iterações necessárias para atingirmos uma determinada tolerância.** "
   ]
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   "source": [
    "### Ordem de Convergência (Definição)\n",
    "\n",
    "Suponha que a sequência $\\{x_k\\}$ seja convergente, isto é, $\\lim_{k \\to \\infty} x_k= \\bar{x}$, e seja $e_k$ o erro da aproximação, isto é, $e_k = |x_k - \\bar{x}|$. Uma vez que $x_k$ está numa vizinhança de $\\bar{x}$ (ou seja, está próximo de $\\bar{x}$), se $$e_k \\approx C e_{k-1}^r \\quad (\\star),$$ onde $C > 0$ é uma constante, então dizemos que a **ordem de convergência** é $r$."
   ]
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   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "É possível provar (veja se consegue argumentar isso) que se a ordem de convergência é $r$, e $\\bar{x} \\neq 0$, então o erro relativo $\\dfrac{|x_k - \\bar{x}|}{|\\bar{x}|}$ e o erro relativo da iteração $\\dfrac{|x_k - x_{k-1}|}{|x_k|}$ também satisfaz $(\\star)$, porém tipicamente com uma constante $C$ diferente em cada caso.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4aa0013-fee6-45f6-b772-b9aaaf03dad4",
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   "source": [
    "O método da bissecção satisfaz $e_k \\approx \\dfrac{1}{2} e_{k-1}$, portanto ele é um método de primeira ordem pois tem $r = 1$. Veremos em seguida dois outro método com taxas melhores, por exemplo o método de Newton é de segunda ordem, ou seja, $r=2$ (também dito, ordem de convergência quadrática).\n",
    "\n",
    "Faça o seguinte exercício. Suponha $C=1/2$, se $e_1 = 10^{-1}$, e calcule $e_4$ (aproximadamente) para ambos métodos, ou seja, com $r=1$ e $r=2$."
   ]
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   "metadata": {},
   "source": [
    "## Método de Newton"
   ]
  },
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   "id": "f15ddcfb-14f4-47ec-b7f2-9d725ceaef51",
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   "source": [
    "Dado $x_0$, consideremos as iterações\n",
    "$$\n",
    "x_k = x_{k-1} - \\dfrac{f(x_{k-1})}{f'(x_{k-1})},\n",
    "$$\n",
    "para $k = 1, 2, 3, \\ldots$."
   ]
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   "source": [
    "def naive_Newton(f, dfdx, x, eps, debug=False): \n",
    "    while abs(f(x)) > eps: \n",
    "        x = x - (f(x))/dfdx(x)\n",
    "        if debug:\n",
    "            print(x)\n",
    "    return x"
   ]
  },
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   "execution_count": 3,
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x - 2.1)*(x - 0.1)*(x + 1.1)\n",
      "(x - 2.1)*(x - 0.1) + (x - 2.1)*(x + 1.1) + (x - 0.1)*(x + 1.1)\n"
     ]
    }
   ],
   "source": [
    "# Usando o pacote simbólico do Python para definir a função \n",
    "# e calcular sua derivada de maneira simbólica e transformar\n",
    "# numa função numérica\n",
    "\n",
    "import sympy as sym\n",
    "\n",
    "x = sym.symbols('x') \n",
    "\n",
    "f_expr = (x - 0.1)*(x - 2.1)*(x + 1.1) # symbolic expression for f(x) \n",
    "dfdx_expr = sym.diff(f_expr, x) # compute f’(x) symbolically \n",
    "\n",
    "print(f_expr)\n",
    "print(dfdx_expr)\n",
    "\n",
    "# turn f_expr and dfdx_expr into plain Python functions \n",
    "f = sym.lambdify([x], # argument to f \n",
    "                 f_expr) # symbolic expression to be evaluated \n",
    "\n",
    "dfdx = sym.lambdify([x], dfdx_expr) "
   ]
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.700999999999999 18.189999999999998\n",
      "x**3 - 1.1*x**2 - 2.21*x + 0.231\n",
      "3*x**2 - 2.2*x - 2.21\n"
     ]
    }
   ],
   "source": [
    "print(f(3), dfdx(3))\n",
    "print(sym.expand(f_expr))\n",
    "print(sym.expand(dfdx_expr))"
   ]
  },
  {
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   "execution_count": 8,
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    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nplot = 200\n",
    "a = -2\n",
    "b = 3\n",
    " \n",
    "x = np.linspace(a,b,nplot)\n",
    "y = f(x)\n",
    "dy = dfdx(x)\n",
    "\n",
    "plt.plot(x,y,label='f')\n",
    "plt.plot(x,dy,label='df/dx')\n",
    "plt.legend(loc='upper right')\n",
    "plt.xticks(np.arange(a, b+1, 1.0))\n",
    "plt.xlim(a,b)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f8621b91-0e0f-4068-9084-f193e80dbb57",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.4117097306212205\n",
      "2.156962173183982\n",
      "2.1024623945180805\n",
      "2.1000049115007156\n",
      "2.1000049115007156\n"
     ]
    }
   ],
   "source": [
    "# Testando o Naive Newton para a função definida acima (a mesma\n",
    "# do método da bissecção\n",
    "\n",
    "x0 = 3.0\n",
    "solApprox = naive_Newton(f, dfdx, x0, 1.0e-4, debug=True)\n",
    "print(solApprox)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7410437f-8ae7-43a7-a972-3c8872502419",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0035813818515786\n",
      "-0.4888968252407817\n",
      "1.7433937951215295\n",
      "2.285685968916457\n",
      "2.122774942191575\n",
      "2.1004098653050622\n",
      "2.1000001364221688\n",
      "2.1000001364221688\n"
     ]
    }
   ],
   "source": [
    "#x0 = -0.4\n",
    "x0 = -0.447\n",
    "#x0 = -0.6\n",
    "solApprox = naive_Newton(f, dfdx, x0, 1.0e-4,debug=True)\n",
    "print(solApprox)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7f878917-da38-4685-a1a1-01b4278abc9a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "9396c8b8-db8c-40f9-9a49-226f087f12f7",
   "metadata": {},
   "source": [
    "### Problema a vista!!! O Método de Newton pode falhar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c2a11fce-dfbe-4989-b75d-319690a6afee",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tanh(x)\n",
      "1 - tanh(x)**2\n"
     ]
    }
   ],
   "source": [
    "x = sym.symbols('x')\n",
    "\n",
    "f_expr = sym.tanh(x)\n",
    "dfdx_expr = sym.diff(f_expr, x)\n",
    "\n",
    "print(f_expr)\n",
    "print(dfdx_expr)\n",
    "\n",
    "f = sym.lambdify([x], f_expr) \n",
    "dfdx = sym.lambdify([x], dfdx_expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ed277c6a-2cf7-4c6a-82be-f877e6555d4a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "nplot = 200\n",
    "a = -5\n",
    "b = 5\n",
    " \n",
    "x = np.linspace(a,b,nplot)\n",
    "y = f(x)\n",
    "dy = dfdx(x)\n",
    "\n",
    "plt.plot(x,y,label='f')\n",
    "plt.plot(x,dy,label='df/dx')\n",
    "plt.legend(loc='upper right')\n",
    "plt.xticks(np.arange(a, b+1, 1.0))\n",
    "plt.xlim(a,b)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "b39af566-a3ae-4631-9f55-ca17d6d1585b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.0933161820201083\n",
      "1.104903543244409\n",
      "-1.1461555078811896\n",
      "1.3030326182332865\n",
