Module B-Section 17.1, 17.2, 17.3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Module B: Section 17.1, 17.2, 17.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Used to compare with custom functions\n",
    "from scipy.interpolate import interp1d, CubicSpline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def my_lin_interp(x: np.array, y: np.array, X: np.array) -> np.array:\n",
    "    \"\"\"\n",
    "    Custom 1D Linear Interpolation function\n",
    "    :param x: x-axis experimental data\n",
    "    :param y: y-axis experimental data\n",
    "    :param X: x-axis values to interpolate\n",
    "    :return: Y: interpolated values\n",
    "    \"\"\"\n",
    "    # Get the length of X\n",
    "    X_len = len(X)\n",
    "\n",
    "    # Initialize Y array with zeros of the same size as X\n",
    "    Y = np.zeros(X_len)\n",
    "\n",
    "    # Iterate through X array\n",
    "    for X_i in range(X_len):\n",
    "        X_val = X[X_i]\n",
    "\n",
    "        i = 0\n",
    "        i1 = 0\n",
    "\n",
    "        # Find the two nearest x values to X_val\n",
    "        for n in range(len(x)):\n",
    "            if x[n] >= X_val:\n",
    "                i = n-1\n",
    "                i1 = n\n",
    "                break\n",
    "\n",
    "        # Calculate the slope between the two nearest x values\n",
    "        # slope = rise / run\n",
    "        slope =  (y[i1] - y[i])  / (x[i1] - x[i])\n",
    "\n",
    "        # Calculate the interpolated value\n",
    "        # y = mx + b\n",
    "        Y_val = slope * (X_val - x[i]) + y[i]\n",
    "\n",
    "        # Assign the interpolated value to Y\n",
    "        Y[X_i] = Y_val\n",
    "\n",
    "    return Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.  3.  2.5]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percent Error: 0.0%\n"
     ]
    }
   ],
   "source": [
    "# Output: [2, 3, 2.5]\n",
    "_x = [0, 1, 2]\n",
    "_y = [1, 3, 2]\n",
    "_X = [0.5, 1, 1.5]\n",
    "\n",
    "interp_test_1 = my_lin_interp(x = _x,y = _y, X = _X)\n",
    "print(interp_test_1)\n",
    "\n",
    "# Check accuracy\n",
    "f = interp1d(_x, _y, kind='linear')\n",
    "\n",
    "x_new = np.linspace(min(_x), max(_x), 100)\n",
    "y_new = f(x_new)\n",
    "linear_1 = f(_X)\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.plot(x_new, y_new, 'b')\n",
    "plt.plot(_x, _y, 'ro')\n",
    "plt.plot(_X, linear_1, 'k*')\n",
    "\n",
    "plt.title('Linear Interpolation')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()\n",
    "\n",
    "# Calculate Percent Error\n",
    "linear_error_1 = round(\n",
    "                np.mean(\n",
    "                    (linear_1 - interp_test_1)/linear_1)*100,\n",
    "                4)\n",
