CotaKaren_TrabajoFinalMetNum.ipynb

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  "metadata": {
    "colab": {
      "name": "CotaKaren_TrabajoFinalMetNum.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/roilhi/MetNum_ITECI_2020/blob/gh-pages/CotaKaren_TrabajoFinalMetNum.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iudgI88pN1mS",
        "colab_type": "text"
      },
      "source": [
        "# Universidad de Ensenada\n",
        "\n",
        "**Curso de Métodos Numéricos**\n",
        "\n",
        "*Repaso y Programación de algunos métodos vistos*\n",
        "\n",
        "**Karen Nohemy Cota Quezada**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wiiChBn9Hi90",
        "colab_type": "text"
      },
      "source": [
        "Unidad 1: Raíces de ecuaciones."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rOaf5gYrH2qi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Primero importamos las librerías necesarias\n",
        "import numpy as np # Librería numérica\n",
        "import sympy # Procesamiento simbólico\n",
        "import matplotlib.pyplot as plt # Librería para las gráficas"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OdviivubJWRE",
        "colab_type": "text"
      },
      "source": [
        "Cálculo del error relativo porcentual, nos servirá para todos los métodos.\n",
        "$$\\epsilon_r = \\left \\lvert \\frac {V_r-Vn}{Vn} \\right \\rvert \\times 100$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RNw-MTkDMmR8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo (vreal, vnum):\n",
        "  epsilon = abs((vreal-vnum)/vreal)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mwSJYa83ODIY",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Método de bisección\n",
        "\n",
        "Estimar la raíz de la función $f(x)=x-\\cos(x)$ en el intervalo $[0.5, 1]$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p-qNZ24WNuXB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Valores iniciales\n",
        "a =0.5\n",
        "b =1\n",
        "Vanalítico =0.73909\n",
        "def fx(x_int):\n",
        "  fx = x_int-np.cos(x_int)\n",
        "  return fx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "75gTytebQY2x",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        },
        "outputId": "d2a6c6a7-9d67-4ca1-fc42-410dd233cc98"
      },
      "source": [
        "numIter = 0\n",
        "N = int(input('Defina un número N de iteraciones'))\n",
        "x_old =0\n",
        "while numIter<N:\n",
        "  x_i = (a+b)/2\n",
        "  if fx(a)*fx(x_i)<0:\n",
        "    b = x_i\n",
        "  elif fx(a)*fx(x_i)==0:\n",
        "    raizAproxBisec = x_i\n",
        "  else:\n",
        "    a = x_i\n",
        "  numIter = numIter+1\n",
        "  raizAproxBisec = x_i\n",
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"La raíz estimada por el método de bisección es =\",+raizAproxBisec, \"iteración i =\",+numIter)\n",
        "  print(\"El error relativo es =\",+ErrorBisec, \"iteración i =\",+numIter)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Defina un número N de iteraciones10\n",
            "La raíz estimada por el método de bisección es = 0.75 iteración i = 1\n",
            "El error relativo es = 100.0 iteración i = 1\n",
            "La raíz estimada por el método de bisección es = 0.625 iteración i = 2\n",
            "El error relativo es = 20.0 iteración i = 2\n",
            "La raíz estimada por el método de bisección es = 0.6875 iteración i = 3\n",
            "El error relativo es = 9.090909090909092 iteración i = 3\n",
            "La raíz estimada por el método de bisección es = 0.71875 iteración i = 4\n",
            "El error relativo es = 4.3478260869565215 iteración i = 4\n",
            "La raíz estimada por el método de bisección es = 0.734375 iteración i = 5\n",
            "El error relativo es = 2.127659574468085 iteración i = 5\n",
            "La raíz estimada por el método de bisección es = 0.7421875 iteración i = 6\n",
            "El error relativo es = 1.0526315789473684 iteración i = 6\n",
            "La raíz estimada por el método de bisección es = 0.73828125 iteración i = 7\n",
            "El error relativo es = 0.5291005291005291 iteración i = 7\n",
            "La raíz estimada por el método de bisección es = 0.740234375 iteración i = 8\n",
            "El error relativo es = 0.2638522427440633 iteración i = 8\n",
            "La raíz estimada por el método de bisección es = 0.7392578125 iteración i = 9\n",
            "El error relativo es = 0.13210039630118892 iteración i = 9\n",
            "La raíz estimada por el método de bisección es = 0.73876953125 iteración i = 10\n",
            "El error relativo es = 0.06609385327164573 iteración i = 10\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kjKgy_8cZW9I",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "029e7503-c5f6-4127-c7e4-8c735c604908"
      },
      "source": [
        "# Datos para la graficación\n",
        "ejeX = np.linspace(0,2*np.pi,101)\n",
        "# Graficando la función\n",
        "plt.plot(ejeX,fx(ejeX), label='$f(x)$')\n",
        "# Graficar la raíz encontrada en el método\n",
        "plt.plot(raizAproxBisec,fx(raizAproxBisec), 'o', label= 'raíz encontrada $x_i$')\n",
        "plt.xlabel('$x$')\n",
        "plt.ylabel('$f(x)$')\n",
        "plt.title('Raíz de la función $f(x)=x-cos(x)$ método de bisección')\n",
        "plt.legend() # Muestra la leyenda\n",