      "-2.064923002377556\n",
      "13.473142800576014\n",
      "-126055913647.13739\n",
      "inf\n",
      "nan\n",
      "nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\adrim\\AppData\\Local\\Temp\\ipykernel_2828\\2852368626.py:3: RuntimeWarning: divide by zero encountered in scalar divide\n",
      "  x = x - (f(x))/dfdx(x)\n",
      "C:\\Users\\adrim\\AppData\\Local\\Temp\\ipykernel_2828\\2852368626.py:3: RuntimeWarning: invalid value encountered in scalar subtract\n",
      "  x = x - (f(x))/dfdx(x)\n"
     ]
    }
   ],
   "source": [
    "# Para quais x0´s abaixo o método de Newton falha?\n",
    "\n",
    "#x0 = 1.07\n",
    "#x0 = 1.08\n",
    "x0 = 1.09\n",
    "\n",
    "solApprox = naive_Newton(f, dfdx, x0, 1.0e-4, debug=True)\n",
    "print(solApprox)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c72bc3d2-1e7a-4cb1-9560-d7bffc1022e2",
   "metadata": {},
   "source": [
    "### Tomando cuidado com o problema da derivada se aproximar de zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "37186bcf-8662-4e0d-9c66-29cf2baf671f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "def Newton(f, dfdx, x, eps, debug=False):\n",
    "    \n",
    "    f_value = f(x)\n",
    "    iteration_counter = 0\n",
    "    \n",
    "    while abs(f_value) > eps and iteration_counter < 20:\n",
    "        \n",
    "        try:\n",
    "            div = f_value/dfdx(x)\n",
    "        except ZeroDivisionError:\n",
    "            print('Error! - derivative zero for x = ', x)\n",
    "            sys.exit(1)     # Abort with error\n",
    "        \n",
    "        x = x - div\n",
    "        \n",
    "        if debug:\n",
    "            print(x)\n",
    "            \n",
    "        f_value = f(x)\n",
    "        iteration_counter = iteration_counter + 1\n",
    "\n",
    "    # Here, either a solution is found, or too many iterations\n",
    "    if abs(f_value) > eps:\n",
    "        iteration_counter = -1\n",
    "    return x, iteration_counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f165b9f5-8d6e-4f3c-a659-aaefec434ca7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.0933161820201083\n",
      "1.104903543244409\n",
      "-1.1461555078811896\n",
      "1.3030326182332865\n",
      "-2.064923002377556\n",
      "13.473142800576014\n",
      "-126055913647.13739\n",
      "inf\n",
      "nan\n",
      "(nan, 9)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\adrim\\AppData\\Local\\Temp\\ipykernel_2828\\3875822610.py:11: RuntimeWarning: divide by zero encountered in scalar divide\n",
      "  div = f_value/dfdx(x)\n",
      "C:\\Users\\adrim\\AppData\\Local\\Temp\\ipykernel_2828\\3875822610.py:16: RuntimeWarning: invalid value encountered in scalar subtract\n",
      "  x = x - div\n"
     ]
    }
   ],
   "source": [
    "#x0 = 1.07\n",
    "#x0 = 1.08\n",
    "x0 = 1.09\n",
    "\n",
    "solApprox = Newton(f, dfdx, x0, 1.0e-3, debug=True)\n",
    "print(solApprox)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e92dfe65-1b1d-47ae-bbae-2796d1162ef4",
   "metadata": {},
   "source": [
    "### Mais um exemplo de falha e melhorando os critérios de convergência do método"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "7dc29933-e62e-4954-87be-d3cdc527322a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x/(x**2 + 1)\n",
      "-2*x**2/(x**2 + 1)**2 + 1/(x**2 + 1)\n"
     ]
    }
   ],
   "source": [
    "x = sym.symbols('x')\n",
    "\n",
    "f_expr = x/(1+x*x)\n",
    "dfdx_expr = sym.diff(f_expr, x)\n",
    "\n",
    "print(f_expr)\n",
    "print(dfdx_expr)\n",
    "\n",
    "f = sym.lambdify([x], f_expr) \n",
    "dfdx = sym.lambdify([x], dfdx_expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "ac461cf8-652a-4a2c-9724-b170a13c9710",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MmDFu6X5yd/l6xTCbzW5vUXKSZEkI4d2cA7Wd3WtNERgF+ftOjHUSQkdGo7FVH/JGo5Gamhp8fX3dksy4u/y2iqEnGeAthPBuzpalpoxXcjp5kLcQotOTZEkI4d2c0wY05Uo4J+e+0rIkhMADk6U33niD7t274+vry9ChQ1m1alWj+y9YsIBBgwbh7+9PbGwst9xyC/n5+W1UWyFEu3N2wwU2pxuudl+ZmFIIgYclSwsXLmTWrFk8+uijpKamMnr0aCZPnkx6enqD+//666/ceOONTJ8+nZ07d/LFF1+wceNGbrvttjauuRCi3ZQ3Y44lJ1fLknTDCSE8bID3Sy+9xPTp013Jzrx581iyZAlvvvkmzzzzTL39161bR1JSEvfeey8A3bt358477+T5558/bQyr1YrVanX9XFJSAmgj91tz9UJjnOW6q/y2iOEN5yAxOk75esYwlh7HANT4haOeUtbpYii+4ZgAR9lx7K2M70mvVXuVLzE6VgxvOAe9y1ZUD5l7vbq6Gn9/f7744guuvPJK1/b77ruPrVu3smLFinrHrFmzhvHjx/P1118zefJkcnJy+OMf/0i/fv146623Gowzd+5cnnjiiXrbP/30U/z9/fU7ISFEmxi/ew7BVRms6flXcoP7N+mY0PIDjN37BBXmcFL6z3NvBYUQblFRUcHUqVMpLi4mODi4VWV5TMtSXl4edrud6OjoOtujo6PJzs5u8JiRI0eyYMECrr32WqqqqqipqeHyyy/ntddeO22cOXPmMHv2bNfPJSUlxMfHM378eCIiIvQ5mVPYbDZSUlKYOHGiW+e0cGcMbzgHidFxytczhmnvAwCcO/4SiD6naTGK0mHvE/ipFUyZPBlaMWmeJ71W7VW+xOhYMbzhHABdxyd7TLLkdOpMn6qqnnb2z127dnHvvffy97//nYsuuoisrCwefPBBZsyYwXvvvdfgMRaLBYvFUm+72Wx2+1wQ3hDDG85BYnSc8lsdw+GAigKtnOBoOE059WIEa1/KlJoqzNjAHNCy+I3FcINO//uWGB5Vvrtj6FmuxyRLkZGRGI3Geq1IOTk59VqbnJ555hlGjRrFgw8+CMDAgQMJCAhg9OjRPPXUU8TGxrq93kKIdmQtBtWuPW7OsiU+AWDyhZoqKM/TfhZCdFoeczWcj48PQ4cOJSUlpc72lJQURo4c2eAxFRUV9Rboc86a6iFDtYQQrVHbqoRPkLbmW1MpCvjXdrtXyFQjQnR2HpMsAcyePZt///vfvP/+++zevZv777+f9PR0ZsyYAWjjjW688UbX/pdddhlfffUVb775JgcPHmT16tXce++9DB8+nLi4uPY6DSFEW3EmOi1ZDFeSJSFELY/phgO49tpryc/P58knnyQrK4v+/fuzaNEiEhMTAcjKyqoz59LNN99MaWkpr7/+Og888AChoaFccMEFPPfcc+11CkKItuRKllpwcYYkS0KIWh6VLAHMnDmTmTNnNvjc/Pnz62275557uOeee9xcKyFEh6RHslSep199hBAeyaO64YQQollakywFRNYtQwjRaUmyJITwXrp0w0nLkhCdnSRLQgjvpcsA7wL96iOE8EiSLAkhvJcz0ZEB3kKIVpBkSQjhvfQYsyQDvIXo9CRZEkJ4L5lnSQihA0mWhBDeS48B3pWF4LDrVychhMeRZEkI4Z3sNVBZpD1uSbLk52yNUrWESQjRaUmyJITwTlVFQO0akH5hzT/eaALfUO2xjFsSolOTZEkI4Z2cXXC+IWA0t6wMmZhSCIEkS0IIb9Wa8UpOMjGlEAJJloQQ3krXZElaloTozCRZEkJ4J0mWhBA6kWRJCOGd9EyWyiVZEqIzk2RJCOGdXEudtGBCSicZ4C2EQJIlIYS3kgHeQgidSLIkhPBOuiRL0rIkhJBkSQjhrVzdcDJmSQjROpIsCSG8ky4tS+F1yxJCdEqSLAkhvJMeLUvOAd41lVBd3vo6CSE8kiRLQgjvY7eBtVh73JpkyScQjD7aY2ldEqLTkmRJCOF9nK1KikFbG66lFEUGeQshJFkSQnghZ2LjFwYGY+vKkkHeQnR6kiwJIbyPHoO7nQJkriUhOjtJloQQ3kfPZMk1MWVB68sSQngkSZaEEN5Hz2TJT6YPEKKzk2RJCOF99FgXzsnVsiTJkhCdlSRLQgjv445uuErphhOis5JkSQjhfXRNlpzdcJIsCdFZSbIkhPA+bkmWpBtOiM5KkiUhhPeRq+GEEDqSZEkI4X30WBfO6eQB3qra+vKEEB5HkiUhhPdxtSzpcDWcc+oAhw2spa0vTwjhcSRZEkJ4F1sl2Mq1x3q0LPn4g8lPeyzjloTolDwuWXrjjTfo3r07vr6+DB06lFWrVjW6v9Vq5dFHHyUxMRGLxULPnj15//3326i2Qog25+yCM5jAEqxPmTJ9gBCdmqm9K9AcCxcuZNasWbzxxhuMGjWKt99+m8mTJ7Nr1y4SEhIaPOaPf/wjx48f57333qNXr17k5ORQU1PTxjUXQrQZ1yK64aAo+pTpHw4lx2SQtxCdlEclSy+99BLTp0/ntttuA2DevHksWbKEN998k2eeeabe/osXL2bFihUcPHiQ8HBt3EFSUlKjMaxWK1ar1fVzSUkJADabDZvNptOZ1OUs113lt0UMbzgHidFxym9NDKU0BxOg+odTc4ZjmxrD6BeGAagpzUFtZn068mvVUcqXGB0rhjecg95lK6rqGZd3VFdX4+/vzxdffMGVV17p2n7fffexdetWVqxYUe+YmTNnsnfvXoYNG8bHH39MQEAAl19+Of/4xz/w8/NrMM7cuXN54okn6m3/9NNP8ff31++EhBBu0bVwHcMOv0FeYF9Wn/WILmUOPfQG3YrWsaPrVA5GXaxLmUII96qoqGDq1KkUFxcTHNy6LnmPaVnKy8vDbrcTHR1dZ3t0dDTZ2dkNHnPw4EF+/fVXfH19+frrr8nLy2PmzJkUFBScdtzSnDlzmD17tuvnkpIS4uPjGT9+PBEROgwWbYDNZiMlJYWJEydiNps9MoY3nIPE6DjltyaGYWMmHIbwbmcxZcoUXWIYlqyETes4OymGvuMaL7OlMVqjM/++JYb8vk8nP1+/CzI8JllyUk4Zg6Cqar1tTg6HA0VRWLBgASEhIYDWlfeHP/yBf/3rXw22LlksFiwWS73tZrPZbb9Qb4rhDecgMTpO+S2KYS0CwBAQiaGJx50xRmAXAIxVhRhbeL4d8rXqYOVLjI4Vw9PPQc9yPeZquMjISIxGY71WpJycnHqtTU6xsbF07drVlSgB9OvXD1VVOXbsmFvrK4RoJ3rO3u3kJ0ueCNGZeUyy5OPjw9ChQ0lJSamzPSUlhZEjRzZ4zKhRo8jMzKSsrMy1be/evRgMBrp16+bW+goh2ok7kiXn5JaVhfqVKYTwGB6TLAHMnj2bf//737z//vvs3r2b+++/n/T0dGbMmAFo441uvPFG1/5Tp04lIiKCW265hV27drFy5UoefPBBbr311tMO8BZCeDi3JEsnLXkihOh0PGrM0rXXXkt+fj5PPvkkWVlZ9O/fn0WLFpGYmAhAVlYW6enprv0DAwNJSUnhnnvuYdiwYURERPDHP/6Rp556qr1OQQjhbnquC+fkL91wQnRmHpUsgTYdwMyZMxt8bv78+fW29e3bt17XnRDCizln2dZjXTgnV8tSgbaYrl6TXQohPIJHdcMJIUSjVNW9A7xlMV0hOiVJloQQ3sNWATVV2mM9kyUffzDXTkorXXFCdDqSLAkhvIczkTFawCdA37KdrUuymK4QnY4kS0II73FyF5ze44pcg7wlWRKis5FkSQjhPdwxXslJpg8QotOSZEkI4T0q3HAlnJMkS0J0WpIsCSG8h1tblqQbTojOSpIlIYT3kG44IYQbSLIkhPAekiwJIdxAkiUhhPdwZ7LkF6bdy2K6QnQ6kiwJIbyHDPAWQriBJEtCCO/halmSZEkIoR9JloQQ3qM8T7v3j9S/7JOTJVXVv3whRIclyZIQwjs4HCdafQLckSw5F9OtadJiuja7g9T0Qr7dmsmWPIX9OWWokmQJ4ZFM7V0BIYTQhbUYVLv22B0DvM1+2mK6tgotKfMNbnA3h0NlwfojvPbLfnJKrbVbjXy4bw2JEf5MG5HIn0Yk4ms26l9HIYRbSMuSEMI7lNe2KvkEgcninhiurriGJ6asqK7hzws287dvd5JTaiXU38yI7mEkBar4mg0cya/gqf/t5sIXV7DuoIx9EsJTSMuSEMI7uLrg3NCq5OQfDsVHobJ+smR3qNzzaSo/78nBx2hgzpS+3HBeIopqZ9GiRYybcCGLduby6s/7yCiqZOq767j7grO494JemIzyvVWIjkzeoUII71DhHNztxmTJz7nkSf1WoZdT9mqJksnAx9OHc8uo7viYTvyL9fcxcf3wBH6aPZY/DuuGQ4VXf97HTR9soLTK5r46CyFaTZIlIYR3cOeVcE6nmT5gV2YJb644AMALfxjIeT1On7AFWEw8/4dBvHr9EAJ8jKzen89176wjp7TKbdUWQrSOJEtCCO/gztm7nRoYs6SqKo99swO7Q2XKgBiuGNy1SUVdPiiOz+9IJiLAh52ZJfzhzbUcK6xwR62FEK0kyZIQwju01Zilk2MBy/fmsiW9CH8fI3+/9JxmFTegWwhf/nkkCeH+pBdUcMO/15NdLC1MQnQ0kiwJIbyDq2Wp7brhVFXltZ/3AfCnEYnEhPg2u8ikyAAW3jmC+HA/juRXcMO/15HrmnJACNERSLIkhPAO5W0wwNvVsqR1w206UsiW9CJ8TAZuG929xcXGhvjx6W0jiAvx5UBuOdPeW09hebUeNRZC6ECSJSGEd3BeDeeO2budnIlY7dQBn284CsDvB8cRFdT8VqWTxYf78+ntI4gKsrAnu5Qb399AmbWmVWUKIfQhyZIQwju0RTfcSVMHlFTZ+N+OTACuPTdBl+KTIgP49PbziAjwYUdGMX/+ZDPVNQ5dyhZCtJwkS0II7+CcwdvZVeYOJ41Z+mFrJlU2B2dFBfK7hFDdQvSKCuL9m8/Fz2xk1b48Hv5yu6wpJ0Q7k2RJCOH5bJVgK9ceu7Ub7sRiust2aPMqXfW7biiKomuYQfGhvPGn32E0KHyVmsFzi9N0LV8I0TySLAkhPJ+zC85gBkvDC9zqwuwH5gAADhw6AsDk/jFuCTW+TxTPXjUAgLdWHGD+6kNuiSOEODNJloQQnu/kK+F0buWpp7blKkQtpm9MEEmRAW4Ldc2weP4yqTcAT/ywi0U7stwWSwhxepIsCSE8n2tCSjd2wTnVxohQSrjYTa1KJ7trfC+mjUhEVWHWwq2sP1h/XTohhHtJsiSE8HwVbTC4u5bD/0SydEHfKLfHUxSFuZefw0XnRFNd4+C2jzaxJ7vE7XGFECdIsiSE8HxtsYhurXxCAOjmU0b/uBC3xwMwGhReuW4IwxLDKK2q4ab3N8g6ckK0IUmWhBCerw274Q5V+AFwTkg1BoObx0edxNds5N83DeOsqECOl1i58f0NMsu3EG3E45KlN954g+7du+Pr68vQoUNZtWpVk45bvXo1JpOJwYMHu7eCQoi2V9EGS53U2llsAaCnX9u37IT6+/DhrcOJDfHlYG45t364kYpqmeVbCHfzqGRp4cKFzJo1i0cffZTU1FRGjx7N5MmTSU9Pb/S44uJibrzxRi688MI2qqkQok25xiy5N1mqqK5hR5EJgGhTuVtjnU5cqB8f3TqcED8zqelF3P1pKja7zPIthDt5VLL00ksvMX36dG677Tb69evHvHnziI+P580332z0uDvvvJOpU6eSnJzcRjUVQrSp8rbphtuaXkSuQ5vHybe6wK2xGnNWdBDv3zwMi8nAL3tyeOzbXcgk30K4j6m9K9BU1dXVbN68mYcffrjO9kmTJrFmzZrTHvfBBx9w4MABPvnkE5566qkzxrFarVitVtfPJSXaVSc2mw2bzdbC2jfOWa67ym+LGN5wDhKj45Tf3Bim8lwUoMYnBLUZdWrueaw/mEe+qiVLalkONU04zl2v1cC4IF7540BmfraVr1IzKYkzMKmT/L4lRud6f7c2hh4U1UMWHcrMzKRr166sXr2akSNHurY//fTTfPjhh6Sl1V8OYN++fZx//vmsWrWK3r17M3fuXL755hu2bt162jhz587liSeeqLf9008/xd/fX5dzEULo6+Idd2GpKeWXvk9T6tfNbXHe3GWgoLiYDb534cDA94PfB6V9G+jXHlf4/KARgCsS7VwQ5xH/0oVwu4qKCqZOnUpxcTHBwa2b2d9jWpacTl2DSVXVBtdlstvtTJ06lSeeeILevXs3ufw5c+Ywe/Zs188lJSXEx8czfvx4IiLcMx7CZrORkpLCxIkTMZvNHhnDG85BYnSc8psVw2HHlFoGwOiLroDAaP1jAHaHyqNblmElCAADDqaMH3nGuZ3c/VpNAaJ/2ccryw7x7REjQwb244bh8brG6FC/b4nRud7frZCfr98Erh6TLEVGRmI0GsnOzq6zPScnh+jo+v8cS0tL2bRpE6mpqdx9990AOBwOVFXFZDKxdOlSLrjggnrHWSwWLBZLve1ms9ltv1BviuEN5yAxOk75TYpRXgJorSnm4GgwNr8+TTmPA9kllFlrCPCxoPqGoFQVY64ugpCmJWfufK3uGt+LnWkH+CnTwNzvdxPo68MfhurfwtYhft8So81iePo56Fmuxwzw9vHxYejQoaSkpNTZnpKSUqdbzik4OJgdO3awdetW123GjBn06dOHrVu3ct5557VV1YUQ7uScNsA3tEWJUlNtP1YMwIBuISgBXbSNzskw25miKFya4ODGEQkA/PW/2/h+W2Y710oI7+ExLUsAs2fPZtq0aQwbNozk5GTeeecd0tPTmTFjBqB1oWVkZPDRRx9hMBjo379/neOjoqLw9fWtt10I4cHK22aOpR21ydLAbqGQ3QXy90N5rltjNoeiwGOT+1BtV/l841HuX7gVX7ORiWc3vVtSCNEwj0qWrr32WvLz83nyySfJysqif//+LFq0iMTERACysrLOOOeSEMLLOFuW3DxtwPYMLVnq3zUESmtjdaBkCbQWpn9eOYAqm51vtmZy14ItvD1tKOPbYA07IbyZx3TDOc2cOZPDhw9jtVrZvHkzY8aMcT03f/58li9fftpj586d2+iVcEIID1SWo907u8bcwGZ3sDtLm0ZkYNeQE7E6SDfcyYwGhf+7ZhCT+8dQbXdwx8ebWLIz+8wHCiFOy+OSJSGEqMOZLDXjKrjm2nu8lOoaB0G+JhIj/E9KljpWy5KTyWjg1euHcMmAWGx2lZkLtsgYJiFaQZIlIYRnK3cmS+7ravqttgtuQNcQbaoS/47ZDXcys9HAK9cN5qohXbE7VO77PJWvthxr72oJ4ZEkWRJCeLay2oTFjcnS7qxSAM6OrZ3Yzjk+qkK/eVzcwWQ08MI1g7ju3HgcKjzwxTY+3yDjOoVoLkmWhBCerey4dh/gzmRJG6/U15UsdexuuJMZDQpPXzmAG5MTUVV4+KsdvL3iAB6yeIMQHYIkS0IIz1bu3jFLqqqSdlxrWeobo83e7UnJEoDBoPDE5edwx5geADzz4x6e/GEXDockTEI0hSRLQgjPpaonDfB2z9VwOaVWiipsGA0KvaICtY3OZKmyEOzuWwhUT4qi8MiUfjw6pR8AH6w+zD2fpVJls7dzzYTo+CRZEkJ4Lmsp1FRpj93UDefsgkuK8MfXrC1Yi1/YiQV0O/i4pVPdPqYHr1w3GLNR4X87srjx/Q0UV3hGwidEe5FkSQjhuZzdYD5B4OPvlhBp2bVdcLEnrVpuMJyYMdxDuuJOdsXgrnx4y3CCLCY2HCrgmrfXcLSgor2rJUSHJcmSEMJzOQd3u6kLDmCPM1mKDqr7RAeemLIpRvaKZOGdyUQFWdh7vIwr/rWadQc9q5VMiLYiyZIQwnO1wYSU+3K0ZOmsesmSc64lz0yWAM6OC+abu0ZxTlwwBeXV/Onf6/lk3ZH2rpYQHY4kS0IIz+XmpU4cDpUDOeUAJwZ3O3nYFXGnExfqx39njOTSgbHUOFQe++Y3Hv16B9U1jvaumhAdhiRLQgjP5eZpA7JKqqi02TEZFG2Zk5N5SbIE4Odj5LXrh/DgRX1QFFiwPp0/vbeenNKq9q6aEB2CJEtCCM/lGrPknivh9ueUAZAUGYDZeMq/S1c3XI5bYrc1RVG4a3wv3p02jMDagd9TXvmV1fs9t5tRCL1IsiSE8FzOpU7c1A13oDZZ6tUlsP6Tztas0uNuid1eJpwdzTd3jaJPdBB5ZVb+9N565v28H5m/UnRmkiwJITyXm7vh9ufWJkunjlcCCIrV7suy3RK7PfWKCuSbu0Zx3bnxqCr8a/lB/rXLyPES6ZYTnZMkS0IIz+W6Gs693XANJkuuliXvS5ZAG8f07NUDeeW6wQT4GNlfonD5G2tZutM7z1eIxkiyJITwTHWWOnFPsnSwtmWpZ0PdcM6WpfI8j1nypCWuGNyVr/88gq7+KgXlNu74eDOz/7OV4krvPWchTiXJkhDCM1UVg92qPXbDUielVTbyyqoB6N4loP4O/hFgMAEnJW1eqntkALMH2LljdBIGBb7aksHF81by6z4Z/C06B0mWhBCeyXnJviUEzL66F38kX1v+IyLAh0CLqf4OBsOJJM0Lxy2dymSAByf15osZySRF+JNVXMWf3lvP3775jdIqaWUS3k2SJSGEZ3J1wbnnSrj02rXS6s2vdLKgGO3eS8ctNWRoYjiL7hvNjcmJAHy87ggTX1rJ4t+yUFW5ZE54J0mWhBCeyTnHkhu64AAO52szdydGNNAF59QJkyUAfx8TT17RnwW3nUdihD/ZJVXM+GQLt3+0iYyiyvaunhC6k2RJCOGZnN1wbhrcnZ4vLUtnMqpXJEtmjeHu8b0wGxV+2p3DxJdW8O7Kg9jsslyK8B6SLAkhPJObZ+8+0bLUSLIUWJssdYIxS6fjazbyl4v6sOje0ZybFEZFtZ1/LtrNRfNW8sue49I1J7yCJEtCCM/k5mkDTrQsSTdcU5wVHcTCO5J57uoBRAT4cDC3nFvnb+LG9zew73hpe1dPiFaRZEkI4ZmcyZIbxixV2exk1c5WnRgu3XBNZTAoXHtuAsseHMedY3vgYzSwal8eF7+yir998xu5pdb2rqIQLdLsZOnmm29m5cqV7qiLEEI0Xbn7WpaOFVagqhBkMREe4HP6HSVZalCwr5k5k/uRMnsMF58Tg92h8vG6I4x5fhkvLNlDcYVMNSA8S7OTpdLSUiZNmsRZZ53F008/TUZGhjvqJYQQjSvJ0u6dM2nr6HCe1gWXEOGPoiin39E5Zqk8F+w1utfD0yVGBPDWtKF8dvsIBseHUmmz869lBxj9/C/8a9l+KqrlNROeodnJ0pdffklGRgZ33303X3zxBUlJSUyePJn//ve/2GzybUEI0QbsNSdaltyQLB2pnWMpqbHxSgABkaAYAfVEfUQ9yT0j+HrmSN69cRh9ooMoqarhhSVpjHl+GW8s3y+TWooOr0VjliIiIrjvvvtITU1lw4YN9OrVi2nTphEXF8f999/Pvn379K6nEEKcUJ4DqkNbbiRA/0kpj9ReCZfQ2JVwAAbjiW5A6YprlKIoTDw7mkX3jWbetYNJCPcnr6ya5xenMfLZX3j5p/2USc4kOqhWDfDOyspi6dKlLF26FKPRyJQpU9i5cydnn302L7/8sl51FEKIupxdcIEx2rIjOnMudZJ0pmQJZNxSMxkNCr8f0pWfHxjLi9cMomeXAEqranhjxUGe2GLkn4v2kFUsE1uKjqXZ/2VsNhtffvkll156