    "\n",
    "print(f\"Percent Error: {linear_error_1}%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.   3.   5.   6.5 10. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percent Error: 0.0%\n"
     ]
    }
   ],
   "source": [
    "# Output: [1, 3, 5, 6.5, 10]\n",
    "_x = [0, 1, 2, 3, 4, 5, 6, 7]\n",
    "_y = [1, 3, 2, 6, 4, 8, 5, 10]\n",
    "_X = [0, 1, 3.5, 5.5, 7]\n",
    "\n",
    "\n",
    "interp_test_2 = my_lin_interp(x = _x,y = _y, X = _X)\n",
    "print(interp_test_2)\n",
    "\n",
    "# Check accuracy\n",
    "f = interp1d(_x, _y, kind='linear')\n",
    "\n",
    "x_new = np.linspace(min(_x), max(_x), 100)\n",
    "y_new = f(x_new)\n",
    "linear_2 = f(_X)\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.plot(x_new, y_new, 'b')\n",
    "plt.plot(_x, _y, 'ro')\n",
    "plt.plot(_X, linear_2, 'k*')\n",
    "\n",
    "plt.title('Linear Interpolation')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()\n",
    "\n",
    "# Calculate Percent Error\n",
    "linear_error_2 = round(\n",
    "                np.mean(\n",
    "                    (linear_2 - interp_test_2)/linear_2)*100,\n",
    "                4)\n",
    "\n",
    "print(f\"Percent Error: {linear_error_2}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cubic Spline Interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def my_cubic_spline(x: np.array, y: np.array, X: np.array) -> np.array:\n",
    "    \"\"\"\n",
    "    Custom 1D Cubic Spline Interpolation function\n",
    "    :param x: x-axis experimental data\n",
    "    :param y: y-axis experimental data\n",
    "    :param X: x-axis values to interpolate\n",
    "    :return: Y: interpolated values for given X values\n",
    "    \"\"\"\n",
    "    X_len = len(X)\n",
    "\n",
    "    # Initialize Y array\n",
    "    Y = np.zeros(X_len)\n",
    "\n",
    "    # Iterate through x and y arrays\n",
    "    # Get the next 3 values for each\n",
    "    for i in range(0, len(x) - 2):\n",
    "        x_3 = x[i:i+3]\n",
    "        y_3 = y[i:i+3]\n",
    "\n",
    "        # Left-hand side of the equation\n",
    "        \"\"\"\n",
    "        A = np.array([\n",
    "        [0, 0, 0, 1, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 1, 1, 1, 1],\n",
    "        [1, 1, 1, 1, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 8, 4, 2, 1],\n",
    "        [3, 2, 1, 0, -3, -2, -1, 0],\n",
    "        [6, 2, 0, 0, -6, -2, 0, 0],\n",
    "        [0, 2, 0, 0, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 12, 2, 0, 0]])\n",
    "\n",
    "        \"\"\"\n",
    "        x1 = x_3[0]\n",
    "        x2 = x_3[1]\n",
    "        x3 = x_3[2]\n",
    "\n",
    "\n",
    "        A = np.array([\n",
    "            [x1**3, x1**2, x1,      1, 0, 0, 0, 0],\n",