        "plt.grid() # Muestra la cuadrícula\n",
        "plt.show() # Muestra la gráfica"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GekGMGmGr5ny",
        "colab_type": "text"
      },
      "source": [
        "Unidad 2: Interpolación Numérica"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rq6ZMJoQiEU4",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Método de interpolación de Lagrange\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AstXbapSmDVB",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "Se reformula el polinomio de Newton evitando el cálculo de las diferencias divididas.\n",
        "\n",
        "$f_n(x)=\\sum_{i=1}^{n}L_i(x)f(x_i)$\n",
        "\n",
        "Donde los valores Li's son los coeficientes de Lagrange y se calculan mediante.\n",
        "\n",
        "\n",
        "$L_i(x)=\\prod_{j=0\\;\\;j\\neq i}^{n}\\frac{x-x_j}{x_i-x_j}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JudzzjF6I3mn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import sympy\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "plt.style.use('ggplot')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YlrTIjDWN0qD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def arg_prod(i, j):\n",
        "    \"\"\" Argumento de las bases polinómicas de \n",
        "    Lagrange.\n",
        "    \"\"\"\n",
        "    # Variable simbólica\n",
        "    x_sim = sympy.symbols('x')\n",
        "    return (x_sim-x[i]) / (x[j]-x[i]) if i != j else 1\n",
        "\n",
        "def interpolacion_lagrange(x, y, num_puntos=100):\n",
        "    \"\"\" Estima la curva generada por el polinomio de lagrange que \n",
        "    interpola los puntos datos\n",
        "    \n",
        "    args:\n",
        "        x (np.array): Datos del eje x\n",
        "        y (np.array): Datos del eje y\n",
        "        num_puntos (int): Número de puntos estimados a partir del polinomio\n",
        "    \n",
        "    returns:\n",
        "        Puntos (x, y) estimados a partir del polinomio encontrado. Tupla\n",
        "    \"\"\"\n",
        "    # Variable simbólica\n",
        "    x_sim = sympy.symbols('x')\n",
        "    \n",
        "    # Número de puntos ingresados\n",
        "    points = len(x)\n",
        "    \n",
        "    # Bases polinómicas lj = [l1, l2, ..., lk]\n",
        "    lj = []\n",
        "    for k in range(points):\n",
        "        lk = np.prod([arg_prod(i, k) for i in range(points)])\n",
        "        lj.append(lk)\n",
        "\n",
        "    # Polinomio de lagrange\n",
        "    pol = sum(y*lj)\n",
        "    \n",
        "    # Se generan los datos x, y a partir del polinomio encontrado\n",
        "    x_test = np.linspace(min(x), max(x), num_puntos)\n",
        "    y_pol = [pol.subs(x_sim, i) for i in x_test]\n",
        "    \n",
        "    return x_test, y_pol\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BpDTVoluN1pU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "92025d0e-2671-4632-9439-2468f7583af2"
      },
      "source": [
        "# Datos\n",
        "x = np.linspace(-np.pi, np.pi, 4)\n",
        "y = np.array([np.sin(i) for i in x])\n",
        "\n",
        "# Puntos generados por el polinomio de Lagrange\n",
        "x_test, y_pol = interpolacion_lagrange(x, y)\n",
        "\n",
        "# Gráfica\n",
        "plt.plot(x_test, y_pol)\n",
        "plt.scatter(x, y)\n",
        "plt.legend(['Lagrange', 'Datos'], loc='best')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f2930460cc0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KqkG86Ugukf/mhQhgWmvst16C/fuwRoxB1a1vOpLfUX1vgrAI7I9nmI7iMil8IQKYXjIfvl+Jum4Yqmlr03H8kqpRE3XVQNj8PXrLD6bjuEQKX4gApbduRs95G9omo3r2MR3Hr6muV0FMLPaHb6Jt/53FVgpfiACkc7Ods1/WrY91y30uneQgQIWGYl03DNJ3o1d8ZTpOpUnhCxFgdGmpc177okKsu8YG1VTHHtU2Gc5vip7/LrrguOk0lSKFL0SA0Z/Mhu1bUDfchYrz77NKfIlSCqv/LXAkF730U9NxKkUKX4gAorf8gF70EeqSHlgXdzUdJ+CohCbQqh36y3no/LzyP+BjpPCFCBA6Nwf79RcgLh41eLjpOAHLunYo5B9Dp35iOkqFSeELEQC0bWO/ORkKC7Du/AcqLMx0pICl4hOgzcXo1AXovKOm41SIFL4QAUAvmQ8/b0QNvgNVv5HpOAHPumYoFBxHL15gOkqFSOEL4ef0b9vR82ZCYjLqkh6m4wQF1fBvqKRL0F8tRB89YjrOWZPCF8KP6YLj2K89D7XqYN14j5xv70Xq6sFQVIBeutB0lLMmhS+EH9MfvA4HD2Dd9iCqWnXTcYKKqt8ILuqAXvoZuiDfdJyzIoUvhJ/SaavR3y1BXd4P1bi56ThBybr8OucZO8sXm45yVqTwhfBD+sgh7HemQvx5qGuGmI4TtNR5F8KFLdFL5qOLi03HKZcUvhB+RmuN/fYUOJ7vvJmJI9R0pKBmXdkfcnPQa5aZjlIuKXwh/Iz+djH8uM455bFMnWBe04sgPgH9xVyfn0lTCl8IP6KzDqA/fBOatEJ1u8p0HMEfc+xccR0cSIe0NabjnJEUvhB+Qtu28+5VCqyb75f70vqSth0hqi72V749qZr8xAjhJ/TXn8PWTaiBt6GiYkzHEf9DWSGobr1h22b0nl2m45yWFL4QfkAf+B099y1omSRX0/oo1akHVAnz6QuxpPCF8HFlQzmOUKyb7paraX2UqlYdldwNvWY5+uhh03FOyeGOhaSlpTFjxgxs26Z79+706XPi/TOXLVvGzJkziYyMBODyyy+ne/fu7li1EAFPf/057NiCuuV+VO0o03HEGahuV6OXLUIv/xLVe6DpOCdxufBt2+aNN97gn//8J1FRUYwdO5akpCQaNmx4wvuSk5O57bbbXF2dEEFFH8xAz30bWiSiOnYzHUeUQ9VvCM3boJd9ju7VD+Vwyz6127g8pLNjxw5iY2OpV68eDoeD5ORk1q1b545sQgQ15wVWL0NICNaNMpTjL6zuVzsvxNqw0nSUk7j8309OTg5RUX/+mhkVFcX27dtPet+aNWv4+eefqV+/PsOGDSM6Ovqk96SmppKamgrAxIkTT/ked3A4HB5btjdIfvO8sQ35i+dzdOsmatw1hqqNm7h12fI98BzdpSfZH7yOtWopkVf2O+37TOT3yu8biYmJdOrUidDQUJYsWcLUqVMZP378Se9LSUkhJSWl7HFWVpZH8kRHR3ts2d4g+c3z9DbonCzsGS9D09bktUkm383rku+BZ9mdUiid+w4HN6ehYhue8j2eyh8XF3fa11we0omMjCQ7O7vscXZ2dtnB2f+qUaMGoaHO+T66d+/Orl2+e56qEKZprbHfmwZ2qQzl+CnVqTuEhDinwfAhLhd+QkIC+/fvJzMzk5KSElauXElSUtIJ7zl06FDZ39evX3/SAV0hxJ/0+hWwcS3q2utRMbGm44hKUDXrOOfKX/kVurjIdJwyLg/phISEcOuttzJhwgRs26Zr1640atSIDz74gISEBJKSkli0aBHr168nJCSE6tWrM3LkSHdkFyLg6GNH0LNfhXPOR3W/xnQc4QLr0suxv1+