KYmJiXzxxRfcf//9ZGVl8eGHH7J06VI+/vhjnnzySXfUVwghoDRTu3cmKjpztSyFn6EbDmSupRYyGw1cPbQbKfeP5a0//Y7+ccFUOxTmr01nzPPLuH/hVrYdLWrvagoBQAOrQzYuNjYWh8PB9ddfz4YNGxg8eHC9fS666CJCQ0N1qJ4QQjTA2bIUrP94pRq7g2OFWstGUqS0LLmbwaBwcf9YLugdwcufLWZTZSQbDxfydWoGX6dm8LuEUG4e1Z3J/WMwG2W2G9E+mp0svfzyy1xzzTX4+p5+le+wsDAOHTrUqooJIcRplTqvhIvTvejMoipqHCo+JgPRQaf/P+ciyZIuFEWhb6jK7Knnsiu7nPlrDvPD9ky2pBexJT2V6GAL00Ykcu25CXQJsrR3dUUn0+w0fdq0aY0mSkII4XauZEn/brgjBbXLnIT7YzA0Mm2AkyRLuhsUH8rL1w5m9cMXMGvCWUQGWjheYuX/lu4l+ZmfmfHxZpal5WB3yFIqom14XJvmG2+8Qffu3fH19WXo0KGsWrXqtPt+9dVXTJw4kS5duhAcHExycjJLlixpw9oKIdyipHbMUrD+LUtHmrKA7slkzJLbRAX5MmtCb1Y/PJ6Xrx3EkIRQahwqi3dmc8sHGzn/uV94KWUvxwor2ruqwst5VLK0cOFCZs2axaOPPkpqaiqjR49m8uTJpKenN7j/ypUrmThxIosWLWLz5s2MHz+eyy67jNTU1DauuRBCV6Xum5Ayo0gbr9Q11K9pB0jLkttZTEauHNKNr2eOYsmsMdw6qjuh/mayiqt49ed9jH5+GTf8ex1fbDoqczYJt2j2mKX29NJLLzF9+nRuu+02AObNm8eSJUt48803eeaZZ+rtP2/evDo/P/3003z77bd8//33DBkypC2qLIRwB2di4oaWpazaZCm2ucmScxZvo0f9W/U4fWKC+PtlZ/PXi/uwdNdxFm5MZ/X+fNftsW9+Y0K/aK4YHMe4PlH4mDyqTUB0UB7zrq6urmbz5s08/PDDdbZPmjSJNWvWNKkMh8NBaWkp4eHhp93HarVitZ5Y7LGkpATQpkxw1wzlznLdOQO6u2N4wzlIjI5TfqMxrKWYrbXvS98IaEUdGorhbFmKDjQ37fx8QjEpRhTVjq0os94VevL7dk8MIzD57C5MPrsLRwsr+H5bNt9tz+JAbjn/25HF/3ZkEeJn4qKzo7nonGhGdA9HUe3NitESHfG16mjlt3UMPSiqqnrECLnMzEy6du3K6tWrGTlypGv7008/zYcffkhaWtoZy3jhhRd49tln2b17N1FRDS++OXfuXJ544ol62z/99FP8/Zs4hkEI4TZBlRlcsGcO1UZ/fhz4lu7lP7HFSIFV4b5zaugR3LRjJv42C39bASt7/53CgF6610k0japCRgVszDWwJU+hxHZigL6fUaV/mMqgCJU+ISo+xnasqGgTFRUVTJ06leLiYoKDm/hmPg2PaVlyOnVRS1VVG1/ostZnn33G3Llz+fbbb0+bKAHMmTOH2bNnu34uKSkhPj6e8ePHExER0fKKN8Jms5GSksLEiRMxm80eGcMbzkFidJzyG4uhHPgF9oA5IokpU6boGsPhUPnLhp8AlasnX0BsSNOu/DXmvg7HNjCyfyJqv7p1kt9328e4A7A7VNYfKmDxzuOk7M4hr6yajXkKG/PAz2xkXO9ILjonmtG9Igj20++cPO21ao/y2ypGfn6+bmV5TLIUGRmJ0WgkO7vuIMqcnByio6MbPXbhwoVMnz6dL774ggkTJjS6r8ViwWKpP4eH2Wx22y/Um2J4wzlIjI5TfoMxyrXB3UpIvG6xnTFySqqw2VUMCsSFBWBq6iSIofFwbAOmsiw4TZ3k9922MczA2L4xjO0bw1MOlc1HClm0PYNvNx+hsNrOjzuP8+PO4xgNCsMSwxjfN4rxfaLoHR3YpC/gbXUe7RnD089Bz3I9Jlny8fFh6NChpKSkcOWVV7q2p6SkcMUVV5z2uM8++4xbb72Vzz77jEsuuaQtqiqEcKfiY9p9SDfdi3aNVwr2bXqidHJdijN0r5NoPaNBYXj3cIZ0C2KwepCEwaNI2ZPH0p3ZHMgtZ/2hAtYfKuDZH/fQNdSPcX26ML5PFCN7ReDv4zEfk8KNPOqvYPbs2UybNo1hw4aRnJzMO++8Q3p6OjNmzAC0LrSMjAw++ugjQEuUbrzxRl555RVGjBjhapXy8/MjJCSk3c5DCNEKzoTEDclSVnEVAHFNvRLOKSReuy8+qnONhN4UBQZ0DeF3SZE8dHFf0vMrWL43h1/25LD2QD4ZRZUsWJ/OgvXpmI0KQ+LDGNkrglG9IhkcHypLrnRSHpUsXXvtteTn5/Pkk0+SlZVF//79WbRoEYmJiQBkZWXVmXPp7bffpqamhrvuuou77rrLtf2mm25i/vz5bV19IYQenAmJG5KlTOe0AU0cq+QS3FW7d7Z6CY+REOHPjclJ3JicRGW1nXUH8/llTw7L0nI4VljJhsMFbDhcwLyf9uHvY2R493BG9YxkZK8I+sUEN22Wd+HxPCpZApg5cyYzZ85s8LlTE6Dly5e7v0JCiLblxm64zCKtZanJE1I6OetSIt1wnszPx6iNXeobhaqqpBdUaPM3Hchj7YF8CsqrWZ6Wy/K0XADC/M2cmxTOuUnhDEsK45y4ECR18k4elywJIToxh+PEUidu6YZrYcuSsy7luWCrArOsn+npFEUhMSKAxIgApp6XgMOhsie7lDUH8li9P48NhwoorLCxdNdxlu46DoCv2cCgbiGEVBsI2pfHsB6RBPu6d4C0aBuSLAkhPEdFHtitgOKWpU4ymzt7t5NfGJj9wVahtS5F9NS9bqJ9GQwKZ8cFc3ZcMLeN7oHN7mD7sWI2HS5g4+FCNh0poKjCxvpDhYCBpR9tQVGgT3QQQxJCGdgtlEHdQukdHdi8iwdEhyDJkhDCczjHKwXFglH/b+yZxS3shlMUrXUpb6/WTSjJktczGw0MTQxjaGIYd44Fh0PlYF4Z6w7k8e2a38iuCeBoYSV7skvZk13KZxu0v11fs4H+cSEMig9lYLcQBseHkhDur8t0BcJ9JFkSQniOIvcN7rbW2Mkt1ZY6anY3HJyULMkVcZ2RwaDQKyqIxDBfgnK2M2XKaAoq7Ww5Usi2Y8VsP1bE9mPFlFlr2HSkkE1HCl3HhvqbGdA1RGu5ig3mnLhgkiKaMc+XcDtJloQQnqPoiHYflqh70ceLtUTJYjIQHuDT/AJCa+tUeETHWglPFh3sy+QBsUweoHUZa61P5Ww7WsT2Y0VsO1bMrswSiipsrNqXx6p9ea5jLSYDfWOCODsumH6xWhLVNzaYQIt8bLcHedWFEJ6j8LB2H6p/spRZO7g7LtSvZV0izgTOWUchTqG1PgXSKyqQq4dqraPVNQ7SskvZnlHE7qwSdmWWsCe7lIpqO9uOFbPtWHGdMhLC/enVJQBDqYHqrZn0iwulZ5dA/GSxO7eSZEkI4TmcrTZhSboX3eI5lpycdSqSliXRdD4mAwO6hTCg24mJkh0OlSMFFezKLGFXltb6tDurlOySKtILKkgvqAAM/PTlb4A2ZC4+zJ/e0YH0igqid3QgvaODJInSkSRLQgjP4cZuuBbP3u0k3XBCJwaDQvfIALpHBnDJwBNXfeaXWUnLLmVPVjE/b9pFtV8E+3PKKKywuZKon3bn1CkrLsSX7l0CSIrQyutR+zg+3F9mI28GSZaEEJ7B4YCi2hn63dENV9uyFNfalqWybLBVgrmFSZcQpxERaGFkLwvnJoYQUfAbU6aci8lkIr+8mr3HS9mfU8be46XsO17GvpwyCsqrySyuIrO4itX78+uUZTQoJIT7kxThT/fIQLpHaveJEf5E+ktr1KkkWRJCeIbSLLBXg2I8sbyIjlo8x5KTXxj4BEF1qZbUdemjY+2EaJiiKEQGWogMtDCyZ2Sd5/LLrBzOL+dQXgWH8so4lHficZXNUftzOctqZyR3MhoUQs1GPj++iYTwAOLD/YgP99duYf5EBvp0uqkOJFkSQngGZxdcaDwY9f/X1epuOEXRWpeO79C64iRZEu0sItBCRKCFoYnhdbY7HCrHS6tcydKh3HIO55dzMK+cYwWVVNsd5FsV1h4sYO3Bgnrl+pmNWgIVpiVQ3cL86BrqR2yoH3EhvkQGWrxuzTxJloQQnsE5FsgNXXAAGa3thgNtLNXxHTLIW3RoBoNCbIgfsSF+9VqjHA6VYwVl/PfHX+jWZzCZJVaOFlRytLCCYwUVZJVUUWmzs/d4GXuPlzVYvtmoEB3sS1yIH3Ghvq4kKjbEj9hQbXuAh60CI8mSEMIzuHFwd5m1htKqGqAV3XBw0iDvw62vlBDtQEukfOkZDFOGxGE2181qrDV2MouqOFpQwdHCClcilVVUSVZxFcdLqrDZVY4VVnKssPK0cfzMBoKMRhYe30RMiB9Rwb5EBVmIDvYlKthCdJB272vuGOOnJFkSQniG/APafXgP3Yt2dsEF+5paN+lfeHftvuCgDrUSouOxmIyuK/UaUmN3kFNqJbOoksziKlcSlVl7n1VcSV5ZNZU2B5U2hZwGuvlOFuxrIirYl+hgC1G1CVRU0Imfo4O18VoBbp6sU5IlIYRnKHAmS/qvu9bq8UpOzjXh8ve3skZCeCaT0UBcqF+j76Uqm51j+WV8s3QFif0GkV9Rw/GSKnJKrOSUVnG89r7K5qCkqoaSqjL25zTc5efkZzYSGeTjGuweGWghQK3S77x0K0kIIdxFVU8kIBG9dC9ev2Sptm4Fh8BhB0PH6EIQoiPxNRtJjPDnrBCVKYPrd/UBqKpKSVUNuSclT8dLrOSUWDleWkVu7f3xEi2pqrTZtS7BghNdfw5rhW51lmRJCNHxVRRAVe2yD86uLh05k6UWz97tFNwNjBawW7XpA9xQVyE6A0VRCPEzE+JnpldU0Gn3U1WV8mo7eaVW8sq0W25ZNXmlVo5m5/KyTvWRZEkI0fE5W5VC4t0y2WOmXi1LBoM2pip3t9ZtKMmSEG6lKAqBFm2sYdIp46jy8yN0S5ZkrnMhRMfnHK8Uof94JYBsV7LUypYlOGnc0oHWlyWE6BAkWRJCdHzOliU3DO4GyCxydsPp0Golg7yF8DqSLAkhOj5nK40bBnerKmSXaMlS19Z2w8GJOkrLkhBeQ5IlIUTHl7dPu3dDslReA9YaB4oC0cF6dMPV1tFZZyGEx5NkSQjRsTlqIL828XDDemuF1tqiAy34mHT4l9ilr3ZfnA7WxueGEUJ4BkmWhBAdW8EhsFeDOUC7Gk5nhdXagp+tWubkZP7hEBClPc5L06dMIUS7kmRJCNGhKXl7tAdd+miX5uusqLZlqVUL6J4qqrZ1KWePfmUKIdqNJEtCiA5NyXUmS33dUn6hVWtZavUcSydz1jV3t35lCiHajSRLQogOzZUsRbkpWarW7ls9e/fJukjLkhDeRJIlIUSHpjjH/XTp55bynS1Lukwb4BRVW9dcSZaE8AaSLAkhOixFrTkxX5GbWpaKnC1L7uiGKz4K1lL9yhVCtAtJloQQHVZQZSaKwwaWELdcCVdjd1BcmyzpOsDbPxyCuwKg5OzUr1whRLuQZEkI0WGFVh7WHsQOBEXRvfycUisqCmajQmSgRd/CYwYCoGRv17dcIUSbk2RJCNFhhVQe0R7UJh56y6pdQDc62BeDQedkLNaZLO3Qt1whRJuTZEkI0WGFVNQmS7HuSZYyi50L6OrYBecUI8mSEN5CkiUhRMekOgipTNceu7llSdfxSk6xg7T7vD0YHDb9yxdCtBmPS5beeOMNunfvjq+vL0OHDmXVqlWN7r9ixQqGDh2Kr68vPXr04K233mqjmgohWqXgICZHFarJFyJ7uyVEtjtblkK6gV8YiqOGoKpj+pcvhGgzHpUsLVy4kFmzZvHoo4+SmprK6NGjmTx5Munp6Q3uf+jQIaZMmcLo0aNJTU3lkUce4d577+XLL79s45oLIZpLyUoFQI06G4wmt8RwazecokDsYADCKg7pX74Qos14VLL00ksvMX36dG677Tb69evHvHnziI+P580332xw/7feeouEhATmzZtHv379uO2227j11lv5v//7vzauuRCiuZRjmwBQu57rthhZ7kyWALppdQ8r3+ee8oUQbcI9X9fcoLq6ms2bN/Pwww/X2T5p0iTWrFnT4DFr165l0qRJdbZddNFFvPfee9hsNsxmc71jrFYrVqvV9XNJSQkANpsNm8094w6c5bqr/LaI4Q3nIDE6TvkAxmMbAKiJGYLDTXGcyVKXAJNbzkWJ/R0mILx8v/y+JYbHxPCGc9C7bEVVVVW30twoMzOTrl27snr1akaOHOna/vTTT/Phhx+SlpZW75jevXtz880388gjj7i2rVmzhlGjRpGZmUlsbGy9Y+bOncsTTzxRb/vCTz7ANyAIFaNb5nsRQpxgtFuZsv1ODDhYes5LVPpE6h6j2g4PbtC+Lz5zbg3+bvjqaK4pZ8qOPwPw44B/UW0K0j+IEOIEVUXBjkG1U1lexh+nTae4uJjg4OBWFesxLUtOyimJiqqq9badaf+GtjvNmTOH2bNnu34uKSkhPj6ei3+7l2CLdoxqMIOx9mYwg8EERh9tXIVB26a6nq99zmA6sf9Jz6lGHxwYOHw0g6QeZ2EwW2r3cR7ng2qygMkHTL7aNte9BdVoAVPt7dTHJ52jzWYjJSWFiRMnNtii1lruLl9idKwY7i5fObIaw3YHleYwzp9yHWYfH91jHMorhw2rsRhULr94Aj5uiAHgyHgRQ8F+xp8VhLHfFLfE8PTft8ToWDEaLN9RA7ZKqKkCuw3sVu2+xopit4GjGmqqwV7/ppz8c0012G04bJWkH9pPQtdYjGrNKcfYtHtHjXaz21AcNeCwac/VbnM977CBXbtXHDWu8yix6tcW5DHJUmRkJEajkezs7Drbc3JyiI6ObvCYmJiYBvc3mUxEREQ0eIzFYsFiaXwmX8Vh0345jbTwNaftyQicBZDzYzOOakrBJxIrk8nChdYa/I6Fo5gs2naTD5j9wewH5oDaez9tm4//Sc+d9NjnlP1cN+0NZTab3fYPwklidJwYbis/azMAhQG96OLj45YYOWXaP9UwC/i4KQaAo9twKNiPOXsLxoFXuCWGk8f+viVGy2KYTJjVaqguh+oyqK446XE52CpOJDi2SqixQk0l2KpOuq866fkqsFVhqqlkYkkhfmkKivM51a5r3Y1AT4BcXYt1G49Jlnx8fBg6dCgpKSlceeWVru0pKSlccUXD/4CSk5P5/vvv62xbunQpw4YNa/Yfse2e7RAaXJvRVtfNbp0ZsOvxiSxX2/ekjNhuq/fYbrNycH8aPRLjMar2us+7svGq2j/02pvd2sDPVXUr7TwWLXkLBMg93qzzbiqTwcxkxYzpQBhYgsESCJYg7eYTdOKxJaj2ueCTnnfuGwy+wVqrm+jcDmlTguQH9KaLm0JkFlcCEOrj3pEIjoRkDNs/RTnyq1vjCA+hqtriytYSqCqBquKTHhedeOxMeFz3JxIhU3U5l1QWY0ytBvT/+1UAfzh9g4DBXNuDYdZ6MYw+2pdvo89ptvm4ekO0532wKyYOHD5Kz979MPr4njim9vkTPTPmE70tzp4Z188nb6u/r62oBJ7tqstr4jHJEsDs2bOZNm0aw4YNIzk5mXfeeYf09HRmzJgBaF1oGRkZfPTRRwDMmDGD119/ndmzZ3P77bezdu1a3nvvPT777LPmB7cEaYtjuoHDZmNX5SKSJk3B2JpvIqpa2yxaVS/BqqkqY+2vK0g+93eYsJ/0XKX2raG6XLu3VZz4NmKr0N6gru2VYHPuV3tM7RtVcdjwwQYlFUBG614QnyDwC9VuvqHgFwZ+YRgswfQ6fhxlSy4ERtZur30+oIvW2iU8X40V0tcBkBt0Dn3dFCarSPtyEabzknCnUpNGA6Bkpmofgr6tGzshOgi7DSoLoSIfKgpq7/MxlOVxzrFNGL9fdEoiVAzWYi1RUh2tCq3QwIe3OUBr+fcJ0L6A+pzU8m+yaP8fTb4n7k2+YPZtcFuNYmb1+i2MHHshZt+AuscaLWBo/YX0DpuN3YsW0X1MKz/3GmOynnmfphalW0lt4NprryU/P58nn3ySrKws+vfvz6JFi0hMTAQgKyurzpxL3bt3Z9GiRdx///3861//Ii4ujldffZWrr766vU7BvRSldmxT/bEXqs1GQWAWavcxri6zVlNV7YPNVoGtsoSVP/3I2BFDMdkra785lWrfiqwltT+XnbS99MRj53ZbuVZude3zxUfrhDMC5wBk/qfh+vgEaklTQBcIjIKASAiIqt0WWbut9nm/MBmo31Ed2wg1lagBXSj11edbYUMyi7SWpTCLm69xCelGmSWaQOtxOLIG+lzs3nii5arLoew4lB7X7uvcclwJERWFWuLTACPQC87cvWQwa4mzJRh8Q056HKo99gnUWuHN/rXJz4lEyGbwYfmajYybeAnmgFAw+emSwDipNhtFvxVBVD/9Pi88nEclSwAzZ85k5syZDT43f/78etvGjh3Lli1b3FyrTkpRtG8mZl8wB1HmG4caN6Tlby57jZZYVRZCZZF2X1Xk+tlenkfG/t/oFhGIwVp80n4FWktadZl2K2zCBIBGCwTHQlAcBDtvXVECogkrPwQlWRDWFQzGlp2LaLmDKwBQE893a0J7ohvObSFc8gLP1pKlQyskWWoPqqolOfmHiC3ahGHDUSjLgpKMuolRdVkzC1a0L17+4eAfAX7hOHzDOJBdSI9zzsUYEH4iEfINPTHUwDdEa6lp6d+3zUaFJV37AijJTJvwuGRJeDGjqfafTsPdnQ6bjVTbImKnTMFw8j8IVdWSrLJcKHfecqA8T/s2WJ6rPS6vfVxVrI3xKjys3U5iAsYA7H0CFCMEd4WwxNpbEoQmafdhiVoLlbRO6e/gMgAcSWMgy31hTrQsuS+GU27Q2STlL4MDv7g/WGekqtqXp/wDUHBQ+8JUfBSKj5241VRhBoYDNPZ9yuwPgdEQFKMlI4HRtbco8I/UkiJncuQbUu8Lld1mY9eiRSSNdGP3kmhzkiwJz6cotd/eQiCy15n3r7FCaTaUZEJppnZfkgklGTiKM6jKOYhfTTGKaofidO12uIE1CM3+WuIU0Utbu6xLH4g8CyLO0prPRfOVHgfnzN09J0Dtkid6U1XVNSGluwd4A+QG9UdVjCi5e7QP8/Aebo/plapKIG8v5O8/kRgVHISCA9qXoDNQA6MpdAQSmtgfQ2i8tn6fKzGqTYgsMheWqE+SJdH5mCwnWotOYbfZSFm0iCkXX4TZWgBF6VB4RGuBKqq9LzyiNd/bKiBnl3Y7VXA3LXHq0kdLpGIGQvTZ2pgDcXr7lgAqxA3RuklxT7JUUllDRbV2KXRbdMPZTAGoCcnaFXFpiyG54aEEopa1DPLSIGcP5O6GnN3a45IzLEgc3FVLRMOSIDRRS4act+A4alQDqxYtYsqprdNCnIEkS0I0xGA8MZYpYUT952usWtN+wUHI26f9Y8/bB7lpUJGn/VMvOebqUgJAMUBEL4xR59CryIxywBe6DdG+zQpNWu1cY33cM3mjU0ZtF1x4gBkfY80Z9taH2vtiOPIrpC2SZOlkVcWQtQ3Dsc0MPbQY05tztffV6QTGaF9EwntARE/tPrynliD5+Dcey41LawjvJsmSEC1hsmj/qCN6wlkT6z5XUaB1FThvx3fB8d+0AaR5ezHk7dWu6vu89qq+kHjoNgy6DYf44VorVANXNHo9aykcqE0u+0x2a6is2sHd2gK6lW6N5eQ462KMKY9pV8SV52lXaHY2NVbI2qZNDZGZCllbXYmREeh28r4BURDVF7r0q3vvF9YOFRednSRLQujNP1xrjTq1Rar0OBzfgT1jK1mpS+lqzEfJP1A7EPUo7Pxa289ogdhBWuIUfx4kne+2Ob46lN3fa/N+RfSC6P5Q474Wn8za8Uqxwb5ui1FPWBLEDtYShN++hPPubLvY7aWiAI6u15Kjo+shY4t2ccWpQhNwxAxiT7Evvcf9EVO333XOZFJ0WJIsCdFWgqIhKBpH4lg2F51F9JQpmB1WyNwCRzdo8wsd3aBNhXBsg3Zb+zqgQEx/6D4Wuo+BhGTvnNhw2+fa/cDr3H6VofNKuNjQNp7IdNB1WrK07XPvTJaqyyF9LRxcrt2yd9Tfxz8C4kdoralxg7UE0j8cu83GvkWLOKvHeLkcXnQ4kiwJ0Z4sgVoC1H2M9rOqat0SzsTpyBptgGv2Du229nVtSoOuv4NeE6H3RVorlKdPYVCcAYdWao8HXuP2cFnOZCnEAiVuD3dC/z/Akke1BDk3TbsAwJOpqtatti9FS46OrteWazpZZG+thTRhhJYkRfT0/L9X0elIsiRER6IoJ8ZCDbpO21Z6XJu64NBK7d6ZTB3bCMuf1ga8njURel8MPcZ55rQFm94DVEg8X+uucrPM2qVO4kL82jZZCuwCZ02CvT/Cxn/DlBfaMLhObJXa32Laj7B3iTb9xsmCu0HPcdB9nPYlIKjhhc6F8CSSLAnR0QVFw4A/aDeAoqPaVXZ7l2gDosuyIfVj7Wb0gR7jUfpehqnGQ2Yft1XCpg+0x23UNZV50gDv7KNn2Flv592hJUtbP4ULHtPmB+voqkqIz1+F8YvPtFnIbRUnnjP7Q4/x0OsC7T68h7QcCa8jyZIQniY0Hn53o3arscKR1VritHexNg/UviWY9i1hsmKEii+h/1XQd0rHvYpo2+faOK2QBOh7idvD2R0qx0tqB3iH+JLt9oin6DEeuvSF3D2w+UMYdW9b16BprKXanFA7v8K0/yd+Z68+8VxwV60ls89kSBqtLXkkhBeTZEkIT2ayQM8LtNvFz2ofwLu+Rd35NYbcPXDgJ+32vRl6TdC69vpM1o7rCGxVsPL/tMcj/twma/HllVmx2VWMBoUuge0wRYOiQPLd8N3dsHoeDLul48waXWPVku4d/4V9S6FGSyoVoNQ3Dv9zb8B49mXa9BbSeiQ6EUmWhPAWiqKtEh7Vj5pRD7Dyq3cZ16UI457vtVnG9/6o3XxDtdamQVO1K5La80Nv0/va5J3BXWHYrW0S0nklXHSQBZNRv5Xam2XQdfDry9oyHWvfgHEPtU894MQg7a0LYMcX2hprTuE9of9V2Ppczi+bDjFljKx3JjonSZaE8FJlvl1xjL4d4wWPaFdebfscti/UlmrZ9L52C+8Jg66HQddCaELbVrAkE5Y/oz0e+9c268pxrgkX19bTBpzMaIbxj8CX07WkaeA1bb9eXFku7PgPpC6AnJ0ntgfFafXpf/WJFiSbjcZXnxXCu0my1EST5v1KTJdwugRZ6BJo0e5rb1FBvq7HAT5GFGmeFh1Nlz4w4XFtQPHhVbD1M9j9ndaysewp7dZ9DAy+Afpd5v417FQV/vcXsJZA16EwZJp7452k3eZYOlX/q2HLh9qVZd/fB9O+BYObW7rsNq17LXWBtg6fo3biT6NFGy82+AboOb5NukOF8CSSLDVRblk1+bYzX2PsZzaeSKQCT06oLESH+BIb4ktMsC8hfmZJqkTbMxi16QV6jAPri1rCtPXTE1MTHFoJ/3sAzv49DJ4KiSPd00235jVI+x8YTHD5a2364Xxi2oB2HpSsKHDpPHhzlPa6L38GLnjUPbGyf9N+z9sXamsXOsX9Tvs9D/hDx70AQIgOQJKlJvp0+rnYzP7kllpP3Mqs5JbU3pdaKbPWUGmzk15QQXpBRaPl+ZoNxIb4ERPsS1SQD+W5BgrWpxMXFqAlVCG+RAZYMBgkoRJuYgnUPigHT4WidNi2UBu3UngItn6i3cKStLFNg66DsER94v72Jfz0uPb44mch+hx9ym0iZ8tSu3bDOUX0hMvmwdd3wsrnT1zpqIfyfG0M0tYFkL39xPaALjDwWq0VKfpsfWIJ4eUkWWqifrFBRERENLpPRXUNeaXV5JZV1Umqcmpv2cVVZJdUUVBeTZXNwaG8cg7lldcebeCnzD11yjMZFKKDtcQpJsSXrqF+dAvTbl1D/ekW5keARX6FQgehCTD2QRjzF20dr60LYOc32lQEy5/WbkmjtQ/Ysy8HpQVXkakqbHgXFj8EqgOG3gzn3qbziZxZ3UV0O4BB12kLLa95Db67ByryYdSslrXo2Sph/xLY9pk2nYRzNm2DGfpcrP3+ek3QxkwJIZpMPml15O9jIiHCREKEf6P7Vdns5JRYySquJLukimMF5azfnoZveAzHS6vJLq4kt9RKjUMlo6iSjKLTr4oe5m+mW5h/3UQqzN/1OMhX/imKZlAUSEzWbpOfg90/aImTc/bww6vgfw9g7DGOhIpoKBkCEU0YGJ6bBkv/po2TAW2M0iUvt8uVeJkdYYD3qSb+A+w1sP5N+GmuNtnoRf+EmAFnPraiAGXPj5x78H1ML8+oO2Fk7GAtQRrwh86xGLMQbiLJUjvwNRtJiPB3JVU2m41upbuZMmUw5trLcmvsDnLLrGQVV5FdXEVWcRUZhZUcK6zgWKGWQBVX2iissFFYUcyOjOIGY4X4mUmK8Cc+zA9bgQFraiY9o4NICA8gMtBHxk2J0/MJ0K6SG3StNmv49s+1cS8FBzGk/Y8hAK+9D136aQuixgyE4DjtQ9lo0VpIcnfD/l/gyK9amQYTTHwSRsxsl0TJWmMnt1Rb9b5DJUuKAhc/ow3E//EhbZbst87X1lLrNUGbEsISCChQXQYFhyB/H6Svh9zdmIA4Z1nB3eCc32vdq23cxSmEt5JkqYMyGbUxTbEhp/+HXlJlq02gKsmoTaKcidSxwgoKK2wUV9rYdqyYbceKAQNLvvrNdXyAj5HEiACSIv21+wjtvkeXALoEWiSREieExsOYB2H0XyBrK/Y9iyne9AVhFQdRcndrSdG2zxopQIE+U2DCXOjSu61qXU92bauSxWQgzN9MTU1Nu9WlHkXRJqjsMQ5+fgJ2fQdH12m3M1C79GWvoTc9LrkXc3w7z50lhBeSZMmDBfuaCY410y82uMHny601pBdUcCS/goO5Jfy6NQ0CIjlSUElmcSXl1XZ2ZZWwK6v+VX7BviZ6RgXSq0tgnfv4ML/2m8hPtD9FgbghOLr0Z1Xp2UwZOxxzdqo2gDh7B5TnaZMa2q3ammfhPbTWkT6T9Rsg3goZhVqXdtcwv477ZSC8O1wzH4ozIG0RpK/VFk+uqdbGepl9tYH3Yd0hbggkJFNjCWXPokX0iB0siZIQbiDJkhcLsJjoFxtMv9hgbLYIupbsZsqUYZjNZqw1do4WVHIkv5zD+RWk194fzi/naEEFJVU1pKYXkZpeVKdMH6OB7pEB9IwKcCVQZ0UFkRDWQZbPEG0rIFJbd67vlPauSZMcqx3/17UjdcGdTkhXGH67djsTm8399RGiE5NkqZOymIz0igqkV1RgveeqbHYO55dzIKec/Tll7M8t40BOGQfzyqiyOUg7Xkra8dI6x5gMCl0sRn4q387ZcaH0jQ2iX0ww0cHSnSc6DmfLUrcwD0iWhBAdhiRLoh5fs5G+McH0janbveeovTrPmTztr73tPV5KSVUNWZUK32/P5vvtJ9ZxD/M3a2XVJk99Y4PoExOExSQzBIu2l+FJLUtCiA5DkiXRZAaDQny4