    "            [0, 0, 0, 0, x2**3, x2**2, x2, 1],\n",
    "            [x2**3, x2**2, x2, 1, 0, 0, 0, 0],\n",
    "            [0, 0, 0, 0, x3**3, x3**2, x3, 1],\n",
    "            [3*x2**2, 2*x2, 1, 0, -3*x2**2, -2*x2, -1, 0],\n",
    "            [6*x2, 2, 0, 0, -6*x2, -2, 0, 0],\n",
    "            [6*x1, 2, 0, 0, 0, 0, 0, 0],\n",
    "            [0, 0, 0, 0, 6*x3, 2, 0, 0]\n",
    "        ])\n",
    "\n",
    "        # Right-hand side of the equation\n",
    "        b = np.array([y_3[0], y_3[1], y_3[1], y_3[2], 0, 0, 0, 0])\n",
    "\n",
    "        # Solve the system of equations\n",
    "        p = np.dot(np.linalg.inv(A), b)\n",
    "\n",
    "        for X_i in range(X_len):\n",
    "            _X_i = X[X_i]\n",
    "\n",
    "            # Solve for the cubic spline\n",
    "            if x_3[0] < _X_i < x_3[1]:\n",
    "                _Y = p[0] * (_X_i ** 3) + p[1] * (_X_i ** 2) + p[2] * _X_i + p[3]\n",
    "\n",
    "                if Y[X_i] == 0:\n",
    "                    Y[X_i] = _Y\n",
    "                else:\n",
    "                    Y[X_i] = (Y[X_i] + _Y)/2\n",
    "            elif x_3[1] < _X_i < x_3[2]:\n",
    "                _Y = p[4] * (_X_i ** 3) + p[5] * (_X_i ** 2) + p[6] * _X_i + p[7]\n",
    "\n",
    "                if Y[X_i] == 0:\n",
    "                    Y[X_i] = _Y\n",
    "                else:\n",
    "                    Y[X_i] = (Y[X_i] + _Y)/2\n",
    "\n",
    "            # If X is in x\n",
    "            elif _X_i == x_3[0]:\n",
    "                Y[X_i] = y_3[0]\n",
    "            elif _X_i == x_3[1]:\n",
    "                Y[X_i] = y_3[1]\n",
    "            elif _X_i == x_3[2]:\n",
    "                Y[X_i] = y_3[2]\n",
    "\n",
    "    return Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.28125 3.      2.78125]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percent Error: -0.0%\n"
     ]
    }
   ],
   "source": [
    "# Output: [1, 2.78125, 2]\n",
    "_x = [0, 1, 2]\n",
    "_y = [1, 3, 2]\n",
    "_X = [0.5, 1, 1.5]\n",
    "\n",
    "cubic_spline_test_1 = my_cubic_spline(x = _x,\n",
    "                                      y = _y,\n",
    "                                      X = _X)\n",
    "print(cubic_spline_test_1)\n",
    "\n",
    "# Check accuracy\n",
    "f = CubicSpline(_x,\n",
    "                _y,\n",
    "                bc_type='natural')\n",
    "\n",
    "x_new = np.linspace(min(_x), max(_x), 100)\n",
    "y_new = f(x_new)\n",
    "cubic_spline_1 = f(_X)\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.plot(x_new, y_new, 'b')\n",
    "plt.plot(_x, _y, 'ro')\n",
    "plt.plot(_X, cubic_spline_test_1, 'k*')\n",
    "\n",
    "plt.title('Cubic Spline Interpolation')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()\n",