J3rAK1aGL6TiAm8bw27ZtS9u2bU94btCgQWV/Hzp0KEOHDnXHqoQIaPrDNyH/GNaoJ1AhIabjCFc0aQUxsejlX4KPFL5caSuEj9A/b0SvWorq2RfV6FzTcYSLlGWhOvdyzq+zf5/pOIAUvhA+QRcVYr/7CtStj7pqUPkfEH5BdermPHj7nW8cvJXCF8IH6M8+gsz9WDeMRFUJMx1HuImqWQdaJqFXL0OXmr85ihS+EIbp9N3oL+egOnZFNW1tOo5wM6tjNziSC1t+MB1FCl8Ik7RtY8+cChFVUQNkrqmA1CoJqtdAr1xqOokUvhAm6e8Ww85fUANuRdWoaTqO8ADlCEW174JOW43OO2Y0ixS+EIboI7noOW/DhS1lJswAp5K7QUkJet23RnNI4QthiP7oTSgsxLr+Lpk+IdDFJ0CDc9ArvzIaQwpfCAP0zxvRq5ehrrjOOYe6CGhKKedvcb9uQ2eYOydfCl8IL9PFxdizpkFMLOqK/qbjCC9RHbqAZRk9eCuFL4SX6S/nwIF051COnHMfNFTtSGjSGr3uW7TWRjJI4QvhRTpzP/qzj1BJl6CatzEdR3iZan8pZB2AXVuNrF8KXwgv0Vpjz34VHA7UIDnnPhipNheDI9TY2TpS+EJ4y4ZVsHmDc5772lHlv18EHFW1GrRMRK//zshUC1L4QniBLjiO/f5r0OhcVNfepuMIg6z2l8LhQxT95P2pFqTwhfAC/en7kJvtPFAr89wHt1btICyCgm+XeH3VUvhCeJhO34NO/QR1SQ9UQhPTcYRhqkoYqk0HClctQxcXe3XdUvhCeFDZDcnDIlD9hpmOI3yEat8FnXcUftrg1fVK4QvhQXrtcti2GdXvJpkcTfypaWtUjVpeP1tHCl8ID9HH853z5fztAlTnHqbjCB+iHA7CO1yK/nGdV4d1pPCF8BD9yXtwJBdr6AiUJQdqxYnCOnaFguOwJc1r65TCF8ID9L7f0Es/RXXuhTr3AtNxhA+q0jIRIqqhv1/htXVK4QvhZmUHaiOqofreYDqO8FEqNBR1UXv0xrXokhKvrFMKXwg302u+ge1bnAdqq8uBWnF6qm0y5B+DrZu8sj4pfCHcSB/PR388A85tjLpEDtSKcjRvA2ERXhvWkcIXwo30J7OdB2qH3Imy5J+XODMVWgXVKgmdtgZte35uHfmJFMJNdPoe9NKFqM495UCtOGsqMRmOHobtWzy+Lil8IdygbOrjiGqoPjeajiP8SYtEqFLFK8M6UvhCuIFe/x1s3YTqc4NcUSsqRIWFQ7O26LS1Hr8TlhS+EC7SBcfRH74J8QmoS3uajiP8kLqoAxzKgr27PLoeKXwhXKQ//9A59fHQO+WKWlEpqlUSKIVOW+vR9UjhC+ECnZGOXrwAldxdpj4WlaZq1IKEJuiNazy6Hil8ISpJa439/nSoUgV13U2m4wg/py7qAHt2oXMOemwdUvhCVNbGNfDTD6hrhqJq1jGdRvg51bo9AHrjOo+tQwpfiErQhYXY778ODc6Re9QKt1CxDaFeA48O6zjcsZC0tDRmzJiBbdt0796dPn36nPB6cXExU6ZMYdeuXdSoUYMHHniAunXrumPVJ7EPZsCCWejcHFTtSLj2eqyYWI+sSwSvvPmzIDsT66EJco9a4T6Nm8N3Syh95mFUVIzb+8vlPXzbtnnjjTd45JFHmDx5MitWrGDfvn0nvGfp0qVUq1aNl19+md69ezNr1ixXV3vqLAcz0JPHOSev2roJveYb9ORxzv8EhHATnXWAvLnvoNp1Rl3Y0nQcESDsgxmwaT1oDTu2eKS/XC78HTt2EBsbS7169XA4HCQnJ7Nu3YljUOvXr+eyyy4D4OKLL2bz5s2eucBgwSz46xfnjz1+IdzF/vANUBaq/y2mo4hAsmAW5Oac+Jyb+8vlIZ2cnByioqLKHkdFRbF9+/bTvickJISqVaty9OhRatY88YrE1NRUUlNTAZg4cSLR0dEVy5J3lFPdLMyRd5TI/1mWw+Go8LJ9ieQ3p/CH1eT+sJqaN91NRGP/PQ3Tn78H/+Xv2/DX/GfbXy6t0y1LcZOUlBRSUlLKHmdlZVXo83a1Gqd8vqRajROWFR0dXeFl+xLJb4YuKcZ+dRLUjSP8qgF+uQ3/5a/fg//l79vw1/xn21/liYuLO+1rLg/pREZGkp2dXfY4OzubyMjI076ntLSU/Px8atQ49ca55Nrr4a8HOGJinc8L4SKd+gkcSMcafAcqtIrpOCLQeKG/XC78hIQE9u/fT2ZmJiUlJaxcuZKkpKQT3pOYmMiyZcsAWL16Nc2bN0cp5eqqT2LFxKJGPQFtOzqfaHAOatQTcpaOcJk+lI3+9ENo3R7VMtF0HBGA/ttfqkMXuLAlqkMXt/eXy0M6ISEh3HrrrUyYMAHbtunatSuNGjXigw8+ICEhgaSkJLp168aUKVO49957qV69Og888IA7sp+SFRMLd42ldOI/oLhYyl64hf74LSgtwRp0u+koIoBZMbFw+4MeW75bxvDbtm1L27ZtT3hu0KBBZX+vUqUKo0ePdseqzppq3QE99210ThYq0n8P7Ajz9LbN6LXfoK4ajJIdCOHHAvZKW3VRBwD0j56dfU4ENl1aiv3eqxAZg7r8OtNxhHBJwBY+sQ2gbhw6zbOzz4nAppctgvTdWINuQ4WFmY4jhEsCtvCVUqiL2sMvm9DH803HEX5IH8lFL5gFzS6CNh1NxxHCZQFb+OAcx6e0BH7aYDqK8EN67ttQVIg1ZLhHzioTwtsCuvBJaALVa6J/kGEdUTF65y/oFV+hUq5xzmIoRAAI6MJXISGoizqgf1yLLj7VRctCnEzbfxyorR2Jumqg6ThCuE1AFz6ASkyGguOwJc10FOEn9PLFsGcnasCtqPCqpuMI4TYBX/g0aQUR1dAbVppOIvyAPnoEPW8mNG6BatfZdBwh3CrgC185QlGt26PT1qBLSkzHET5Oz3sHCvKxho6QA7Ui4AR84cMfwzr5x2DrJtNRhA/Tu7aiv1viPFDbIN50HCHcLigKn+ZtICxChnXEaZUdqK1ZB3X1YNNxhPCIoCh8FVoF1SoJ/cNqtF1qOo7wQfrbJbB7B2rALXKgVgSsoCh8+GNY5+hh2L7FdBThY/TRw+i57zinpG1/qek4QnhM0BQ+LRKhShX0+hWmkwgfo+e+A4XHsYbeKQdqRUALmsJXYeGolu3Q369Al8rZOsJJ7/zlzwO1cXKgVgS2oCl8wPnr+tHDFG363nQU4QN0aSn2rP9A7SjUVXKgVgS+oCp8WiZCRFUKvl1iOonwAfqbRbD3V+fUx+ERpuMI4XFBVfgqtAqqTUcKV3+DLi4yHUcYpA8fQs9/F5q2hsROpuMI4RVBVfjgHNbR+XkgwzpBTX/4JhQXyRW1IqgEXeHTpBVWrTrotctNJxGG6J83Ou9Re/l1qNgGpuMI4TVBV/gqJISw5G7oH9ehC+ROWMFGFxdjvzcNYmJRV/Q3HUcIrwq6wgcI79wDiovkfrdBSC+eBxnpWEPuRFWRe9SK4BKUhR96YQuIqotevcx0FOFF+mAG+rMPoW0yqmWi6ThCeF1QFr6yLNTFl8GWjejcbNNxhBdorZ1DOVYI1uA7TMcRwoigLHwA1bEbaFv28oOEXr8CNm9A9bkeVSfKdBwhjAjewq8XBwlN0CuXorU2HUd4kM7PQ3/wOsQnoLr2Nh1HCGOCtvABVHI32L8XftthOorwID3/XThyCOuGkaiQENNxhDAmuAs/6RIIrYJe9ZXpKMJD9K/b0Ms+R112BercC0zHEcKo4C78qtVRF3VAr/0WXVxsOo5wM11Sgv3OFKgViep7k+k4QhgX1IUPfwzr5B2FH9eZjiLcTKcugH2/YQ0ZjoqQu1gJEfSFT7OLoHYk9opU00mEG+mDGeiFs+Gii1FtO5qOI4RPCPrCV1YIKrk7bN6AzjloOo5wA6019rv/cZ5zP2S46ThC+IygL3wAdUkPQKO/k3nyA4FevQy2/IDqeyMqMtp0HCF8hhQ+oGJiodlF6O9S0aWlpuMIF+gjuc5z7hOaoC67wnQcIXyKFP4frEsvh0NZsFnmyfdn+oPXoeA41k33oCw5516I/+Vw5cPHjh1j8uTJHDx4kJiYGEaNGkX16tVPet+gQYOIj3feIDo6OpoxY8a4slrPaNUOatXB/uYLQlq3N51GVIL+cR167XLU1UPkhuRCnIJLhT9//nxatmxJnz59mD9/PvPnz+eGG2446X1VqvQzD5gAABCySURBVFThueeec2VVHqccDlSnHuhFH6OzD6KiYkxHEhWgj+c7D9TGxaOulHnuhTgVl4Z01q1bR5cuXQDo0qUL69b597nsqrMcvPVX+uO3IDfHOZTjCDUdRwif5NIe/uHDh6lTpw4AtWvX5vDhw6d8X3FxMQ8//DAhISFce+21tG9/6iGT1NRUUlOd58NPnDiR6GjPnGHhcDhOvezoaA5d1IGSFalE3XQXKtQ3i+O0+f2Eu/MX/bieQ8u/oOq1Q6jR4RK3LfdM5Htgnr9vg4n85Rb+k08+SW5u7knPDx48+ITHSqnT3gz6lVdeITIykgMHDvDEE08QHx9PbGzsSe9LSUkhJSWl7HFWVla5G1AZ0dHRp1227twT+4fVHFz8CVaHLh5Zv6vOlN8fuDO/LjiO/fIEqBtHQc9+FHrp6yLfA/P8fRs8lT8uLu60r5Vb+I899thpX6tVqxaHDh2iTp06HDp0iJo1a57yfZGRkQDUq1ePZs2a8dtvv52y8H1C87ZQrwH6q4Xgo4Uv/qTnvwvZmVgPPSW3LBSiHC6N4SclJfHNN98A8M0339CuXbuT3nPs2DGK/5iY7MiRI2zdupWGDRu6slqPUpaF6tYbft2G3rXVdBxxBnrbZvTST1GXXYlq3Nx0HCF8nktj+H369GHy5MksXbq07LRMgJ07d7JkyRJGjBhBeno606dPx7IsbNumT58+Pl344JxQTc9/F/3Vp6jzLjQdR5yCLjiOPeP/ILoe6rphpuMI4RdcKvwaNWowbty4k55PSEggISEBgAsvvJBJkya5shqvU+FVUZ1S0F9/hh5wM6q23BLP1+g5b/05lBMWbjqOEH5BrrQ9DdW1N9g2+psvTEcRf6G3pKGXLUJ1v0aGcoSoACn801B160Orduhli9CFhabjiD/o/Dzst1+C2Aaovidf5CeEOD0p/DOwevWDY0fQK+RCLF+h338NDuVg3Xy/nJUjRAVJ4Z+BuqAZnN8UvXg+uqTEdJygp79fiV61FNV7ACqhiek4QvgdKfxyWJf3h+xM9PpvTUcJajo3B/vdqXDO+ajeg0zHEcIvSeGXp1USNDgHvWgO2rZNpwlKWmvst1+GokKs20ejHC6dXCZE0JLCL4dSCnX5dfD7Hti03nScoKSXfQ6bv0f1vwUV69vXcAjhy6Twz4Jq1xmi6mIv+hittek4QUWn70Z/+Ca0TEJddqXpOEL4NSn8s6BCQlCX94Odv8CWNNNxgoYuKsR+7XmoWg3r5vtOOzmfEOLsSOGfJdWpB0TGYC+YJXv5XqI/fgvSd2Pd8gCqZm3TcYTwe1L4Z0mFhqJ6D4Rft8lYvhfotDXorz9D9bgW1aKt6ThCBAQp/ApQyd0hJhZ7wXuyl+9BOjvTOTFafAKq702m4wgRMKTwK0A5HKirBsGenfDDatNxApIuKcGe/hxoG+vOf/jsXceE8EdS+BWkOlwG9Rpgf/Ie2i41HSfg6HkzYddW571p69Y3HUeIgCKFX0EqJAR17VBI341e9bXpOAFFb1yLXjzPeUOTJO/cm1aIYCKFXwkq6RI4tzF63rvowgLTcQKCzvwd+43JznH7gbeajiNEQJLCrwSlFNbA2+BwDvrLuabj+D1dWIj9n4lgWVh3PYwKrWI6khABSQq/ktT5TVGJndBfzkPnZpuO47e01uh3pzrPt799NCq6nulIQgQsKXwXqOuGgV2Knv+u6Sh+S3/9GXr1MtTVQ1AtEk3HESKgSeG7QMXEorpdjV65FP3rNtNx/I7+eSP6g9ehVTvnRW1CCI+SwneRumoQ1KyD/e4r6FI5TfNs6YMZ2K8+C/UaYN3+IMqSH0UhPE3+lblIRVTFGnw77NnlnMZXlMs+noc95d+gNdY9j6IiqpqOJERQkMJ3h8RO0CIRPf9d9CE5gHsm2i7l8AuPQ8Y+55W0deNMRxIiaMitg9xAKYU19E7s8fegP3gdNWKM6Ug+xT6YAQtmoXNzIDeHogPpqKEjUM0uMh1NiKAihe8mKiYW1Xugcy9/wypU246mI/kE+2AGevI4OJhR9pyqWh1kBkwhvE6GdNxI9eoH8QnOA7hHck3H8Q0LZp1Q9gA6/5jzeSGEV0nhu5FyOLBuGwXH87FnTpUplME5jFOB54UQniOF72YqLh7V90ZIW4NeudR0HPNOM02Cqh3p5SBCCCl8D1Ap10DjFuj3p6P/MpwRTHTmfvhtO/zlHPuQeg3g2usNpRIieEnhe4CyLKxb7gfLwp72DLq4yHQkr9PZmdgvPAZouG88qkMXuLAlqkMXaj/+f1gxsaYjChF05CwdD1HR9bBuHYU95d/o2dNRN91jOpLX6Jws7En/hPw8rAefRJ1zPjRvU/a6IzoasrIMJhQiOMkevgep1u1RV/RHf7sYe8VXpuN4hc7Nxp70KBw7gjXqX86yF0L4BCl8D1PXXg9NWqFn/Qe9e4fpOB6lsw9iP/coHM7Fuv9x1LmNTUcSQvwPKXwPUyEhWHc8BDVqYb/8JDrrgOlIHqEz0rGfHQNHD2M98DgqoYnpSEKIv5DC9wJVszbW/eOhuAj7pSfQecdMR3IrvfdX7GcfhuJirIcmoM5vajqSEOIUXCr8VatWMXr0aAYNGsTOnTtP+760tDTuv/9+7r33XubPn+/KKv2WiovHGvkoHNyP/coEdHGx6UhuobekYT83FhyhWP94GhV/nulIQojTcKnwGzVqxEMPPUTTpqffo7NtmzfeeINHHnmEyZMns2LFCvbt2+fKav2WurAF6ub7YdtP2P952u9L3/52MfZL/4LIGKwxz6BiG5qOJIQ4A5cKv2HDhsTFnXl62x07dhAbG0u9evVwOBwkJyezbt06V1br16wOXVA3jIRN6/8off87R1/bpdhz3ka/MwWatHKWfVSM6VhCiHJ4/Dz8nJwcoqKiyh5HRUWxffv2U743NTWV1NRUACZOnEh0dLRHMjkcDo8t+6xcdwP5NWpw9D/P4HjteWqPeRoVFnbWHzeZ3z58iMOTn6Ro4zoievWlxh2jUCEV+zEy/vV3A3/fBn/PD/6/DSbyl/sv9cknnyQ39+SZHwcPHky7du3cGiYlJYWUlJSyx1keujgnOjraY8s+a207oW66h6KZU8l89C6skY+gatY+q4+ayq93bcV+9Rk4ctiZvXNPsg9VfFZQn/j6u8jft8Hf84P/b4On8p9p1KXcwn/sscdcWnlkZCTZ2X/eBSo7O5vISJk4C8Dq3BMdURX7zRexn3oI695xqAbxpmOdRJeWohd9jP70fagdhfXwM3JBlRB+yOOnZSYkJLB//34yMzMpKSlh5cqVJCUleXq1fkMlXYL196egpBj7mX+g01abjnQCnZGO/cwY9IJZqLbJWI9NlrIXwk+5VPhr165lxIgRbNu2jYkTJzJhwgTAOW7/9NNPAxASEsKtt97KhAkTGDVqFB07dqRRo0auJw8g6tzGWI88DzH1sac+hf3OFHTBcaOZdHER9qfvYz9xPxz4HXXHQ1jD/46qVsNoLiFE5Sntw3fp+P333z2yXF8d+9PFxehP3kN/ORdiYrGG3Ydq3Pyk93kyv9YaNq7F/vANOJiBSroENeg2VO2o8j98lnz1618R/r4N/p4f/H8bfHIMX3iPCg1FXTcM3TLROa7/3Fhom4x13TBU3foeXbfWGn7agP3JbPh1G9RvhDX6SVTT1h5drxDCe6TwfZBq3ALrX1PRS+ahF83B3rgW1bknqttVqPruvbhJFxWiv1+J/vozZ9FHxqBuGInqlIJyyI+HEIFE/kX7KBUWhrpqMPqSHuhPZqO/W4xe9jk0b0PBldeh489HhVet1LJ1SQns/NlZ9GuWQX4e1K2PuvFuVHI3lCPUvRsjhPAJUvg+TtWOQt10D7rPDejlX6KXLeLwc/+EEAdc2ALVpDWq4d+gQTzUiUYpdcLntdZwJBf2/Ybe9xv6162wJQ2O54PDgWqbjOrc03k3qr98VggRWKTw/YSqWRt11SD0Ff2pdfB3cr9NRf+4Fj33bcqOuoc4IDzC+ceynHvu+Xmg7T8XFBntPBDbIhGatkZFVO63BCGE/5HC9zMqJIQqLdpgxTaCAbeg845C+h7073sgOxMKj0PBcSgtharVnX9q1kY1PAcanIOqXtP0JgghDJHC93OqWg1o3PyUp28KIcT/khugCCFEkJDCF0KIICGFL4QQQUIKXwghgoQUvhBCBAkpfCGECBJS+EIIESSk8IUQIkj49Hz4Qggh3Cco9/Affvhh0xFcIvnN8/dt8Pf84P/bYCJ/UBa+EEIEIyl8IYQIEiGPP/7446ZDmHDeeeeZjuASyW+ev2+Dv+cH/98Gb+eXg7ZCCBEkZEhHCCGChBS+EEIEiaC8Acr777/P+vXrUUpRq1YtRo4cSWRkpOlYFTJz5ky+//57HA4H9erVY+TIkVSrVs10rLO2atUqPvroI9LT03nqqadISEgwHemspKWlMWPGDGzbpnv37vTp08d0pAp55ZVX2LBhA7Vq1WLSpEmm41RYVlYWU6dOJTc3F6UUKSkpXHnllaZjVUhRURHjx4+npKSE0tJSLr74YgYOHOidlesglJeXV/b3zz77TL/66qsG01ROWlqaLikp0VprPXPmTD1z5kzDiSpm7969Oj09XY8fP17v2LHDdJyzUlpaqu+55x6dkZGhi4uL9UMPPaT37t1rOlaF/PTTT3rnzp169OjRpqNUSk5Ojt65c6fWWuv8/Hx93333+d33wLZtffz4ca211sXFxXrs2LF669atXll3UA7pVK365427CwsLUUoZTFM5rVu3JiQkBIDGjRuTk5NjOFHFNGzYkLi4ONMxKmTHjh3ExsZSr149HA4HycnJrFu3znSsCmnWrBnVq1c3HaPS6tSpU3ZmS0REBA0aNPC7n32lFOHh4QCUlpZSWlrqtQ4KyiEdgNmzZ7N8+XKqVq3K+PHjTcdxydKlS0lOTjYdI+Dl5OQQFRVV9jgqKort27cbTBTcMjMz+fXXXzn//PNNR6kw27YZM2YMGRkZ9OrViwsuuMAr6w3Ywn/yySfJzc096fnBgwfTrl07hgwZwpAhQ5g3bx5ffPGF98bQKqC8bQCYO3cuISEhdO7c2dvxynU2+YWojIKCAiZNmsTNN998wm/s/sKyLJ577jny8vJ4/vnn2bNnD/Hx8R5fb8AW/mOPPXZW7+vcuTNPP/20TxZ+eduwbNkyvv/+e8aNG+eTw1Jn+z3wF5GRkWRnZ5c9zs7O9ruD/YGgpKSESZMm0blzZzp06GA6jkuqVatG8+bNSUtL80rhB+UY/v79+8v+vm7dOr8bSwbn2SILFixgzJgxhIWFmY4TFBISEti/fz+ZmZmUlJSwcuVKkpKSTMcKKlprpk2bRoMGDbjqqqtMx6mUI0eOkJeXBzjP2Pnxxx9p0KCBV9YdlFfaPv/88+zfvx+lFNHR0QwfPtzv9tTuvfdeSkpKyg7AXXDBBQwfPtxwqrO3du1a3nzzTY4cOUK1atX429/+xqOPPmo6Vrk2bNjA22+/jW3bdO3alX79+pmOVCEvvvgiW7Zs4ejRo9SqVYuBAwfSrVs307HO2i+//MK4ceOIj48v+612yJAhtG3b1nCys7d7926mTp2KbdtorenYsSP9+/f3yrqDsvCFECIYBeWQjhBCBCMpfCGECBJS+EIIESSk8IUQIkhI4QshRJCQwhdCiCAhhS+EEEHi/wEYRpDaX8X3gQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1IUVIA1JN7x3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "cb001c7a-3302-477e-b1e0-848da901c94a"
      },
      "source": [
        "# Datos\n",
        "x = np.linspace(-np.pi, np.pi, 15)\n",
        "y = np.array([np.sin(i) for i in x])\n",
        "\n",
        "# Puntos generados por el polinomio de Lagrange\n",
        "x_test, y_pol = interpolacion_lagrange(x, y)\n",
        "\n",
        "# Gráfica\n",
        "plt.plot(x_test, y_pol)\n",
        "plt.scatter(x, y)\n",