P/Hh/ozvE+XarqoqR/PL+OSHZQR168Pe3Ar2ZJVwMK+cwgobaw/ms/Zgvmt/s1Ghb0wwA7qFMLBrCAO6hdA7OgizjIUSbnaiZanx6T2EEOJkkiyJVlMUhdgQX84JU5kytodr+oMqm539OWXsziphT3Ype7JL2JlZQlGFjR0Z2nQHn9aW4WMycHZsMAO7hTCgawgDu4VyVlSgzGAudOVqWZJuOCFEM0iyJNzG12ykf9cQ+ncNcW1TVZVjhZXsyChm+7FidmQUsf1YMaVVNWw9WsTWo0WufYN8TQxJCGNoQhhDE8M4J9bNi7sKr+ZwqK7Zu6UbTgjRHJIsiTalKCe68qYMiAW0D7H0ggq2ZxSz41hRbRKlJVAr9+aycm8uAAYFYv2MrLfv4tzuEZybFC7dKaLJckqt2OyqaxkhIYRoKkmWRLszGBSSIgNIigzg8kHaPMQ1dgd7skvZkl7I5iOFbDpcqC39UqHw6YZjfLrhGKBd1ZTcI4LknhGM6BHRsWZlFh1KRpG2DEhMiC9G6d4VQjSDJEuiQzIZDa4uvBuTkwA4ml/K+98ug8gebDlazG8ZxRwrrOSLzcf4YrOWPCVG+JPcQ0uckntGSAuCcDlWKF1wQoiWkWRJeIyYYF8GR6hMmdwHs9lMmbWGTYcLWHswn3UH8tmRUcyRfG3G8s83HgXgrKhAxvbuwtg+XTg3KRxfs0xZ0FnJ4G4hREtJsiQ8VqDFxLg+UYyrncagtMrGxsMFrDtYwNoD+ezMLGZfThn7csr496+H8DUbSO4RUZs8RdE9UgaMdybOlqVu0rIkhGgmSZaE1wjyNXNB32gu6BsNQHGFjV/357Fibw4r9uZyvMTKsrRclqXlwve7SIrwZ+LZ0Uw6J4bfJYTJOBYvd/K6cEII0RwekywVFhZy77338t133wFw+eWX89prrxEaGtrg/jabjccee4xFixZx8OBBQkJCmDBhAs8++yxxcXFtWHPRXkL8zVwyMJZLBsaiqippx0tZkZbLir25bDxcwOH8Ct5ddYh3Vx0iIsCHC/tFcUGfSKrt7V1z4Q4nZu+WKyiFEM3jMcnS1KlTOXbsGIsXLwbgjjvuYNq0aXz//fcN7l9RUcGWLVv429/+xqBBgygsLGTWrFlcfvnlbNq0qS2rLjoARVFcS7jcObYn5dYaVu3LZenO4/y8J4f88mr+s+kY/9l0DB+DkaWlW7l0UBwTz47G38dj3ibiNFRVlXXhhBAt5hGfArt372bx4sWsW7eO8847D4B3332X5ORk0tLS6NOnT71jQkJCSElJqbPttddeY/jw4aSnp5OQkNAmdRcdU4DFxMX9Y7m4fyw2u4ONhwpYuus4S3dmk1lcRcruHFJ25+BnNjLh7GguGxjL2D5dZE07D1VYYaPSpjUZxobKFZJCiObxiGRp7dq1hISEuBIlgBEjRhASEsKaNWsaTJYaUlxcjKIop+26A7BarVitVtfPJSUlgNatZ7PZWnYCZ+As113lt0UMTz+HcxNDODcxhAcvTGL+tz9REtyTH3flkF5QyffbMvl+WybBviYmnR3NJQNiGNE9DFML17Lz9NeqLcrXO8aR3FIAooIsGFQHNptD9xin4w0xvOEcJEbHKb+tY+hBUVVV1a00N3n66aeZP38+e/furbO9d+/e3HLLLcyZM+eMZVRVVXH++efTt29fPvnkk9PuN3fuXJ544ol62z/99FP8/WWsQ2eiqpBeDlvyDKTmKRTbTgwADzarnNtF5bwoB9HSq9PhbctXeH+vkaRAlfsHyKA0ITqDiooKpk6dSnFxMcHBwa0qq11blk6XmJxs48aNgDbm5FSqqja4/VQ2m43rrrsOh8PBG2+80ei+c+bMYfbs2a6fS0pKiI+PZ/z48URERJwxVkvYbDZSUlKYOHGiaxFaT4vhDefQWAy7Q2XTkUJ+2JHNkp3HKayw8XOmws+ZBoYlhnL177oy+ZxoAixnfkt5w2vlaedwfM0R2JvGOUmxTJky0C0xTscbYnjDOUiMjlN+W8XIz8/Xrax2TZbuvvturrvuukb3SUpKYvv27Rw/frzec7m5uURHRzd6vM1m449//COHDh3il19+OWN2abFYsFgs9babzWa3/UK9KYY3nENDMczA+b2jOb93NE9e4eCXPTn8Z9NRlqflsOlIEZuOFPHU//Zw2aA4/jQisc7iwU2N4Q7y+9ZklWhd690i/Bssy1POo71jeMM5SIyOU767Y+hZbrsmS5GRkURGRp5xv+TkZIqLi9mwYQPDhw8HYP369RQXFzNy5MjTHudMlPbt28eyZcvc1jIkOhcfk4GL+8dwcf8YjpdU8eWWY3yx6RiH8sr5fONRPt94lKGJYdw0MomLz4nBx9SysU1CP0cLtHXh4mXhZSFEC3jEf/F+/fpx8cUXc/vtt7Nu3TrWrVvH7bffzqWXXlpncHffvn35+uuvAaipqeEPf/gDmzZtYsGCBdjtdrKzs8nOzqa6urq9TkV4mehgX2aO68UvD4zlP3cmc8XgOMxGhc1HCrn3s1RGPfcLL6fsJaekqr2r2qkdzteSpaQImbVdCNF8HpEsASxYsIABAwYwadIkJk2axMCBA/n444/r7JOWlkZxcTEAx44d47vvvuPYsWMMHjyY2NhY123NmjXtcQrCiymKwvDu4bxy3RBWP3QB90/oTVSQhdxSK6/8vI+Rz/7CA//Zxr7jpe1d1U7H4VBJr21ZSoyQliUhRPN5xNQBAOHh4Y1exQbagG+npKQkPOBCP+GFooJ9uW/CWfx5XE+W7Mzmo7WH2Xi4kC+3HOPLLce4sG8XBnjMO8/zZZdUUV3jwGxUiA2ROZaEEM0n/7KFcBMfk4HLBsVx2aA4th4t4q3lB1iyK5uf9+TyMyZWl21k5rhejOvTpUlXdYqWOVLbBdctzL/Fc2MJITo3+c8hRBsYHB/KW9OG8tPssVwztCtGRWXj4UJumb+Ry17/lWV7cqQl1E2O5JcD0gUnhGg5SZaEaEM9uwTy9O/P4e9D7EwflYi/j5HfMkq4Zf5GrnpzDb/uy5OkSWdHnOOVwiVZEkK0jCRLQrSDUAs8fHEffn3oAu4c0wNfs4HU9CL+9N56rntnHZuPFLZ3Fb3GiZYluRJOCNEykiwJ0Y7CA3yYM6UfK/86nptHJuFjNLD+UAFXv7mGuz7d4pofSLScc8ySdMMJIVpKkiUhOoCoIF/mXn4OK/46jmuHxaMo8L/tWVz44gqeXrSb4kr3LTbpzVRVPSlZkpYlIUTLSLIkRAcSG+LHc38YyKJ7RzP6rEiq7Q7eWXmQcS8s45N1R7A7ZDxTcxSUV1NmrUFRID5cVjwWQrSMJEtCdED9YoP56NbhfHDLufSKCqSwwsZj3/zGVW+uYcex4vaunsdwztwdF+KHxWRs59oIITyVJEtCdFCKojC+TxSL7xvN3MvOJshiYtvRIq741688/u1v0jXXBOkF2uDuBLkSTgjRCpIsCdHBmYwGbh7VnZ8fGMsVg+NwqPDh2iNc+OIKftie2d7V69AO59WuCRcpyZIQouUkWRLCQ0QF+/LKdUP49Lbz6NElgLwyK3d/msrMBZvJK7O2d/U6JOe0AQnhMrhbCNFykiwJ4WFG9opk8X1juO/CszAZFBbtyGbSyyullakBzgkpk2TaACFEK0iyJIQH8jEZuH9ib765axR9Y4IoKK92tTLlSyuTi3PagARJloQQrSDJkhAerH/XEL67+3zuPamVafIrq1h7ML+9q9buSqpsFJRXAzLHkhCidSRZEsLD+ZgMzK5tZTorKpCcUis3zd/M9+kGbHZHe1ev3RzM1cYrdQmyEGgxtXNthBCeTJIlIbyEs5Xp+uEJqCr8lGFg6nsbO+2SKftzygDo1SWwnWsihPB0kiwJ4UX8fIw8c9UAXr12IH5Gla1Hi5ny6ioW/5bd3lVrcwdya5OlKEmWhBCtI8mSEF5ocv8Y/jrIzu8SQimtqmHGJ5t5cWlap1ouxdWyJMmSEKKVJFkSwkuFW2DBrcOYfn53AF77ZT+3fbix08z8fUCSJSGETiRZEsKLmYwG/nbp2cy7djAWk4Flablc8fqvpGWXtnfV3Kq6xuGaY6mnjFkSQrSSJEtCdAK/H9KVL/88kq6hfhzOr+DKN1azdKf3jmM6nF+O3aESaDERHWxp7+oIITycJEtCdBL9u4bw/T3nM7JnBBXVdu78ZDPzVx9q72q5hXO8Us8uASiK0s61EUJ4OkmWhOhEwgN8+OjW4Uw9T5teYO73u/jHD7tweNnA7z213Yy9o4PauSZCCG8gyZIQnYzJaOCfv+/PQxf3BeC9Xw8xc8EWqmz2dq6ZftKySwDoGxvczjURQngDSZaE6IQUReHP43ryynWD8TEaWLwzm+vfXedaHsTTOQew942RliUhROtJsiREJ3bF4K58PH04IX5mUtOL+OPbazleUtXe1WqViuoa15VwkiwJIfQgyZIQndx5PSL48s/JxIb4sj+njGveWuvRS6TsPV6GqkJkoIWIQLkSTgjRepIsCSHoFRXEf+5MJiHcn/SCCq55a63rijJPsydLG6/UL1ZalYQQ+pBkSQgBQHy4P1/MSOasqECyS6q49u217Mosae9qNZvzSrg+ciWcEEInkiwJIVyig31ZeGcy58QFk19ezXXvrGXr0aL2rlaz7MgoBuCcrnIlnBBCH5IsCSHqCA/w4dPbRzA0MYySqhqmvbee32oTkI6uxu5wtYYN6BravpURQngNSZaEEPWE+Jn56NbhDEsMo7Sqhj+9t57dWR2/S+5AbjmVNjsBPkZ6RAa0d3WEEF5CkiUhRIMCLCY+uOVcBseHUlRh44Z/r2ff8Y69AK+rCy4uBINBljkRQuhDkiUhxGkF+Zr58Nbh9O8aTEF5Nde/u54DuR33Krkdx4oAGNAtpH0rIoTwKh6TLBUWFjJt2jRCQkIICQlh2rRpFBUVNfn4O++8E0VRmDdvntvqKIQ3CvEz88n08+gXG0xemZWp765zTfrY0ThblgZ0lWRJCKEfj0mWpk6dytatW1m8eDGLFy9m69atTJs2rUnHfvPNN6xfv564uDg311II7xTq78Mn04fTOzqQ4yVWbpm/mZIOtjJKlc3ObxnauKpB8aHtWxkhhFfxiGRp9+7dLF68mH//+98kJyeTnJzMu+++yw8//EBaWlqjx2ZkZHD33XezYMECzGZzG9VYCO8TEWjhk9vOIyHcn6OFlby120hJpa29q+XyW0Yx1XYHkYE+JEX4t3d1hBBexNTeFWiKtWvXEhISwnnnnefaNmLECEJCQlizZg19+vRp8DiHw8G0adN48MEHOeecc5oUy2q1YrVaXT+XlGjfVG02Gzabez4YnOW6q/y2iOEN5yAxzizM18j7N/2Oa9/ZQEZ5NXd8soX5Nw/D12zUNQ40/xzWHcgDYEh8KDU1NW6J0RLeEMMbzkFidJzy2zqGHhRVVVXdSnOTp59+mvnz57N3794623v37s0tt9zCnDlzGjzumWeeYdmyZSxZsgRFUUhKSmLWrFnMmjXrtLHmzp3LE088UW/7p59+ir+/fFsVAiCjHF7baaTSrtA/zMGtfRwY2/nis3f3GPit0MDvE+2Mj+vw/9aEEG5WUVHB1KlTKS4uJji4dZPUtmvL0ukSk5Nt3LgRAEWp/59YVdUGtwNs3ryZV155hS1btpx2n4bMmTOH2bNnu34uKSkhPj6e8ePHExER0eRymsNms5GSksLEiRPd1lXo7hjecA4So3nlV9lTeDvNh98K4VdrN5698pxmvdeaEqOp56CqKnO3LQds3HBRMoObOGbJG34XbRHDG85BYnSc8tsqRn5+vm5ltWuydPfdd3Pdddc1uk9SUhLbt2/n+PHj9Z7Lzc0lOjq6weNWrVpFTk4OCQkJrm12u50HHniAefPmcfjw4QaPs1gsWCz1Vyo3m81uH/PkDTG84RwkRtP0DIZXrh3IXZ9t46vUTLoE+TJnSj/d4zTlHPZkl1BYYcPXbGBQQgRmU/OGY3r676KtYnjDOUiMjlO+u2PoWW67JkuRkZFERkaecb/k5GSKi4vZsGEDw4cPB2D9+vUUFxczcuTIBo+ZNm0aEyZMqLPtoosuYtq0adxyyy2tr7wQggv7RvHsVQN48L/beXvlQboEWbhtdI82r8ev+7TxSud1j8CnmYmSEEKciUcM8O7Xrx8XX3wxt99+O2+//TYAd9xxB5deemmdwd19+/blmWee4corryQiIqJet5nZbCYmJua0A8KFEM13zbB48sqqeW7xHp76324iAy38fkjXNq3DqtpkafRZZ/7yJYQQzeUxX8EWLFjAgAEDmDRpEpMmTWLgwIF8/PHHdfZJS0ujuNgzFvwUwpvMGNuDW0d1B+AvX2xj5d7cNottrbGz/pA2NuF8SZaEEG7gES1LAOHh4XzyySeN7nOmC/tON05JCNE6iqLw2CX9yCuz8t22TGZ8spnPbh/RJpNDbj5cSJXNQZcgC32ig9weTwjR+XhMy5IQomMzGBT+75pBnN8rkopqO7fM38ihvHK3x126S7v4Y1zvLrpejSeEEE6SLAkhdONjMvDWtKEM6BpCQXk1N76/npySKrfFczhUFv+WDcDkATFuiyOE6NwkWRJC6CrQYuKDW84lKcKfowWV3PTBRkqq3DNL77ZjRWSXVBFoMTGyp4xXEkK4hyRLQgjdRQZa+OjW84gMtLA7q4Q7PtpElc2ue5z/bc8CYHzfKLcsuSKEECDJkhDCTRIi/Jl/y7kEWkysO1jA7P9sxe7QbxmS6hoHX6dmAHD5oDjdyhVCiFNJsiSEcJv+XUN4Z9pQfIwGFu3I5onvd57xqtWm+nn3cfLLq4kKsjC+TxddyhRCiIZIsiSEcKuRvSJ56dpBKAp8tPYIr/+yX5dyP92QDsAfhnbDZJR/ZUII95H/MEIIt7t0YBxzLzsHgBdT9vLx2sOtKm/7sSJW7cvDaFC47tyEMx8ghBCtIMmSEKJN3DQyibvH9wLgb9/u5L1fD7W4LGfr1BWD4kiI8NelfkIIcTqSLAkh2swDk3ozY2xPAP7xwy7+tWx/s8cwrTuYz9Jdx1EUmDm+pzuqKYQQdUiyJIRoM4qi8NDFfZg14SwAXliSxsNf7qC6xtGk4601dh79egcAU4cn0CtKljcRQrifJEtCiDalKAqzJvTmb5eejUGBhZuOcsO/15Fbam30OFVVmfPVDg7klhMZaOGvF/dtoxoLITo7SZaEEO1i+vndee/mcwmymNh4uJCL5q3k69RjOBqYi8nuUHnyh118tSUDo0HhpT8OIsTP3A61FkJ0RpIsCSHazfg+UXx91yj6xgRRUF7N/Qu3MeXVVXy09jB7skvJq4Iff8vmqjfX8MHqwwDMvexsxvSWeZWEEG3H1N4VEEJ0br2iAvnu7vN5d9VB3lx+gD3Zpfz92521z5ogdTsAfmYjL1wzkEsHymzdQoi2JcmSEKLd+ZgM3DW+F1OHJ/DllmOk7DrO7qwSKqttJEUGckHfaG4b3YMuQZb2rqoQohOSZEkI0WGEBfhw2+ge3Da6BzabjUWLFjFlyijMZhmfJIRoPzJmSQghhBCiEZIsCSGEEEI0QpIlIYQQQohGSLIkhBBCCNEISZaEEEIIIRohyZIQQgghRCMkWRJCCCGEaIQkS0IIIYQQjZBkSQghhBCiEZIsCSGEEEI0QpIlIYQQQohGSLIkhBBCCNEISZaEEEIIIRohyZIQQgghRCNM7V2Bjk5VVQBKS0sxm81uiWGz2aioqKCkpMRjY3jDOUiMjlO+xOhYMbzhHCRGxym/rWKUlpYCJz7HW0OSpTPIz88HoHv37u1cEyGEEEI0V35+PiEhIa0qQ5KlMwgPDwcgPT291S/26ZSUlBAfH8/Ro0cJDg72yBjecA4So+OULzE6VgxvOAeJ0XHKb6sYxcXFJCQkuD7HW0OSpTMwGLRhXSEhIW77hToFBwd7fAxvOAeJ0XHKlxgdK4Y3nIPE6Djlt1UM5+d4q8rQoR5CCCGEEF5LkiUhhBBCiEZIsnQGFouFxx9/HIvFIjHasXyJ0bFieMM5SIyOU77E6FgxvOEc9I6hqHpcUyeEEEII4aWkZUkIIYQQohGSLAkhhBBCNEKSJSGEEEKIRkiyJIQQQgjRCEmWGvHPf/6TkSNH4u/vT2hoaIP7pKenc9lllxEQEEBkZCT33nsv1dXVLY65ZcsWJk6cSGhoKBEREdxxxx2UlZW1uLyG7N27lyuuuILIyEiCg4MZNWoUy5Yt06385cuXoyhKg7eNGzfqFud///sf5513Hn5+fkRGRnLVVVfpVjZAUlJSvfo//PDDusZwslqtDB48GEVR2Lp1q65lX3755SQkJODr60tsbCzTpk0jMzNTt/IPHz7M9OnT6d69O35+fvTs2ZPHH3+8Ve+DUzXlvdhcb7zxBt27d8fX15ehQ4eyatUqXcp1WrlyJZdddhlxcXEoisI333yja/nPPPMM5557LkFBQURFRfH73/+etLQ0XWO8+eabDBw40DVxYHJyMj/++KOuMU72zDPPoCgKs2bN0rXcuXPn1nsvx8TE6BojIyODP/3pT0RERODv78/gwYPZvHmzbuU39P9IURTuuusu3WLU1NTw2GOPud7LPXr04Mknn8ThcOgWA7Q122bNmkViYiJ+fn6MHDmyVZ8NZ3qvqarK3LlziYuLw8/Pj3HjxrFz585mxZBkqRHV1dVcc801/PnPf27webvdziWXXEJ5eTm//vorn3/+OV9++SUPPPBAi+JlZmYyYcIEevXqxfr161m8eDE7d+7k5ptvbsVZ1HfJJZdQU1PDL7/8wubNmxk8eDCXXnop2dnZupQ/cuRIsrKy6txuu+02kpKSGDZsmC4xvvzyS6ZNm8Ytt9zCtm3bWL16NVOnTtWl7JM9+eSTdc7jscce0z0GwF//+lfi4uLcUvb48eP5z3/+Q1paGl9++SUHDhzgD3/4g27l79mzB4fDwdtvv83OnTt5+eWXeeutt3jkkUd0i3Gm92JzLVy4kFmzZvHoo4+SmprK6NGjmTx5Munp6bqUD1BeXs6gQYN4/fXXdSvzZCtWrOCuu+5i3bp1pKSkUFNTw6RJkygvL9ctRrdu3Xj22WfZtGkTmzZt4oILLuCKK65o9gdNU2zcuJF33nmHgQMH6l42wDnnnFPnvbxjxw7dyi4sLGTUqFGYzWZ+/PFHdu3axYsvvqhbYg/a63Ny/VNSUgC45pprdIvx3HPP8dZbb/H666+ze/dunn/+eV544QVee+013WIA3HbbbaSkpPDxxx+zY8cOJk2axIQJE8jIyGhReWd6rz3//PO89NJLvP7662zcuJGYmBgmTpzoWmi3SVRxRh988IEaEhJSb/uiRYtUg8GgZmRkuLZ99tlnqsViUYuLi5sd5+2331ajoqJUu93u2paamqoC6r59+1pU91Pl5uaqgLpy5UrXtpKSEhVQf/rpJ11inKq6ulqNiopSn3zySV3Ks9lsateuXdV///vfupR3OomJierLL7/s1hiqqv0d9e3bV925c6cKqKmpqW6N9+2336qKoqjV1dVui/H888+r3bt3173c070Xm2v48OHqjBkz6mzr27ev+vDDD7e67IYA6tdff+2Wsp1ycnJUQF2xYoVb44SFhen+3istLVXPOussNSUlRR07dqx633336Vr+448/rg4aNEjXMk/20EMPqeeff77bym/Ifffdp/bs2VN1OBy6lXnJJZeot956a51tV111lfqnP/1JtxgVFRWq0WhUf/jhhzrbBw0apD766KOtLv/U95rD4VBjYmLUZ5991rWtqqpKDQkJUd96660mlystS62wdu1a+vfvX6dF4KKLLsJqtbao+dVqteLj41NnHRs/Pz8Afv3119ZXGIiIiKBfv3589NFHlJeXU1NTw9tvv010dDRDhw7VJcapvvvuO/Ly8nRrIduyZQsZGRkYDAaGDBlCbGwskydPdsu33eeee46IiAgGDx7MP//5T127lgCOHz/O7bffzscff4y/v7+uZTekoKCABQsWMHLkSMxms9viFBcX67J4pTtUV1ezefNmJk2aVGf7pEmTWLNmTTvVqvWKi4sB3Pa62+12Pv/8c8rLy0lOTta17LvuuotLLrmECRMm6Fruyfbt20dcXBzdu3fnuuuu4+DBg7qV/d133zFs2DCuueYaoqKiGDJkCO+++65u5Z+qurqaTz75hFtvvRVFUXQr9/zzz+fnn39m7969AGzbto1ff/2VKVOm6BajpqYGu92Or69vne1+fn66fc6d7NChQ2RnZ9d5v1ssFsaOHdus97skS62QnZ1NdHR0nW1hYWH4+Pi0qEvrggsuIDs7mxdeeIHq6moKCwtdXRlZWVm61FlRFFJSUkhNTSUoKAhfX19efvllFi9erGuT8cnee+89LrroIuLj43Upz/lPbu7cuTz22GP88MMPhIWFMXbsWAoKCnSJAXDffffx+eefs2zZMu6++27mzZvHzJkzdStfVVVuvvlmZsyYoVv35Ok89NBDBAQEEBERQXp6Ot9++63bYh04cIDXXnuNGTNmuC1Ga+Tl5WG32+u9d6Ojo3Xrim5rqqoye/Zszj//fPr3769r2Tt27CAwMBCLxcKMGTP4+uuvOfvss3Ur//PPP2fLli0888wzupV5qvPOO4+PPvqIJUuW8O6775Kdnc3IkSPJz8/XpfyDBw/y5ptvctZZZ7FkyRJmzJjBvffey0cffaRL+af65ptvKCoq0n2IxkMPPcT1119P3759MZvNDBkyhFmzZnH99dfrFiMoKIjk5GT+8Y9/kJmZid1u55NPPmH9+vW6fc6dzPmebvX7vdVtXh7m8ccfV4FGbxs3bqxzzOma/m+//XZ10qRJ9babzWb1s88+a1HMBQsWqNHR0arRaFR9fHzUv/zlL2p0dLT63HPP6XJeDodDvfzyy9XJkyerv/76q7p582b1z3/+s9q1a1c1MzNT99fu6NGjqsFgUP/73/82WnZzyl+wYIEKqG+//bbr2KqqKjUyMvKMzaotOQen//73vyqg5uXl6RLjlVdeUUeOHKnW1NSoqqqqhw4danI3XHPPIzc3V01LS1OXLl2qjho1Sp0yZcoZm+9b8lplZGSovXr1UqdPn677OaiqPt1wGRkZKqCuWbOmzvannnpK7dOnT6vKPh3c3A03c+ZMNTExUT169KjuZVutVnXfvn3qxo0b1YcffliNjIxUd+7cqUvZ6enpalRUlLp161bXNnd0w52qrKxMjY6OVl988UVdyjObzWpycnKdbffcc486YsQIXco/1aRJk9RLL71U93I/++wztVu3bupnn32mbt++Xf3oo4/U8PBwdf78+brG2b9/vzpmzBgVUI1Go3ruueeqN9xwg9qvX79Wl33qe2316tUqUO/z7bbbblMvuuiiJpdranpa5R3uvvturrvuukb3SUpKalJZMTExrF+/vs62wsJCbDZbnSy2OTGnTp3K1KlTOX78OAEBASiKwksvvUT37t0bPb6pMX755Rd++OEHCgsLCQ4OBrSrglJSUvjwww8bvdqrJa/dBx98QEREBJdffnmjxzWnfOegvJO/3VosFnr06HHGAbqt+f2PGDECgP379xMREdHqGE899RTr1q2rt27RsGHDuOGGG/jwww9bHcMpMjKSyMhIevfuTb9+/YiPj2fdunWNdqc0N0ZmZibjx48nOTmZd955p9HjWlK+XiIjIzEajfW+Vebk5NT79ukJ7rnnHr777jtWrlxJt27ddC/fx8eHXr16Adrf5saNG3nllVd4++23W1325s2bycnJqTMEwG63s3LlSl5//XWsVitGo7HVcU4VEBDAgAED2Ldvny7lxcbG1mtt69evH19++aUu5Z/syJEj/PTTT3z11Ve6l/3ggw/y8MMPu96XAwYM4MiRIzzzzDPcdNNNusXp2bMnK1asoLy8nJKSEmJjY7n22mvP+DnXEs6rHrOzs4mNjXVtb+77vdMlS84PDT0kJyfzz3/+k6ysLNcvYenSpVgsljpv/pbEdP4S33//fXx9fZk4cWKj+zc1RkVFBUCdcVHOn890eWhzz0NVVT744ANuvPHGJo2PaWr5Q4cOxWKxkJaWxvnnnw+AzWbj8OHDJCYm6hKjIampqQB13nCtifHqq6/y1FNPuX7OzMzkoosuYuHChZx33nm6xGiIWrscpNVq1S1GRkYG48ePZ+jQoXzwwQf1/r5aW76efHx8GDp0KCkpKVx55ZWu7SkpKVxxxRVtXp+WUlWVe+65h6+//prly5e75YPmdHHP9LfTVBdeeGG9q9JuueUW+vbty0MPPeSWRAm0v/3du3czevRoXcobNWpUvWkb9u7de8b/Ry3xwQcfEBUVxSWXXKJ72RUVFfXeu0ajUfepA5wCAgIICAigsLCQJUuW8Pzzz+seo3v37sTExJCSksKQIUMAbczXihUreO6555peUKvbvLzYkSNH1NTUVPWJJ55QAwMD1dTUVDU1NVUtLS1VVVVVa2pq1P79+6sXXnihumXLFvWnn35Su3Xrpt59990tjvnaa6+pmzdvVtPS0tTXX39d9fPzU1955RW9TknNzc1VIyIi1KuuukrdunWrmpaWpv7lL39RzWZznaZwPfz0008qoO7atUvXclVVuxKka9eu6pIlS9Q9e/ao06dPV6OiotSCggJdyl+zZo360ksvqampqerBgwfVhQsXqnFxcerll1+uS/kNaU43XFOtX79efe2119TU1FT18OHD6i+//KKef/75as+ePdWqqipdYji73i644AL12LFjalZWluumlzO9F5vr888/V81ms/ree++pu3btUmfNmqUGBASohw8f1q3OpaWlrnoCrr+nI0eO6FL+n//8ZzUkJERdvnx5nde8oqJCl/JVVVXnzJmjrly5Uj106JC6fft29ZFHHlENBoO6dOlS3WKcyh3dcA888IC6fPly9eDBg+q6devUSy+9VA0KCtLt971hwwbVZDKp//znP9V9+/apCxYsUP39/dVPPvlEl/Kd7Ha7mpCQoD700EO6lut00003qV27dlV/+OEH9dChQ+pXX32lRkZGqn/96191jbN48WL1xx9/VA8ePKguXbpUHTRokDp8+PAWX6F7pvfas88+q4aEhKhfffWVumPHDvX6669XY2Nj1ZKSkibHkGSpETfddFOD4yiWLVvm2ufIkSPqJZdcovr5+anh4eHq3Xff3aoPoWnTpqnh4eGqj4+POnDgQPWjjz7S4Uzq2rhxozpp0iQ1PDxcDQoKUkeMGKEuWrRI9zjXX3+9OnLkSN3LVVVtOoIHHnhAjYqKUoOCgtQJEyaov/32m27lb968WT3vvPPUkJAQ1dfXV+3Tp4/6+OOPq+Xl5brFOJU7kqXt27er48ePV8PDw1WLxaImJSWpM2bMUI8dO6ZbjA8++OC0Y4700pT3YnP961//UhMTE1UfHx/1d7/7ne6X3C9btqzBOt900026lH+61/yDDz7QpXxVVdVbb73V9Rp16dJFvfDCC92aKKmqe5Kla6+9Vo2NjVXNZrMaFxenXnXVVbqNu3L6/vvv1f79+6sWi0Xt27ev+s477+havqqq6pIlS1RATUtL071sVdWmkbnvvvvUhIQE1dfXV+3Ro4f66KOPqlarVdc4CxcuVHv06KH6+PioMTEx6l133aUWFRW1uLwzvdccDof6+OOPqzExMarFYlHHjBmj7tixo1kxFFWtbZMXQgghhBD1yNQBQgghhBCNkGRJCCGEEKIRkiwJIYQQQjRCkiUhhBBCiEZIsiSEEEII0QhJloQQQgghGiHJkhBCCCFEIyRZEkIIIYRohCRLQgghhBCNkGRJCCGEEKIRkiwJIYQQQjRCkiUhRKeSm5tLTEwMTz/9tGvb+vXr8fHxYenSpe1YMyFERyUL6QohOp1Fixbx+9//njVr1tC3b1+GDBnCJZdcwrx589q7akKIDkiSJSFEp3TXXXfx008/ce6557Jt2zY2btyIr69ve1dLCNEBSbIkhOiUKisr6d+/P0ePHmXTpk0MHDiwvaskhOigZMySEKJTOnjwIJmZmTgcDo4cOdLe1RFCdGDSsiSE6HSqq6sZPnw4gwcPpm/fvrz00kvs2LGD6Ojo9q6aEKIDkmRJCNHpPPjgg/z3v/9l27ZtBAYGMn78eIKCgvjhhx/au2pCiA5IuuGEEJ3K8uXLmTdvHh9//DHBwcEYDAY+/vhjfv31V9588832rp4QogOSliUhhBBCiEZIy5IQQgghRCMkWRJCCCGEaIQkS0IIIYQQjZBkSQghhBCiEZIsCSGEEEI0QpIlIYQQQohGSLIkhBBCCNEISZaEEEIIIRohyZIQQgghRCMkWRJCCCGEaIQkS0IIIYQQjfh/PW4tRiwBk7YAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "nplot = 400\n",