    "\n",
    "# Calculate Percent Error\n",
    "cs_error_1 = round(\n",
    "                np.mean(\n",
    "                    (cubic_spline_1 - cubic_spline_test_1)/cubic_spline_1)*100,\n",
    "                4)\n",
    "\n",
    "print(f\"Percent Error: {cs_error_1}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.          3.          4.046875    5.5703125   6.046875    5.62695312\n",
      " 10.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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hY0do1Cg91tbmTqQiiDEVr3I/Jmh+TTJet0UIYTbQEng3Uw5JUqmrrYVu3dIqa4AJE/jqpG7EOdDk+K55s6mg3ngDPvqoctZ3QYYRrxjjO8BVwETgPeDTGOOQYueQJJWHeN75X5euOo1nTuOdE85n993hoovghRfyZFNhzVvfZfFaDiGE1YBDgPWBdYAVQwjH1vN53UIIo0MIo6dMmVLsmJKkzGKERx6BOHFivR9vz0Q+/RQuvRS23Rb69i1yQBXc8OGw6qppjVelyLG4fk9gXIxxSoxxNtAPWKDLxhh7xRhrYow1rVu3LnpISVI+c+bAj38M++4L7zZuX+/nhA7tGTMGJk9Om2sedRT8859FDqqCmre+q1EF7cGQ40uZCOwQQmgZQgjAHsArGXJIkkrUuedC//5w2WWw9o090nkx82vZEnr0AKB1axgyJJW0bt3gj3/MEFgNbupUeOmlyppmhDxrvEYCfYFngf/VZehV7BySpNLUty9cdRWceiqcfz40Pb4r9OoFHTpACOmxVy/o+vXC+pYtYcAA6NwZfvtb+PWv01SlyteIEemx0opXlrsaY4wXAhfmuLYkqXS98gqceGLaLPOvf53vA127fqNo1adZM7jjDlhtNfjTn+DTT+H661NXU/kZPjxNMW63Xe4kDSvXdhKSJH3DZ5/BYYel0at7701Famk1agTXXAMrrQRXXgk77wzHLnD7lsrB8OGwxRbp97KSVNByNUlSuYoRfvpTePNNuPtuaNdu2Z8rBLj88jRFdcYZ8N57DZdTxTF7Njz9NPzoR7mTNDyLlyQpu6uugvvuSwvjO3Va/udr3BhuvhmmT4eTT3a9V7l57rm0ddvOO+dO0vAsXpKkrN54I93FeMQR8MtfNtzzbrRRuvFx0CBPGCo3w4alR4uXJEkN7MILYYUV0tqshl4If+aZTjmWo6FD4bvfhbZtcydpeBYvSVI2L7wAffrAWWfB2ms3/PPPP+XYvbtTjuUgxjTiVYmjXWDxkiRldMEF6UiYs88u3DXmTTkOHAh33lm466hhvPoqfPhhZS6sB4uXJCmT4cPhgQfSZqerrVbYa82bcjz99PRNXaVr6ND06IiXJEkNJEY477w0vXjGGYW/XuPGabP7qVPTHZQqXcOGwVprwYYb5k5SGBYvSVLRPfYY/PvfaapxxRWLc81NN01HCv3jH/DBB8W5ppbe0KFptKtSTxyweEmSimreaFeHDvB//1fca194IcyYkXa1V+mZNAnGj6/c9V1g8ZIkFVn//jB6NFx0UdpGopg22gh+8hO49lq3lyhFlb6+CyxekqQi+uqrNL34/e+nApTD736XjqS54oo819fCDR2azmbccsvcSQrH4iVJKpoHH4RXXkmjXY0b58nw3e/CCSfADTekqS2VjmHD0t2nTZrkTlI4Fi9JUtFcdx2suy4cfnjeHBdcAHPnwh/+kDeHvvbJJ/Dii5U9zQgWL0lSkbz1Fjz8MHTrln9Eo2NHOOkk+Oc/YeLEvFmU/Oc/6caLSl5YDxYvSVKR3HBDml782c9yJ0nOOy9tWXDZZbmTCNL6rqZNYfvtcycpLIuXJKngpk+HG2+Eww6DddbJnSZZbz04+eR0luP48bnTaOhQqKmBFi1yJyksi5ckqeDuvRc+/hhOOSV3km/6zW/S4zXX5M1R7aZPT1uMVPr6LrB4SZKKoGdP2Hhj2G233Em+ad114YgjoHdv+OKL3Gmq16hRaYuPSl/fBRYvSVKBPfssjBiRRrtK8RiYM86ATz+F22/PnaR6zds4daed8uYoBouXJKmgevZM63aOPz53kvrtsANsuy1cfXW6q07FN3QobLYZrL567iSFZ/GSJBXM1Klw553QtSusumruNPULIY16vfoqPPpo7jTVZ/ZsGD68OtZ3gcVLklRAt90G06aV3qL6bzvySFh77TTqpeJ69tm0vq5Tp9xJisPiJUkqiBjTNOP228MPfpA7zaKtsEIqh4MHwxtv5E5TXZ54Ij1avCRJWg5PPZWm70p9tGuek09OG3i6tURxPfEEbLoprLVW7iTFYfGSJBVEbS2suGLarqEctGkDRx+dNlT97LPcaarD7NnpYOxS22akkCxekqQGN3Nm2jT1sMNS+SoXZ5wBn38Ot9ySO0l1eOaZtAawWqYZweIlSSqAhx9OdzR26ZI7ydLZdlv44Q/hH/+AuXNzp6l889Z37bpr3hzFZPGSJDW42lpo3Rr23DN3kqV3xhnw5pupPKqwnngCttgC1lwzd5LisXhJkhrUZ5/BoEFw1FFpsXq5+fGP00Lv3r1zJ6lsM2em/buqaZoRLF6SpAbWvz/MmJE2TS1HTZumXfYHDYLJk3OnqVyjRqXDsatpYT1YvCRJDezOO2H99dNRPOXqpJNgzpy0AawK44kn0qkB1bS+CyxekqQGNHkyPPZYWlRfigdiL6mNN4Yf/QhuvNHzGwvlySdhq61gtdVyJykui5ckqcHcc0+6G7Dc7masz89+Bq+/nvaZUsOaMaM613eBxUuS1IBqa9Moxiab5E6y/I44Alq1cpF9IYwYkRbXV9v6LrB4SZIayJtvpgXTlTDaBWnj186d00awn36aO01leeIJaNQIdtkld5Lis3hJkhrEnXemdV2dO+dO0nB+9rN0512fPrmTVJYnn0wHp6+ySu4kxWfxkiQttxhT8dplF2jXLneahrPNNrDllk43NqTp09NUYzWu7wKLlySpATz7LLz2Wvnu3bUwIaStJcaMgeefz52mMgwfDrNmVef6LrB4SZIawL33QpMmadf3StO1K6ywQtpaQsvvySehcWPYeefcSfKweEmSlkuMcN99sPvusPrqudM0vNVXT4XyjjvSNJmWzxNPQE0NrLxy7iR5WLwkScvlpZfSHY2HH547SeGcdBJMnQr9+uVOUt6++CLd+Vqt67vA4iVJWk79+qW1UIcckjtJ4XTqlI5BuuWW3EnK27//DbNnw1575U6Sj8VLkrRc+vWDnXaCNm1yJymcRo3gJz+Bf/0LJk3KnaZ8DRkCLVqkPy/VyuIlSVpmb70FL7xQ2dOM8xx3XFrPdscduZOUryFD0qHYzZvnTpKPxUuStMz690+Phx2WN0cxfPe7aaTm1ls9OHtZTJwIr74Ke++dO0leFi9J0jLr1y/tQN6xY+4kxXH88ak8jB6dO0n5efTR9GjxkiRpGbz7Ljz9dHVMM85z1FFpT69bb82dpPw88gisu25lHKC+PCxekqRlMmBAeqym4rXKKnDooensxpkzc6cpH199BY89lka7QsidJi+LlyRpmdx3H3z/++mtmhx/PHz8MTz4YO4k5WPMGPjkE6cZweIlSVoGH36Y9mSqptGuefbaK22d4XTjkhsyJI107bln7iT5WbwkSUtt0KA0fVSNxatJk3R+4+DBMGVK7jTlYciQdBPGmmvmTpKfxUuStNT69YMOHWDrrXMnyeP442HOnLTWS4v22WfpJgynGROLlyRpqXz+eRrBOPzw6l0ovfnmqXTedlvuJKXvySdTSbV4JRYvSdJSefBBmDWrOqcZ53fccWnR+Esv5U5S2h55BFZcEXbcMXeS0mDxkiQtlfvvh7XWgh/+MHeSvLp0Seu9XGS/aEOGwG67QbNmuZOUBouXJGmJzZ6dRrwOPBAaN86dJq+11oL99oPa2nSjgRY0diy8+abTjPOzeEmSltjQofDpp3DwwbmTlIaf/CTt4P/447mTlCaPCVqQxUuStMQGDUpH5rgfU3LQQWk3+9tvz52kNA0ZAu3bw0Yb5U5SOixekqQlEmNa37XnnmmxtKB5czj66LSL/xdf5E5TWubMgX/9y2OCvs3iJUlaIi+/DOPGOc34bT/5CUyblvY209dGjEjT0k4zfpPFS5K0RAYNSo8HHpg3R6nZaSdYf32nG79t4EBo2hT22Sd3ktJi8ZIkLZGBA6GmBtZZJ3eS0hJC2tPrX/+CSZNypykdgwZBp07QqlXuJKXF4iVJWqwPPkhTRwcdlDtJaTr22LQGrrY2d5LS8Prr8OqrTkvXx+IlSVqswYNTsfAbaf022CDtzH7bbel1qnbzpqUt6guyeEmSFmvgQFhvPdhyy9xJStdxx6UbEJ57LneS/AYNgi22SAep65ssXpKkRZoxI+3HdNBBbguwKEcdlY7FqfaDsz/6CIYNc3R0YSxekqRFevzxtF2C30gXbbXVUjnt0ycdrVStHnooHaHkNGP9LF6SpEUaOBBWWindoaZFO+64dCPCkCG5k+QzaBC0aZPugNWCLF6SpIWKMX0j3WefdFSQFm3ffWGNNeDWW3MnyWPWrDTiddBB0MiGUS9fFknSQj37bDoE2mnGJdOsGXTpko5W+uST3GmK79//hs8/d5pxUSxekqSFGjgwjVzsv3/uJOXjxBPTyE+fPrmTFN/AgdCiBeyxR+4kpcviJUlaqEGD4Ic/hDXXzJ2kfGy1VdpK4ZZbcicprnnT0nvtBS1b5k5TuixekqR6vfNO2pPKaaOlE0Ia9XrmGXjppdxpiud//4MJE/zzsjgWL0lSvQYPTo8eir30unaFJk3g5ptzJymegQPTo39eFs3iJUmq1wMPQMeOsMkmuZOUn9atUwG5447q2dNr0CDYfvu0lYQWzuIlSVrA2LHv8cADu7LbbpPdrX4ZnXgivP8+PPxw7iSF9957MGqU04xLwuIlSVrA6adfSozD+OCDS3JHKVv77QdrrVUdi+z790+PhxySN0c5yFK8QgirhhD6hhBeDSG8EkL4YY4ckoqktjbNWTVqlB5ra3Mn0kK0aNGCEAIPPtgTmMvgwT0JIdCiRYvc0cpO06Zw7LFpCu7DD3OnKaw+fWDTTWGzzXInKX25Rrz+DjwcY/wesCXwSqYckgqttha6dUu3O8WYHrt1s3yVqLFjx9K5cxdCSPsBtGzZkq5duzJu3LjMycrTCSekNV6V/Md94sR0KHbnzrmTlIeiF68QwirALsCNADHGWTHGqcXOIalIzj8/nbA8