        "plt.legend(['Lagrange', 'Datos'], loc='best')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f292fe15668>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ly5buaQUFBYwbNw6bzUbv3r1p3759qcsmJye7f1FPnTq1xKDrx44dw+6FMUu9sQ4reSN/aGioZYPa2+12y7btDf6cv8h5nPT3XsN+RVNqPj6Zk4vmUOQ8js0RRfVBw7HHuAYt8ed9uBgXlT8qisLJr5O7YBZFzuMom43TP/1A6Jpl1Hr8WZRSvglbBl+/Bz791lu/fj3XX389xlmDRcyYMQOHw8GxY8eYPHkyDRs2dI/xe7aEhAQSEhLcj88dvScvLw+bzeZRPl+OUFYRvJU/Ly/PslG2An2EL3/Nr00T85VJkHcSc9hjnKhWHYa6mhpNIBPgTG5/3YeLddH57VXcrwGA+uwj8pPmkXZlc4xOCedZsOL5eoQyj88acjgcpKf/2fmUnp6Ow1F6O9uGDRvo1KlTieUB6tatS/Pmzdm/f/8l5TAMI6C/xP1FYWFhsUItKge9agn8shU14AHUZQ2sjuOX1K13QbOW6AVvoYPsNFKPjwhiY2M5cuQIqampOBwONmzYwCOPPFJivkOHDpGbm0uzZs3c03JycggNDSUkJISsrCx27txJ7969LylH1apVycvLIz8//5IP60JDQ8nPz7+kZf2Bp/m11hiGQdWqVb2YSlhN/74HnTQPru2AurGH1XH8ljJsGMMew3z2Ecx3pmP883mU4VkrQ6DwuBDYbDaGDRvGlClTME2Trl270qBBAxYuXEhsbCxxcXGAq1moY8eOxb6kDx06xKxZszAMA9M0SUxMLLOT+UKUUlSrVs2jfQmaQ2IRNHRBAeY7r0B4TYyhoyxv+/Z3KrIOavCD6NnT0Ss+QfW0/sQWX1A6QO/JevjwYa+vM9C/SAM9PwT+PvhbfnPx++gVizAenoBq1e6ilvG3fSgvT/NrrdGzpqF//BbjqRdRDWO9mO7iBFwfgRDCP+m9O9ErF6M6xV90ERCu1gV190MQXhNzzqvoIOh7lEIgRCWkT+djznkFIhyo/g9YHSfgqOo1MIY8BAf3oVd+YnWcCieFQIhKSC9fCEcPYfxtNCqsutVxApJqcz2q3Y3o5QvRh363Ok6FkkIgRCWjD+xDf3GmSagSjy/gC2rQcKgWhvnu/6Er8RggUgiEqES0WYT53mtQvQaq3zCr4wQ8VaMWavCDsH8X+stlVsepMFIIhKhE9JfL4bfdqEEPoqrXsDpOpaDiboBr2qE//QCdnmZ1nAohhUCISkIfP+a6cKxVe1RcpwsvIC6KUgpj8IOgNeaCmQToGffnJYVAiErC/PAtOPOlJReOeZeKrIO6YzBs3Qg/fmd1HK+TQiBEJaC3fA9bN6J6DUI5oq2OUymp+F5QvzHmglnos2/hXQlIIRAiwOn8fNfRwOUNXV9WokIoux1j6Eg44UQvXWB1HK+SQiBEgNOffwzpqRhDHkIF+Hga/k41+QvqhpvRa5ZVqmsLpBAIEcD00YOuawY6dEM1a2F1nKCg7rwHqoZVqo5jKQRCBCitNebCt6FKKKrvvVbHCRqqRk3UnXfDzm3oTeutjuMVUgiECFQ/bYKfN6PuGIiqWdvqNEFF3dQDGjZBfzQbnXfK6jgek0IgRADSBQWYH70NlzVAdelpdZygowwbxqAHITPd1UcT4LzSs7RlyxbmzJmDaZrEx8eTmJhY7Pm1a9cyd+5c97CUt9xyC/Hx8e7nFi9eDECfPn3o0qWLNyIJUanpLz+F1CMYjz0rHcQWUVdehbq+C3r1UvSN3VHRJcdaDxQef4JM02T27Nk888wzREZGMn78eOLi4kqMNNaxY0fuv//+YtNycnJYtGgRU6dOBWDcuHHExcURHh7uaSwhKi2d6UQv/8h1BXELuamcldSd96A3f4v+5D3UiLFWx7lkHjcN7d69m5iYGOrWrYvdbqdjx46kpKRc1LJbtmzhmmuuITw8nPDwcK655hq2bNniaSQhKjWdNBeKCjD6y03lrKYcUahb7kL/sB7963ar41wyjwuB0+kkMjLS/TgyMhKn01livu+//54nnniCl156yT0E27nLOhyOUpcVQrjo3/eiN6xBdbsdVaf0YQeFb6nud0JEFObCt9GmaXWcS+KTxsW2bdvSqVMnQkJCWL16NW+88QaTJk0q1zqSk5NJTk4GYOrUqURFRXk9p91ur5D1+kqg54fA34eKzK+1JvPVZykIr0nUPQ9hVNDdReU9KL9T9z5M1vR/Eb5tI9Xib/d4fb7eB48LgcPhID093f04PT3d3Sn8hxo1/vzAxsfHM2/ePPeyO3bscD/ndDpp3rx5qdtJSEggISHB/bgiBnYO9kG7/UGg70NF5tdbN2Ju+wE1cDjOU/lwKr9CtiPvQfnpq9pA42ZkzXuTnL+2RoVW9Wh9ATd4fWxsLEeOHCE1NZXCwkI2bNhAXFxcsXkyMjLc/9+0aZO7I7l169Zs3bqVnJwccnJy2Lp1K61bt/Y0khCVji4sxFw0B+rWQ3W+xeo44hxKKYx+wyDTiV691Oo45ebxEYHNZmPYsGFMmTIF0zTp2rUrDRo0YOHChcTGxhIXF8eKFSvYtGkTNpuN8PBwRo4cCUB4eDh33XUX48ePB6Bv375yxpAQZzHTjsLS+eh9uyD1MAwdKaeL+inVtDm0uR69YhFFB/ZCbg6qtgN6D8Hw81NLlQ7Qm2UcPnzY6+uUQ2LrBfo+eDO/mXYUPX0ipB09awN1UY8/V6FfLPIeXLqiX7bCyxOKT4yOQY2ZXK73LOCahoQQFWTp/OJFAOD4Mdd04ZfU+uSSE88c1fkzKQRC+CmdWfqp1GVNF9YL1PdMCoEQfkrVdpRrurBeoL5nUgiE8FO6Y3zJidEx0HuI78OIi9N7iOs9OltUXb9/z+T0AyH81bqVUCUUWl4bUGegBDMjOgZzzOTiZ3rd1s/v3zMpBEL4Ib1/F2zegOo1EOOOwVbHEeVgRMfAA/9wXfsxcSR8uQzdKR5l2KyOViZpGhLCD5lL5kJ4DdTNiReeWfglZbejEu+GQ7+hv//a6jjnJYVACD+j//sT7NiCurUfqlqY1XGEB1TcDa6RzJbORxcWWB2nTFIIhPAjWmvMxe9DRBSq621WxxEeUoaBkTgU0lPR36y2Ok6ZpBAI4U+2fg/7fkX1GogKqWJ1GuENLa+FK5ujl3+Ezq+YGwV6SgqBEH5CmyZm0nzXjeVKO3VUBCSlFMadd8MJJ3rt51bHKZUUAiH8hE75Dxz6DXXHIJTNf88wEeWnmrWEFm3QKxahT520Ok4JUgiE8AO6qAj96QKo18jVwSgqHSPxbsjNRq9OsjpKCVIIhPAD+ruvIPUwRu8hKEP+LCsjdUVTuLYDevVSdG621XGKkU+cEBbThQXoZR9Coyuh9XVWxxEVyLhjMOTnob9YYnWUYqQQCGEx/c1qSE/FSLwbpZTVcUQFUmea/vSa5ejsE1bHcfPKLSa2bNnCnDlzME2T+Ph4EhOLXw25fPlyvvzyS2w2GzVr1uShhx4iOjoagAEDBtCwYUPANRjD2LFjvRFJiICgC06jP/sIrrwKWrSxOo7wAdVrEHrTevTKxah+91kdB/BCITBNk9mzZ/PMM88QGRnJ+PHjiYuLc49LDHDFFVcwdepUQkNDWbVqFfPmzWPMmDEAVKlShWnTpnkaQ4iApL9eBZlOjGFj5GggSKjL6qOu64xe+xm6eyKqVoTVkTxvGtq9ezcxMTHUrVsXu91Ox44dSUlJKTZPy5YtCQ0NBaBp06Y4nf49SIMQvqBP56NXfAzNWsJfr7E6jvAh1WsAFBaiVyyyOgrghSMCp9NJZGSk+3FkZCS7du0qc/41a9bQunVr9+OCggLGjRuHzWajd+/etG/fvtTlkpOTSU52DQM3depUoqKiPI1egt1ur5D1+kqg54fA34fy5M9dtpCcExlEPPE/VDnTVOoPguk9sExUFCe69SRv3RdEDHoAW2Tx99/X++DT21B//fXX7N27l3/961/uaTNmzMDhcHDs2DEmT55Mw4YNiYkpee/uhIQEEhIS3I8rYmBnGbTbeoG+DxebX+fnYy56D/56DVkxDcCP9jlY3gOr6W694KvPSZ8/C2Pwg8WeC7jB6x0OB+np6e7H6enpOBwlh2X76aefWLJkCU8++SQhISHFlgeoW7cuzZs3Z//+/Z5GEsLv6XWfQ1amjDUQxFR0DKpjPPo/X6Cd1hYujwtBbGwsR44cITU1lcLCQjZs2EBcXFyxefbt28dbb73Fk08+Sa1atdzTc3JyKChw3Zo1KyuLnTt3FutkFqIy0vl56JWL4apWqKbNrY4jLKRu6wdao1da21fgcdOQzWZj2LBhTJkyBdM06dq1Kw0aNGDhwoXExsYSFxfHvHnzyMvL4+WXXwb+PE300KFDzJo1C8MwME2TxMREKQSi0tNrV0D2CYw7BlkdRVhMRdU9c1SwCn3LXSiHNX1FSmutLdmyhw4fPuz1dQZK22JZAj0/BP4+XCi/zs/DHP93aNAY25jJPkx28Sr7e+BvdHoq5tMjUDd2xxgyAgjAPgIhxMVzHw30Gmh1FOEnVGQdVKcE11GBM82SDFIIhPARnZ+H/mIxNG+NulL6BsSf1G19AdArPrFk+1IIhPARvU6OBkTpVGQdVMdu6G9WWXIGkRQCIXxA5+f/eaaQHA2IUvx5BpHvjwqkEAjhA/rrlWeOBuRMIVE6FVUX1aEb+j+rKPJxX4EUAiEqmD6d7+ob+Os1ct2AOC91Wz8wi8hdPM+n25VCIEQF0/9ZBScyMG6XvgFxfio6BtWhK6dWL0Vn+u7mnFIIhKhAuuC0q823WUvUX1paHUcEAHVbfygsQq/y3ShmUgiEqED6m9Wu8QZuH2B1FBEgVJ3LqHpTd/S6FeisTJ9sUwqBEBVEFxS4zgu/srmMNyDKpXrfv0FBIXpVkk+2J4VAiAqiN3wJGccxeg2Q0cdEudjrNUS1vxG99nN0dlaFb08KgRAVQP8x+lSTv8BVrS+8gBDnUD37w+l8dPLSCt+WFAIhKoD+7itIT8W4faAcDYhLoi5rgIq7Ab1mOTo3u0K3JYVACC/TRUXozz+GRldCy2utjiMCmOrZH/JOoZOXVeh2pBAI4WX6+3WQdhTjdukbEJ5R9RrBtR3QXy5Dn8ytsO1IIRDCi9xHA/UbQ6v2VscRlYDRsz+cykWvWV5h2/DK4PVbtmxhzpw5mKZJfHw8iYmJxZ4vKCjg9ddfZ+/evdSoUYPHHnuMOnXqALBkyRLWrFmDYRjcd999tG5dMR1rZtpRWDofnelE1XZA7yEY0TEVsi0RfP74fKUf+g2OHYLBD8rRgPAK1TAW/noN+rOFFO340TWKmZe/vzw+IjBNk9mzZ/PUU08xffp01q9fz8GDB4vNs2bNGqpXr85rr71Gz549mT9/PgAHDx5kw4YNvPzyyzz99NPMnj0b0zQ9jVQyY9pR9PSJrkP2ndvQ369DT5/o+uMVwkNnf76KDu53TVyVJJ8v4RVm2lE4eggKC2HXjgr5/vK4EOzevZuYmBjq1q2L3W6nY8eOpKSkFJtn06ZNdOnSBYDrr7+en3/+Ga01KSkpdOzYkZCQEOrUqUNMTAy7d+/2NFJJS+fDuS/amV9wQnistM/X8WPy+RLesXQ+ZKYXn+bl7y+Pm4acTieRkZHux5GRkezatavMeWw2G2FhYWRnZ+N0OmnatKl7PofDgdNZ+o2WkpOTSU5OBmDq1KlERUVdfMbcbApKmW7PzcZx1nrsdnu51utvAj0/BOY+XOznK1AE4ntwtkDPD8X3wRefL6/0EfhCQkICCQkJ7sflGdjZrF6j1OmF1WsUW0+gDXp9rkDPD4G5Dxf7+QoUgfgenC3Q80PxffDm56vCBq93OBykp/952JKeno7D4ShznqKiIk6ePEmNGjVKLOt0Okss6xW9h8C5HStnOlyE8JS+YzDYz/lNFR0jny/hHaV9f3n58+VxIYiNjeXIkSOkpqZSWFjIhg0biIuLKzZP27ZtWbt2LQDfffcdLVq0QClFXFwcGzZsoKCggNTUVI4cOcKVV17paaQSjOgY1JjJqOs6Q+NmrolXtZKzhoRXGMfOdOQ1bkZIy2tR13VGjZksny/hFcW+v/5ydYV8vjxuGrLZbAwbNowpU6ZgmiZdu3alQYMGLFy4kNjYWOLi4ujWrftS5/8AABtOSURBVBuvv/46o0ePJjw8nMceewyABg0a0KFDBx5//HEMw+D+++/HMCrm0gYjOgYe+AcA5jvT0Slfo/vcg6pZu0K2J4KD1hpz2YcQWQfjyak4YmICvllC+J+zv78qgtJa6wpbewU6fPjwJS+rjx7EnPgwqnsiRt973dMDvW0x0PND4O2D3vEj5vRJqKEjMW66JeDylybQ9yHQ80PF7UOF9REEIhVTH9XOd7d4FZWT+2jAEYXqEG91HCEuWVAWAgDVs9+ZW7x+anUUEah2boPdv6BuuQsVEmJ1GiEuWfAWgssbotp2Qq9Zhs7NsTqOCEDm8oVQy4G64WarowjhkaAtBHDWLV6/lKMCUT761+2wcxvqljtRIVWsjiOER4K7ENS/wnWL1+SKvcWrqHzM5R9CzdqoG2+xOooQHgvqQgBg9Bxw5havFTvwg6g89O5f4JetqB53okJDrY4jhMeCvhCohk2gVXv06k8x5ahAXARz+YdQoxaq861WRxHCK4K+EAAYvQbCyRxOfb7I6ijCz+m9O2H7j6juiajQqlbHEcIrpBAAqtGVcHUcuUsXoPNOWh1H+DFz2YcQXgPV5TarowjhNVIIzjB6DULnZKHXfGZ1FOGn9L5d8PMPqJsTUVWrWR1HCK+RQnCGatyUKtd2QK9OQuedsjqO8EPmsgVQvQaqa0+rowjhVVIIzhI+YBjkZKO/+tzqKMLP6H27YNsm1M29UdXCrI4jhFdJIThLSLMW0KINetUSOSoQxbiPBrrdbnUUIbxOCsE5jF6DICcLvVaOCoSL3i9HA6Jyk0JwDhX7V2h5LfoLOSoQLuayD+VoQFRqUghK4T4q+ErOIAp2ev8u+ClFjgZEpebRCGU5OTlMnz6dtLQ0oqOjGTNmDOHh4cXm2b9/P2+99RanTp3CMAz69OlDx44dAXjjjTfYsWMHYWGuP7BRo0ZxxRVXeBLJK1STv0DLtq6+gq63oarKF0CwMj+VvgFR+XlUCJKSkrj66qtJTEwkKSmJpKQk7r777mLzVKlShYcffpjLLrsMp9PJuHHjaNWqFdWrVwdg6NChXH/99Z7EqBDGHYMwn38CveYz1G39rI4jLKD37nT1Ddw5VI4GRKXmUdNQSkoKnTt3BqBz586kpKSUmOfyyy/nsssuA8DhcFCrVi2ysvx/VDDVuBlcHYdelYQ+JVcbByPz0w8gvCaqm1w3ICo3j44ITpw4QUREBAC1a9fmxIkT551/9+7dFBYWUrduXfe0BQsWsGjRIlq2bMmQIUMIKWOkp+TkZJKTkwGYOnUqUVFRnkQvld1uL7begnsewvnP+6n23ZeE97vP69vztnPzByJ/2YfT/91GxvYfCb9nJNXrN7zo5fwlvycCfR8CPT/4fh8uWAiee+45MjMzS0wfOHBgscdKKZRSZa4nIyOD1157jVGjRmEYrgORwYMHU7t2bQoLC5k5cyZLly6lb9++pS6fkJBAQkKC+3FFDOxcYsDo2tHQqj25SR9w6rquqLDwshf2AzJot/cUvT8DatTiZPsunCpHHn/J74lA34dAzw++H7z+goVgwoQJZT5Xq1YtMjIyiIiIICMjg5o1a5Y638mTJ5k6dSqDBg2iWbNm7ul/HE2EhITQtWtXli3zvzEBjN5DMCc/il69FNV7iNVxhA/oX7e7xhvoN0zuMCqCgkd9BHFxcaxbtw6AdevW0a5duxLzFBYW8uKLL3LTTTeV6BTOyMgAQGtNSkoKDRo08CROhVANGkPbjujkT9E5/t+3ITyjtcZcOg9qRch4AyJoeNRHkJiYyPTp01mzZo379FGAPXv2sHr1akaMGMGGDRv45ZdfyM7OZu3atcCfp4m++uqr7o7jRo0aMXz4cM/2poIYvQZjbv4WvWoJqs/frI4jKtIvW+HX7ahBw2X0MRE0lNZaWx3iUhw+fNjr6zxfu5z51ovoLd9jvPAWqmZtr2/bG6Rt1DNaa8wX/gknnBj/MxNVxokL5yPvgfUCPT/4vo9Ariy+SKrXICgsQK+QUcwqrZ82wb5fUbcPvKQiIESgkkJwkVRMPVTHePTaz9HONKvjCC/TpunqG4iOQXXoZnUcIXxKCkE5qNtdp8zq5QstTiK87sdv4cA+1B2DUHaPus6ECDhSCMpBRUajOt+KXp+MPub9PgphDV1UhJk0Dy5rgGp/k9VxhPA5KQTlpG7rC/YQ9KcLrI4ivER/uwaOHsK4cyjKsFkdRwifk0JQTqpmBCq+Fzrla/TBfVbHER7SBaddRb1xM2h9ndVxhLCEFIJLoHr0gWphmIvnWh1FeEivXQEZx11HA+e5RYoQlZkUgkugqoejbukL2za5bkcgApLOO4n+/GO4qhXqqlZWxxHCMlIILpHqdjvUdmAufo8AvSYv6OlVSZCThXHnPVZHEcJScp7cJVKhoaheg9Bz38Cc9hQYBqq2A3oPwYiOsTqeKIOZdhSWzkcfPwb7foWW16IaN7U6lhCWkkLgAd2sJdhssMvVPKQB9u7EHDNZioEfMtOOoqdPhLSjf0489Dtm2lF5v0RQk6YhD6jlH0JRUfGJZ35xCj+0dH7xIgCQcVzeLxH0pBB4QGc6yzVdWEveLyFKJ4XAA6q2o1zThbXk/RKidFIIPNF7CJzbthwZ7Zou/I6+YzDYz7mraHSMvF8i6HnUWZyTk8P06dNJS0tzD0wTHl5yXN8BAwbQsKFrAPCoqCjGjh0LQGpqKq+88grZ2dk0adKE0aNHYw+gG34Z0TGYYya7zkJJPQL7d0Fsc+l49FPGgX2YhQWuq4irhMpZXkKc4dG3blJSEldffTWJiYkkJSWRlJTE3XffXWK+KlWqMG3atBLT582bR8+ePenUqROzZs1izZo1dO/e3ZNIPmdEx8AD/wDA/GAmet0K9O39UZf537CbwUwXFGB+8i7Ua4Qx7n/lnkJCnMWjpqGUlBQ6d+4MQOfOnUlJSbnoZbXWbN++3T2OcZcuXcq1vD9SvQZCaFXMj+dYHUWcQ3+1HNKOYvQbJkVAiHN4VAhOnDhBREQEALVr1+bEiROlzldQUMC4ceN4+umn2bhxIwDZ2dmEhYVhs7n+KB0OB05nYJ+9oWrUQt0+wHXriZ9/sDqOOENnZ6GXfwQt26JatLE6jhB+54JNQ8899xyZmZklpg8cOLDYY6VUmTftmjFjBg6Hg2PHjjF58mQaNmxIWFhYuYImJyeTnJwMwNSpU4mKiirX8hfDbrd7vF7d717Sv1kNn7xH5I3xKJvv+jy8kd9qFbEPWUve51T+KSL/PgZ7Bb8+8h5YL9Dzg+/34YLfUhMmTCjzuVq1apGRkUFERAQZGRnUrFmz1PkcDtfpeXXr1qV58+bs37+f6667jpMnT1JUVITNZsPpdLrnK01CQgIJCQnuxxUxsLO3BozWfe7BfON50hbPx+ja0wvJLo4M2l2SPvQb5srFqJt6kBlWEyr49ZH3wHqBnh8CbPD6uLg41q1bB8C6deto165diXlycnIoKCgAICsri507d1K/fn2UUrRo0YLvvvsOgLVr1xIXF+dJHP/R6jq4qhV66Qfo3Byr0wQtrTXmwrehahhKThEVokweFYLExER++uknHnnkEbZt20ZiYiIAe/bs4c033wTg0KFDjBs3jn/+8588++yzJCYmUr9+fQCGDBnC8uXLGT16NDk5OXTrVjkGDVdKYfS/H07mouX2Bdb58Vv4ZSuq92BUeOlHq0IIUDpA76F8+LD3xwz29uGY+cGb6LUrMSZOR9Vv7LX1lkUOif+kT+djThwFVathTHgFZfPNmULyHlgv0PNDgDUNifNTvYdA9XDM+TNlzAIf06uSID0VY+DffVYEhAhUUggqkKpeA9XnHti9A/39OqvjBA19/Bh6xcdwbUfUX6+xOo4Qfk8KQQVTnRLgiqboRXPQp05aHScomB++BcrAGHC/1VGECAhSCCqYMgyMwQ9CVib60wVWx6n09JbvYetGVK+BKEe01XGECAhSCHxANW6GurEH+stl6N/3WB2n0tL5+a6jgcsaoOLvsDqOEAFDCoGPqD73QI2amHNnoM2iCy8gyk1//pGrg/juh1ABdBdbIawmhcBHVPVwVP/7Yf8u9NoVVsepdPTB/egvFqM6dEU1a2l1HCECihQCH1Ltb4LmbdBL5qIz0q2OU2loswjz/dehWnVUP+kgFqK8pBD4kFIKY8gIKCpyjV0g1xZ4hf7qc9j3K2rg31E15ApiIcpLCoGPqTqXoXoPhi3foTettzpOwNPpqeglc123mG5/k9VxhAhIUggsoBJ6u64tWDATnV36GA7iwrTWmPNmALg6iMu4DboQ4vykEFhA2WwY9z7iuindgllWxwlY+pvV8PNm1J33oCLrWB1HiIAlhcAiql4j1O0D0Cn/Qf/4ndVxAo5OT0V/NBv+cjWq621WxxEioEkhsJC65S5o0Bhz7hvorJKjwInSadPEfPdV0GDc+wjKkI+xEJ6QvyALKbsd4/7H4dRJzPdfl7OILpJetwL++xOq/zBUVF2r4wgR8KQQWEzVa+S66njrRlebtzgvfeQgetEcaHkt6sbuVscRolLw6Dr8nJwcpk+fTlpaGtHR0YwZM4bw8PBi8/z888+899577seHDx/m0UcfpX379rzxxhvs2LHDPZD9qFGjuOKKKzyJFJBUfC/0tk3ohW+j/9ISVaf0wSOCnS4owHxrGlQJxfjbaDlLSAgv8agQJCUlcfXVV5OYmEhSUhJJSUncfffdxeZp2bIl06ZNA1yFY/To0bRq1cr9/NChQ7n++us9iRHwlGFg3Pso5rOjMd9+GePJF1D2EKtj+R29+D04sA/j4WdQtSOtjiNEpeFR01BKSgqdO3cGoHPnzqSkpJx3/u+++442bdoQGhrqyWYrJeWIwrhnNOz71XWBlChGb/sBnfwpqmtPVKv2VscRolLx6IjgxIkTREREAFC7dm1OnDj/xVHr16/n9ttvLzZtwYIFLFq0iJYtWzJkyBBCQkr/JZycnExycjIAU6dOJSoqypPopbLb7RWy3ovW4w6yftvFqRWfENbkLxTs+JEi53FsjiiqDxqOPeb8TUaW5/eCs/eh8OhhchfMovDYYYr2/oqtXkMiRzyBquK/PyQq23sQiAI9P/h+Hy5YCJ577jkyM0ue2jhw4MBij5VS522zzcjI4Pfffy/WLDR48GBq165NYWEhM2fOZOnSpfTt27fU5RMSEkhISHA/roiBnf1h0GvdaxBsTSF75r/hzFlEBUDeLz+hxkzGiI4pc1l/yO+pP/bBTDuKnj4R0o66nys6eZK0PbvO+xpYrTK9B4Eq0POD7wevv2AhmDBhQpnP1apVi4yMDCIiIsjIyKBmzbJv+PXtt9/Svn177GfdJ/6Po4mQkBC6du3KsmXLLhSn0lMhVSA6Bg7/XvyJtKOwdD488A9rgvna0vnFigAAGceD6zUQwkc86iOIi4tj3TrXoOzr1q2jXbt2Zc67fv16OnXqVGxaRkYG4LpnTEpKCg0aNPAkTuWRd6rUyTrT6eMg1ilrX4PpNRDCVzzqI0hMTGT69OmsWbPGffoowJ49e1i9ejUjRowAIDU1lePHj9O8efNiy7/66qtkZWUB0KhRI4YPH+5JnEpD1XZQ2qVlqrbD51ksE1Kl1MlB9RoI4SMeFYIaNWowceLEEtNjY2OJjY11P65Tpw4zZ84sMd+kSZM82Xzl1XsI7N1ZvGmkVoRrehDQmU44sBcMA0zzzyeiY4LmNRDCl2RgVz9kRMdgjpkMS+ej09Pg4H44fRpVVGh1tAqn8/Mw35jiah4b+TQq5Wt0ptN1JNB7iF93FAsRqKQQ+CkjOsbdKapTj2BOfRLz/57FGPdvVK0Ii9NVDG2anHj1f+C33Rgjn0K1agetyu53EkJ4h9xrKACoOpdhjJ4IWZmYrz2HLqMzOZBprdEfzSZ/wxpU33tRra+zOpIQQUMKQYBQjZtiDH8Sft+LOfN/0YUFVkfyKr3sQ/SXywi7YyDq5kSr4wgRVKQQBBDVqh1q6Ej4eTPmzGnowsrRZ2B+uQy9bAGqUzzh98rN5ITwNSkEAca4sTtq0HDY8h3m2y+ii4qsjuQRc91K9IdvQZvrUUMfliIghAWkEAQgo9vtqP73ww8b0LNfDtgjAzN5KXreDLg6DuPvT6BsNqsjCRGU5KyhAGXc3BvTLEIveheddwrjwSetjlQu5ucfu+6yem1HjL//Q267LYSF5IgggBk9+vzZZ/DyBMys89/91R9oswhz4dvoJXNR13XGGP5PKQJCWEwKQYAzbroFY8RY+H0vzqdGoI8dtjpSmXTeScw3nneNKxDfCzXsMWkOEsIPSCGoBNS1HTDGPIt5IgNzyj/QW88/QJAV9PFjmP87Hn7+ATVkBMbAv6MMKQJC+AMpBJWEataSyJfmQHQM5uvPYS79AG36xxlFetM3mJMfg/RjGKMnYnS5zepIQoizSGdxJWKrcxnG2Kno+W+il3+I3vEjxr2Poi6rb0kenZ+HXvg2+j+roHEz15lBcq8gIfyOFIJKRlUJhXsfgeat0QtmYU5+FJV4NyrhDrQzzXUjOy/fxM08M2jOH+vVdwzGOPQb5odvQcZx1K13oe4YgrLLx00IfyR/mZWQUgp1XWf0X6/BnDcDvWgOeu3ncDofslzDjmqAvTsxLzD85YWcO6SkBvjxO8zT+VCvEcYDL6CaNj/vOoQQ1pI+gkpM1YrAGPkUxqinICfbXQTc/hj+0hOlDSl5Oh8axmI8M12KgBABwKMjgm+//ZaPP/6YQ4cO8fzzzxcbjOZsW7ZsYc6cOZimSXx8PImJrpuKpaam8sorr5CdnU2TJk0YPXp0sTGNheeUUtD6emjYBH79ucTz+twv8XLQuTno/btLf7JamDQFCREgPDoiaNCgAU888QRXXXVVmfOYpsns2bN56qmnmD59OuvXr+fgwYMAzJs3j549e/Laa69RvXp11qxZ40kccR4qIrL0J/bupGjSw5iL5qB/2IA+cqDUW1Zoswh9IgO9/UfMTz+gaPpEzCfugWOHSt+eDCkpRMDw6Cdb/foXPhtl9+7dxMTEULduXQA6duxISkoK9erVY/v27Tz66KMAdOnShY8//pju3bt7EkmUpbThLyOioENX2PcrOnkZumiJa7rNBmHhEBIC9iqQn+dqVtJnho1UBtRrhOrSE92sBXw0G44f+3O9MqSkEAGlwo/dnU4nkZF//hqNjIxk165dZGdnExYWhu3MlaUOhwOn01nmepKTk0lOTgZg6tSpREVFeT2r3W6vkPX6ynnzR0VROPl1chfMosh5HJsjiuqDhmOPuRwAnXeKwkO/UXhgP0UH92PmZqNPn0afzkeFVsUWEYkREYWtXkNCmjbHCKvuXnXh1deWuV6v7kMACPT8EPj7EOj5wff7cMFC8Nxzz5GZmVli+sCBA2nXznfDCCYkJJCQkOB+fPz4ca9vIyoqqkLW6ysXzG+vAkMfBsAEMgHOnr9WlOtfy7gSixYbBufkKde/i12vN/fBzwV6fgj8fQj0/FBx+3D55aX/QLtgIZgwYYJHG3Y4HKSnp7sfp6en43A4qFGjBidPnqSoqAibzYbT6cThkHZlIYTwtQo/fTQ2NpYjR46QmppKYWEhGzZsIC4uDqUULVq04LvvvgNg7dq1xMWV/CUqhBCiYnlUCDZu3MiIESP49ddfmTp1KlOmTAFc/QIvvPACADabjWHDhjFlyhTGjBlDhw4daNCgAQBDhgxh+fLljB49mpycHLp16+bh7gghhCgvpbXWVoe4FIcPe/92y4Hethjo+SHw9yHQ80Pg70Og5wff9xHIlcVCCBHkpBAIIUSQk0IghBBBTgqBEEIEuYDtLBZCCOEdckRwlnHjxlkdwSOBnh8Cfx8CPT8E/j4Een7w/T5IIRBCiCAnhUAIIYKc7V//+te/rA7hT5o0aWJ1BI8Een4I/H0I9PwQ+PsQ6PnBt/sgncVCCBHkpGlICCGCnBQCIYQIcjK6+Dk+/PBDNm3ahFKKWrVqMXLkyIAaJ2Hu3Ln88MMP2O126taty8iRI6levfqFF/Qj3377LR9//DGHDh3i+eefJzY21upIF2XLli3MmTMH0zSJj48nMTHR6kjlMmPGDDZv3kytWrV46aWXrI5TbsePH+eNN94gMzMTpRQJCQncdtttVse6aKdPn2bSpEkUFhZSVFTE9ddfT//+/X2zcS2Kyc3Ndf//s88+0zNnzrQwTflt2bJFFxYWaq21njt3rp47d67FicrvwIED+tChQ3rSpEl69+7dVse5KEVFRfrhhx/WR48e1QUFBfqJJ57QBw4csDpWuWzfvl3v2bNHP/7441ZHuSROp1Pv2bNHa631yZMn9SOPPBJQ74FpmvrUqVNaa60LCgr0+PHj9c6dO32ybWkaOkdYWJj7//n5+SilLExTfq1atXKPA92sWbPzjgPtr+rXr1/m7XL91e7du4mJiaFu3brY7XY6duxISkqK1bHKpXnz5oSHh1sd45JFRES4z7SpVq0a9erVC6jPv1KKqlWrAlBUVERRUZHPvn+kaagUCxYs4OuvvyYsLIxJkyZZHeeSrVmzho4dO1odIyg4nU4iIyPdjyMjI9m1a5eFiYJbamoq+/bt48orr7Q6SrmYpsnYsWM5evQoPXr0oGnTpj7ZblAWgueee47MzMwS0wcOHEi7du0YNGgQgwYNYsmSJaxcudJ37XQX6UL5ARYvXozNZuPGG2/0dbyLcjH7IMSlyMvL46WXXuLee+8tdoQfCAzDYNq0aeTm5vLiiy/y+++/07BhwwrfblAWggkTJlzUfDfeeCMvvPCC3xWCC+Vfu3YtP/zwAxMnTvTbpq2LfQ8ChcPhID093f04PT09oE4yqCwKCwt56aWXuPHGG7nuuuusjnPJqlevTosWLdiyZYtPCoH0EZzjyJEj7v+npKQEXFv1li1bWLp0KWPHjiU0NNTqOEEjNjaWI0eOkJqaSmFhIRs2bCAuLs7qWEFFa82bb75JvXr1uP32262OU25ZWVnk5uYCrjOIfvrpJ+rVq+eTbcuVxed48cUXOXLkCEopoqKiGD58eED9shs9ejSFhYXuTr+mTZsyfPhwi1OVz8aNG3nnnXfIysqievXqXHHFFTz99NNWx7qgzZs3895772GaJl27dqVPnz5WRyqXV155hR07dpCdnU2tWrXo378/3bp1szrWRfvvf//LxIkTadiwoftIeNCgQVx77bUWJ7s4v/32G2+88QamaaK1pkOHDvTt29cn25ZCIIQQQU6ahoQQIshJIRBCiCAnhUAIIYKcFAIhhAhyUgiEECLISSEQQoggJ4VACCGC3P8HnvSjQfzhcRkAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_xkis6DOOM_w",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "44668f9d-bf29-466e-f9c4-33c525c97d0b"
      },
      "source": [
        "# Datos \n",
        "x = np.array([-3.2300, 2.0000, -1.0023, 0.0000, 2.1230, \n",
        "              -3.5120, 0.1223, 5.6420, -2.2574, 5.3410])\n",
        "y = np.array([-3.4360, 3.4120, 0.9300, 1.5960, 0.0000, \n",
        "              0.9315,  4.1230, 0.0140, -0.2320, 2.123])\n",
        "\n",
        "# Puntos generados por el polinomio de Lagrange\n",
        "x_test, y_pol = interpolacion_lagrange(x, y)\n",
        "\n",
        "# Gráfica\n",
        "plt.plot(x_test, y_pol)\n",
        "plt.scatter(x, y)\n",
        "plt.legend(['Lagrange', 'Datos'], loc='best')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f292fdc96a0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E8QHLGVhOqTL",
        "colab_type": "text"
      },
      "source": [
        "Unidad 3: Diferenciación e integración numérica\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r6-z-xRDtd4h",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Método del trapecio\n",
        "\n",
        "Se tiene cuando la función polinomios que aproxima a Newton-Cotes es un polinomio de orden 1 (lineal).\n",