    "a = -10\n",
    "b = 10\n",
    " \n",
    "x = np.linspace(a,b,nplot)\n",
    "y = f(x)\n",
    "dy = dfdx(x)\n",
    "\n",
    "plt.plot(x,y,label='f')\n",
    "plt.plot(x,dy,label='df/dx')\n",
    "plt.legend(loc='upper right')\n",
    "plt.xticks(np.arange(a, b+1, 1.0))\n",
    "plt.xlim(a,b)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "9834fc07-af67-4d25-b5ed-3f6f075f305c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.908806073153887\n",
      "33.936308866114594\n",
      "67.9316028776399\n",
      "135.8926535145931\n",
      "271.8000253252568\n",
      "543.6074091011637\n",
      "1087.218497340497\n",
      "2174.4388342391844\n",
      "4348.878588256102\n",
      "8697.7576364009\n",
      "17395.51550274613\n",
      "(17395.51550274613, 11)\n"
     ]
    }
   ],
   "source": [
    "x0 = 1.07\n",
    "#x0 = 1.08\n",
    "#x0 = 1.09\n",
    "\n",
    "solApprox = Newton(f, dfdx, x0, 1.0e-4, debug=True)\n",
    "print(solApprox)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "417c4e6f-8ed2-4ef7-9906-8dfe200925ae",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def Newton(f, dfdx, x, eps1=1e-4, eps2=1e-4, maxit=20, debug=False):\n",
    "    \n",
    "    f_value = f(x)\n",
    "    iteration_counter = 0\n",
    "    \n",
    "    err = 10*eps2\n",
    "    \n",
    "    while (abs(f_value) > eps1) and (err > eps2) and (iteration_counter < maxit):\n",
    "        \n",
    "        try:\n",
    "            div = f_value/dfdx(x)\n",
    "        except ZeroDivisionError:\n",
    "            print('Error! - derivative zero for x = ', x)\n",
    "            sys.exit(1)     # Abort with error\n",
    "        \n",
    "        x = x - div\n",
    "        \n",
    "        err = abs(div/x)\n",
    "        \n",
    "        if debug:\n",
    "            print(x, err)\n",
    "            \n",
    "        f_value = f(x)\n",
    "        iteration_counter = iteration_counter + 1\n",
    "\n",
    "    # Here, either a solution is found, or too many iterations\n",
    "    if abs(f_value) > eps1 or err > eps2:\n",
    "        iteration_counter = -1\n",
    "    return x, iteration_counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "a9ab43ec-75a9-41fc-a858-eba7aa92924d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.33333333333333326 2.5000000000000004\n",
      "0.08333333333333331 5.0\n",
      "-0.0011655011655011677 72.49999999999986\n",
      "3.166421473329087e-09 368082.49998925836\n",
      "(3.166421473329087e-09, -1)\n"
     ]
    }
   ],
   "source": [
    "#x0 = 1.07\n",
    "#x0 = 1.08\n",
    "#x0 = 1.09\n",
    "x0 = 0.5\n",
    "\n",
    "solApprox = Newton(f, dfdx, x0, eps1=1.0e-4, eps2=1.0e-4, debug=True)\n",
    "print(solApprox)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd5ec657-1f68-411b-8789-b32c2d8712c5",
   "metadata": {},
   "source": [
    "### Teorema da Convergência"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fff8f25b-fb46-4e10-9c56-c17ee5cc7ed6",
   "metadata": {},
   "source": [
    "Notas em sala de aula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e8f4e88-fa22-4b7e-a986-01ff048d5264",
   "metadata": {},
   "source": [
    "## Método da Secante"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee915d1f-f166-4e83-a143-cc8f741ea4c8",
   "metadata": {},
   "source": [
    "Dado $x_0$ e $x_1$, consideremos as iterações\n",
    "$$\n",
    "x_k = x_{k-1} - \\dfrac{f(x_{k-1})}{ \\dfrac{f(x_{k-1}) - f(x_{k-2})}{x_{k-1} - x_{k-2}} },\n",
    "$$\n",
    "para $k = 2, 3, 4, \\ldots$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "a9d3113a-fcd1-4aba-81ce-c00ecddd8fed",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def secant(f, x0, x1, eps, debug=False):\n",
    "    f_x0 = f(x0)\n",
    "    f_x1 = f(x1)\n",
    "    iteration_counter = 0\n",
    "    while abs(f_x1) > eps and iteration_counter < 100:\n",
    "        try:\n",
    "            denominator = (f_x1 - f_x0)/(x1 - x0)\n",
    "            x = x1 - f_x1/denominator\n",
    "        except ZeroDivisionError:\n",
    "            print('Error! - denominator zero for x = ', x)\n",
    "            sys.exit(1)     # Abort with error\n",
    "        x0 = x1\n",
    "        x1 = x\n",
    "        f_x0 = f_x1\n",
    "        f_x1 = f(x1)\n",
    "        \n",
    "        if debug:\n",
    "            print(x)\n",
    "        \n",
    "        iteration_counter = iteration_counter + 1\n",
    "    \n",
    "    # Here, either a solution is found, or too many iterations\n",
    "    if abs(f_x1) > eps:\n",
    "        iteration_counter = -1\n",
    "    return x, iteration_counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "19eecf28-3262-495c-9fc3-43dbd9cb3676",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x - 2.1)*(x - 0.1)*(x + 1.1)\n"
     ]
    }
   ],
   "source": [
    "x = sym.symbols('x') \n",
    "\n",
    "f_expr = (x - 0.1)*(x - 2.1)*(x + 1.1) # symbolic expression for f(x) \n",
    "\n",
    "print(f_expr)\n",
    "\n",
    "# turn f_expr and dfdx_expr into plain Python functions \n",
    "f = sym.lambdify([x], f_expr) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "49fbb7f8-8c44-4dfc-9eb1-5e1554e6ab87",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.261490683229814\n",
      "2.138887588207181\n",
      "2.104536519194257\n",
      "2.100139571920842\n",
      "2.1000005129631965\n",
      "(2.1000005129631965, 5)\n"
     ]
    }
   ],
   "source": [
    "x0 = 3.0\n",
    "x1 = 2.5\n",
    "solApprox = secant(f, x0, x1, 1.0e-4, debug=True)\n",
    "print(solApprox)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b8a2497-5000-4bdc-90b2-28e982d2c203",
   "metadata": {},
   "source": [
    "### Exercício: Modificar a função `secant` para realizar o critério de convergência do erro relativo da iteração."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ff66abbf-69c4-4d51-bf99-b0f0177e2c3a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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