v2nT+PDk83ngAZg5M08s1a9t27bMmdOKGGfQtGlzZsyYQatWrWjjiullsvnmsM02lT3deM896fHoo/PmKBc5RrzWB6YAN4cQngsh9A4hrPjtTwohdAshjA4hjJ4yZUrxU0pabjFCnDix3o+t/uVEDjoo3f3VpQv06wdz5hQ5oOr10kvvA9156KERdO/encmTJ+eOVNZOOAGefz69VaI+fWDbbWGDDXInKQ85ilcT4AdAzxjj1sCXwG+//Ukxxl4xxpoYY03r1q2LnVHScooRzjgDJsT29X48tG/PQw/BUUfBkCHw4x+nO6K++KLIQbWAVVbpx7bbXssee2zJtddeS79+/XJHKmudO6czHCtx1Ov119N5nk4zLrkcxWsSMCnGOLLu531JRUxShYgRfvELuOYaeGqfHsQW3zo/pGVLwuU92Hdf6N0bJk+G666DRx+FXXdNP1ceH3wAI0a4CWZDWmONdLff7bfDjBm50zSsu+5KO/UfdVTuJOWj6MUrxjgZeDuEsHHdu/YAXi52DkmFESOccw78/e9w5pnwk4e6Ev7ZCzp0SP9Cd+gAvXqlrb3rNGkCp5wC998Pr76azgZ87bWMX0QVe+ih9Hto8WpY3brBxx/DffflTtJwYkzTjLvsAuuumztN+QgxxuJfNIStgN5AM2AscGKM8ZOFfX5NTU0cPXp0kdJJWlYxwnnnwRVXwGmnwT/+wVJvvvnMM3DAAfDVV+kIkp12KkxW1e/II2H4cJg0ael/77Rwc+fCxhunXd2HDs2dpmE8/zxsvTVcfz2cfHLuNKUlhDAmxlhT38eybCcRY3y+bv3WFjHGQxdVuiSVjwsvTKXr5JPh6quX7Rv3ttvC00+n6Zk994RHHmn4nKrfrFnp9T7gAEtXQ2vUKP29GDYMXnwxd5qGcdddabT6xz/OnaS8uHO9pAbRsydceimcdFJar9VoOf51+e5306jLxhunRbsLuTFSDWzoUPj8c6cZC+WEE2CFFeCGG3InWX4xpuK1116w5pq505QXi5ek5fbOO/Cb38Dee6flW8tTuuZZc03o2zdtMXH00dVz0HBODzyQisEee+ROUpnWXDNN5d52G3z5Ze40y+fpp9NeyN7NuPQsXpKW21lnpWLUs2fDlK55NtgA/vnPdJfd+ec33PNqQTGmo2123x1WXGBnRTWU7t3hs8/SaFE569MHmjf3bMZlYfGStFwefDCNTP3ud/Cd7zT88x99dPpm9ac/weDBDf/8Sl59Fd56K+2lpsLZccd0nuH11+dOsuzmzEm71R9wALRqlTtN+bF4SVpm06aluxe//304++zCXeevf4Utt4TjjoO33y7cdarZoEHp0fVdhRVC+o/E6NHprRw9+WTa781pxmVj8ZK0zC65BMaPT/97b9ascNdp3jz9D3vWLDjmGNd7FcLAgWlrgPXWy52k8h17LLRsWb6L7P/5T1htNdh//9xJypPFS9IyefFF+POf4cQT0waKhbbRRmnh/vDhqfCp4Xz4YVos7TRjcayySjqf9M474dNPc6dZOpMnp3NVTzwRWrTInaY8WbwkLbW5c9OeRKusAldeWbzrdu6cRgv++Md0RpwaxoMPpt9Ti1fxdO+epurvuCN3kqXTu3da49W9e+4k5cviJWmp3XxzGnn605+Kv4fPn/6Uph7PPDPdiaflN2gQtG0LP/DU3KLZZhuoqUl3Ar/77nvsuuuuTC7xQ0rnzEmjznvuCRtumDtN+bJ4SVoqs2enqb7tt08bQhZbmzZw8cXw8MNfLwjXsps5M72WBx3UsFuBaPFOOw1eeglOPvlShg0bxiUlPoc+eHC6ueXUU3MnKW/+NZO0VPr0STvJX3BBnmNl3nvvPfr335WNNprMWWfB9OnFz1BJ/v1v+OILpxlzOOWUFkDggQd6MnfuXHr27EkIgRYluniqZ890GLZ/VpaPxUvSEps7N53FuMUWaQ+fHC699FL+859hbLzxJYwbl6YetewGDUqLpN2tvvjGjh3L1lt3AVoC0LJlS7p27cq4cePyBqvHm2+mczy7dUvnM2rZWbwkLbH774dXXoHf/rb4o10tWrQghEDPnml0YNCgnkDgwgtbMH58cbNUinm71e+5p3eo5dC2bVu23roVMINGjZozY8YMWrVqRZs2bXJHW8ANN0DjxvCzn+VOUv4sXpKWSIzwhz+k3emPPLL41x87dixdunShZcuvRwcOPbQrLVqM45e/LH6eSvC//6Xz9g4+OHeS6vXJJ++z9dbdiXEEnTt3L8kF9tOnw003wWGHwTrr5E5T/hwwlLREHn8cnnkm/c83x1RD27ZtadWqFTNmzKB58zQ60LZtK37/+zace26aBtlnn+LnKmfzbk7INW0s6NevH++9Bx07QqtW15bk9hL33gsffwynnJI7SWVY7IhXCOH0EMJqxQgjqXRdfnnacuD44/NleP/99+nevTsjRoyge/c0OvCLX6Rb23/xC/jqq3zZytGgQbDttun3Vfm0bZuOw7r55nQUT6np2RM23hh22y13ksqwJFONawPPhBDuCSHsG0KO+5gk5TRqVBrx+uUvYYUV8uXo168f1157LVtuuSXXXnst/fr1Y4UVUil85ZW0E7iWzOTJ6ffVO9RKw9lnp609/vGP3Em+6bnnYMSINNrld/+GsdjiFWO8ANgQuBE4AXgjhHB5COG7Bc4mqUT84Q/pbLaTT86dpH6HHw5bbQUXXeQ5jktq8OC0bs/1XaVh443h0EPh2mvT9h6l4s9/TjdeHHdc7iSVY4kW18cYIzC57m0OsBrQN4RQxMNCJOXw8sswYACcfjqsvHLuNPVr1AguuwzGjk2LgLV4gwalA7G32CJ3Es3zm9/AJ5/AjTfmTpK8+GIaRT799PQfLzWMEBdz5kYI4UzgOOBDoDcwIMY4O4TQCHgjxljwka+ampo4evToQl9GUj1OPBHuuSdtmrrGGrnTLFyMsNNOKeebb6ZjhVS/adOgdet08sC11+ZOo/ntuiuMG5f+DDdrljfL4YfDv/6V/kNTyn/3S1EIYUyMsaa+jy3JiNfqwOExxn1ijPfGGGcDxBjnAgc2YE5JJebjj9NO9ccfX/r/8IYAPXrAO+/A9dfnTlPahgxJ5euww3In0bedd146lue66/LmeOYZ6N8ffvWr0v+7X24WO+JVChzxkvK4+up0GPXzz8OWW+ZOs2T23BP++9/0v/SVVsqdpjQdf3yaanz/fWjaNHcafdt++6UF7W+8UfxD6OfZZx8YMyb9PWrVKk+Gcra8I16SqlCM0KtX2m6gXEoXpFGvKVNSadSCZs9OpeuggyxdperPf4bPP083i+Tw1FNpVPTccy1dhWDxklSvESPgpZfS2WzlZPvtU6n4059g6tTcaUrPU0+lBdxOM5auTTZJ2zdcf336O1hMMcL556cd6k89tbjXrhYWL0n16tUrTdUdc0zuJEvv0ktT6brqqtxJSk///ml7gL33zp1Ei3LRReku4l/+MpWhYnn4YRg2DH73O8/vLBSLl6QFTJ0Kd98NXbqU5zqpLbeEo46Cv/893SCgZO7cVLz23RfqjrxUiVpjjVS+hgyBhx4qzjVjhAsugPXXh5/+tDjXrEYWL0kLuPPOdDBuuU0zzu93v0sbUf7977mTlI5nnoF333WasVycemraWPWXvyzOxsD9+sGzz6bCl3sri0pm8ZL0DTGmg7C33hq22SZ3mmW32WapYFx9NXz6ae40paF//3TA+YFuBFQWmjZNC+1fey2dl1hIH34IZ5wBm24KXbsW9lrVzuIl6RueeSZtx1DOo13znH9+mjbNvSdSKYgxFa9OndyFvJzsv39aj3fRRYU7QDvGtJnuhx/CHXdA48aFuY4Si5ekb/jnP9P6ny5dcidZfttsk/ZE+stf4Msvc6fJ65VX4PXX027kKh8hwF//mqb+jzyyMFOOf/tbOrvzz39OZ56qsCxekv6/zz5LO9Ufc0zl7N9zwQXpf/K9euVOklf//unxkEPy5tDS22STdH7jU0/BL37RsM89enQ6I/LQQ+G00xr2uVU/i5ek/69PnzQyVAnTjPPsuCPsvnva12vGjNxp8unfH3bYIe3PpPLTpQucfXY6W7OhDtH+7DM4+mho2zY9ZwgN87xaNIuXpP+vd2/YfHPYbrvcSRrWBRfAe+/BTTflTpLHxInp+BfvZixvV1yR1nudcgo8/fTyPVeMcPLJMGFCuot59dUbJqMWz+IlCYBXX03TDiecUHn/8+3UKY18/fGPMGtW7jTFN2BAerR4lbfGjeGuu6B9+7RW7513lv25brghPdcll8BOOzVcRi2exUsSkKYZQyjPneoXJ4Q06jVxYrprq9r065e2Cdhww9xJtLxWWw3uvz/tUXf44TBt2tL9+lmz4Kyz0qjZ3nun9V0qLouXJGJM0w277165a4D23Rd+8AO4/HKYMyd3muJ5/30YOtTRrkqy6aZw++1p65fNNkt3JFJbCx07QqNG6bG2doFfN24c/OhHaVPhM86AgQPdOiIHi5cknnkG3nyzMraQWJgQ0r5eb70F996bO03x3HtvOiqoEkcyq9mhh8ITT0Dz5lB7YC0zju+WFmzFmB67dftG+erfP22K/PrrcN99qXytsEK+/NUsxGKevrmMampq4ujRo3PHkCrWWWelnbHffx9WXTV3msKZOzeNEDRuDC+8kAYHKt1OO8Hnn6dNcVV5Zs2C6Wt3ZJWpExb42GerdeAPJ4/n9dfTdPO226YzWNdfP0PQKhNCGBNjrKnvY1Xwz46kRfnqq7TI9sADK7t0QSpa554LL74IDzyQO03hTZgAw4dD5865k6hQmjWDVT6dWO/HVvpkIlddBSNGwK9+BcOGWbpKgcVLqnKPP55Guip5mnF+nTunJTA9eqRZmUp2993p8eij8+ZQgbVvX++7Y7v2zJqV7n686ioPvi4VFi+pyt15Z9ql/oADcicpjiZN0p1co0al0lnJ+vSB7beH73wndxIVVI8e6Zyv+bVsSeMrelTc1jCVwOIlVbHp09NC2x//OC3SrRYnnJB267788txJCufVV+H5551mrApdu6YzsTp0SHeRdOiQft61a+5kqofFS6piDz6YFl5XyzTjPM2bpzUvjz+e1r9Uoj590pq2o47KnURF0bUrjB+f7iAZP97SVcIsXlIVq62FNm1gt91yJym+k09Ox6RU4qhXjOmGiU6d0siepNJh8ZKq1NSpaePFY46pzk0UV1oJzjwTBg2qvK0Wnnsu7dfk3l1S6bF4SVWqX7+0B1C1TTPO7+c/TwXsD3/InaRh9ekDTZumtXuSSovFS6pStbXp7L6aerf4qw6rrw6nngr33JNGiCrB3LlpmnGffdLXJ6m0WLykKvT+++m4kc6dqfrbzX/5y3R0So8euZM0jP/8ByZN8m5GqVRZvKQq1L9/WoB95JG5k+S39trQvXsaAXzzzdxplt9dd0GLFnDwwbmTSKqPxUuqQn37wsYbw6ab5k5SGn7967QmqtxHvebMSYdiH3RQWrsmqfRYvKQq8+GH8OSTcMQRTjPO06ZN2l