        "\n",
        "Regla del trapecio:\n",
        "\n",
        "$I≈(b-a)\\frac {f(a)+f(b)} {2}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-gjtJobEO4MH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def f(x):\n",
        "  return (x*x)\n",
        "\n",
        "  def trapecio_simple (a,b):\n",
        "    if (b>a):\n",
        "      return 0.5*(f(a)+f(b))*(b-a)\n",
        "\n",
        "    def trapecio_compuesto (a,b):\n",
        "      i=a\n",
        "      h=1E-6\n",
        "      area= 0.0\n",
        "      while (i<=b):\n",
        "        if (i+h<=b):\n",
        "          area = area+trapecio_simple(i,i+h)\n",
        "          i= i+h\n",
        "          return area\n",
        "\n",
        "          if __name__ == \"__main__\":\n",
        "            print (\"Area =\") +str(trapecio_simple(0,1))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bcJEV_pIpa7G",
        "colab_type": "text"
      },
      "source": [
        "Unidad 4: Sistemas de ecuaciones lineales."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o92DgeZGI4DO",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Método de eliminación de Gauss Jordan\n",
        "\n",
        "Demostrar que $x=2, y=1, z=-2$ son las soluciones del sistema de ecuaciones lineales:\n",
        "\n",
        "\n",
        "$x+2y+z= 2$\n",
        "\n",
        "$3x+8y+z = 1$\n",
        "\n",
        " $4y+z = -2$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HC3se2bMoHit",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 372
        },
        "outputId": "d687c4cc-23f3-442c-f5f5-4c8fbf986f53"
      },
      "source": [
        "# Método de Gauss-Jordan\n",
        "# Solución a Sistemas de Ecuaciones\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "# INGRESO\n",
        "A = np.array([[1,2,1],\n",
        "              [3,8,1],\n",
        "              [0,4,1]])\n",
        "\n",
        "B = np.array([[2],\n",
        "              [12],\n",
        "              [2]])\n",
        "\n",
        "# PROCEDIMIENTO\n",
        "casicero = 1e-15 # Considerar como 0\n",
        "# Evitar truncamiento en operaciones\n",
        "A = np.array(A,dtype=float) \n",
        "\n",
        "# Matriz aumentada\n",
        "AB = np.concatenate((A,B),axis=1)\n",
        "AB0 = np.copy(AB)\n",
        "\n",
        "# Pivoteo parcial por filas\n",
        "tamano = np.shape(AB)\n",
        "n = tamano[0]\n",
        "m = tamano[1]\n",
        "\n",
        "# Para cada fila en AB\n",
        "for i in range(0,n-1,1):\n",
        "    # columna desde diagonal i en adelante\n",
        "    columna = abs(AB[i:,i])\n",
        "    dondemax = np.argmax(columna)\n",
        "    \n",
        "    # dondemax no está en diagonal\n",
        "    if (dondemax !=0):\n",
        "        # intercambia filas\n",
        "        temporal = np.copy(AB[i,:])\n",
        "        AB[i,:] = AB[dondemax+i,:]\n",
        "        AB[dondemax+i,:] = temporal\n",
        "AB1 = np.copy(AB)\n",
        "\n",
        "# eliminacion hacia adelante\n",
        "for i in range(0,n-1,1):\n",
        "    pivote = AB[i,i]\n",
        "    adelante = i+1\n",
        "    for k in range(adelante,n,1):\n",
        "        factor = AB[k,i]/pivote\n",
        "        AB[k,:] = AB[k,:] - AB[i,:]*factor\n",
        "AB2 = np.copy(AB)\n",
        "\n",
        "# elimina hacia atras\n",
        "ultfila = n-1\n",
        "ultcolumna = m-1\n",
        "for i in range(ultfila,0-1,-1):\n",
        "    pivote = AB[i,i]\n",
        "    atras = i-1 \n",
        "    for k in range(atras,0-1,-1):\n",
        "        factor = AB[k,i]/pivote\n",
        "        AB[k,:] = AB[k,:] - AB[i,:]*factor\n",
        "    # diagonal a unos\n",
        "    AB[i,:] = AB[i,:]/AB[i,i]\n",
        "X = np.copy(AB[:,ultcolumna])\n",
        "X = np.transpose([X])\n",
        "\n",
        "\n",
        "# SALIDA\n",
        "print('Matriz aumentada:')\n",
        "print(AB0)\n",
        "print('Pivoteo parcial por filas')\n",
        "print(AB1)\n",
        "print('eliminacion hacia adelante')\n",
        "print(AB2)\n",
        "print('eliminación hacia atrás')\n",
        "print(AB)\n",
        "print('solución de X: ')\n",
        "print(X)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Matriz aumentada:\n",
            "[[ 1.  2.  1.  2.]\n",
            " [ 3.  8.  1. 12.]\n",
            " [ 0.  4.  1.  2.]]\n",
            "Pivoteo parcial por filas\n",
            "[[ 3.  8.  1. 12.]\n",
            " [ 0.  4.  1.  2.]\n",
            " [ 1.  2.  1.  2.]]\n",
            "eliminacion hacia adelante\n",
            "[[ 3.          8.          1.         12.        ]\n",
            " [ 0.          4.          1.          2.        ]\n",
            " [ 0.          0.          0.83333333 -1.66666667]]\n",
            "eliminación hacia atrás\n",
            "[[ 1.  0.  0.  2.]\n",
            " [ 0.  1.  0.  1.]\n",
            " [ 0.  0.  1. -2.]]\n",
            "solución de X: \n",
            "[[ 2.]\n",
            " [ 1.]\n",
            " [-2.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Se2wtZNPzK39",
        "colab_type": "text"
      },
      "source": [
        "Al final de este ejercicio se comprobó que el valor de $x=2, y=1, z=-2$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8GtRd67lgbHU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}