7i9tvhrbdyp1l2gwfDlClu4SSVMouXVGXuvz8djO0db9/061+n44TKeV+vXr1gnXVg//1zJ5G0MBYvqcr07ZvO7ttqq9xJSss660C3bnDrrTB2bO40S2/CBHjoITjppFQgJZUmi5dURT75BB57zGnGhfnNb8p31Kt37/T4s5/lzSFp0SxeUhUZODAtwD7iiNxJStO668L//V8a9Ro/PneaJTdnDtx4I+y3H7RvnzuNpEWxeElV5L770jfmat40dXF+85t0uHQ5jXo98AC89166QUBSabN4SVXis8/gkUfSonqnGReuXbs0XXfzzeUz6tWrVxqtc1G9VPosXlKVeOCBdDaj04yLd+65aa3X73+fO8nijR8PDz/sonqpXFi8pCrRt2+6c2+HHXInKX3t2sGZZ8Idd8Bzz+VOs2i9e6cRzJNOyp1E0pKweElV4Isv0lYDhx+e1i9p8X77W1httbTmq1TNng033eSieqmc+E+wVAUeeghmzHCacWmsuipccAE8+igMGZI7Tf3mLarv1i13EklLyuIlVYG+fWGtteBHP8qdpLyceip07Jh2tZ87N3eaBd1wg4vqpXJj8ZIq3PTp6Qy/ww6Dxo1zpykvK6yQtpV44QWorc2d5pvGjk0jcS6ql8qLxUuqcI8+Cl9+6dmMy+roo2GbbdK044wZudN87YoroGlTpxmlcmPxkipc//6wyirQqVPuJOWpUSO48kqYOBGuuSZ3mmT8+LTP2P/9X5pqlFQ+LF5SBZszBwYNggMPTKMjWja7757uHOzRAz7+OHeaNP3ZqFG681JSebF4SRXsP/+Bjz6CQw/NnaT8/fGPaff/c8/Nm2P+0a527fJmkbT0LF5SBevfPy0Q33ff3EnK3+abwy9+kY7nefLJfDkc7ZLKm8VLqlAxwoABsNdesNJKudNUhksuge98J402TZtW/Os72iWVP4uXVKGefx4mTEjbSKhhtGyZjuh580246KLiX79HjzTalXu6U9Kys3hJFWrAgPRN+qCDciepLLvtlkac/vxnGD26eNcdNw5uuSVtH+GdjFL5snhJFWrAgLRTfevWuZNUniuvhDZt0uals2cX55qu7ZIqg8VLqkBjx8J//+vdjIWy6qrQs2d6ja+8svDXGzvW0S6pUli8pAo0YEB6tHgVzsEHp13tL7kEXn65cNf56iv46U/T3amOdknlz+IlVaD+/WHLLWH99XMnqWxXXw2tWqWC+9FHhbnGFVfAv/+dds13tEsqfxYvqcJ88EHaONXRrsJba600ujhxIhxySMOf5ThiBFx4IRxzDBx/fMM+t6Q8LF5ShRk0KO3h5TYSxbHTTnD77ansHn88zJ3bMM/76afQpUvar6tnTwihYZ5XUl4WL6nC9O8P7dq9xxln7MrkyZNzx6kKRx6ZFtnfcw+cd97yP1+McOqpaSTtzjvTYn5JlcHiJVWQzz+Hxx6D1Ve/lGHDhnHJJZfkjlQ1zj4bundPZzrecMPyPdftt6fCdeGFsOOODZNPUmnIVrxCCI1DCM+FEB7IlUGqNGus0YKZMwP//W9P5s6dS8+ePQkh0KJFi9zRKl4I8I9/wAEHpNGqu+9eil9cWwsdO0KjRsxapyNPdqtll10aZvRMUmnJOeJ1JvBKxutLFeegg8bSrFkXWrRoCUDLli3p2rUr48aNy5ysOjRpAnfdBdtumxbEd+6cbnZYpNratEHXhAkQI83em8A1M7vR78e1NG5clNiSiihL8QohtAMOAHrnuL5UiWbPhscfb0vHjq2YOXMGzZs3Z8aMGbRq1Yo2bdrkjlc1VloJnnoKLr0U+vWDTTZJ3SrGhfyC889f4MTtlkxjjb+cX/iwkoou14jX34BfAwu9/yeE0C2EMDqEMHrKlClFCyaVq6eegqlTYfXV36d79+6MGDGC7t27u8A+g2bN4IIL4LnnYMMN4dhj0xTksGHwv/+lnejffz+tyYsTJtb/JBMX8n5JZS3Ehf43rEAXDOFAYP8Y46khhE7A2THGAxf1a2pqauLoYp5GK5WhM86A3r3hww+hZcvcaTTPV1/BtdfCuecuMLAFwDg60pEJC36gQwcYP77g+SQ1vBDCmBhjTX0fa1LsMMBOwMEhhP2B5kCrEMIdMcZjM2SRKkKMaSPPvfaydJWaxo1TKT7iCHjhBfjyy6/fpk2D99/uQYfe3Qjzt7KWLaFHj3yhJRVM0YtXjPFc4FyA+Ua8LF3Scnj+eXj7bbj44txJtDDrrJPeFtQVtiOt9Zo4Edq3T6Wra9ciJ5RUDDlGvCQ1sAEDoFEjOHCRk/YqWV27WrSkKpG1eMUYnwSezJlBqgT335+OrmndOncSSdKiuHO9VObGjUtrhw45JHcSSdLiWLykMjdwYHq0eElS6bN4SWVuwADYdFPYYIPcSSRJi2PxksrYRx/B0KGOdklSubB4SWVs8OC0Qeehh+ZOIklaEhYvqYzdf3/aG2qbbXInkSQtCYuXVKamT4eHH07TjI38myxJZcF/rqUy9dhj6cgZ13dJUvmweEllasAAaNUKdtstdxJJ0pKyeEllaM6ctH/XAQdAs2a500iSlpTFSypD//kPfPghHHZY7iSSpKVh8ZLKUP/+sMIKsN9+uZNIkpaGxUsqMzGm4rXXXrDSSrnTSJKWhsVLKjPPPQcTJzrNKEnlyOIllZn+/dO+XQcdlDuJJGlpWbykMtO/P+y8M7RunTuJJGlpWbykMvLGG/DSS04zSlK5snhJZaR///ToodiSVJ4sXlIZ6d8ffvAD6NAhdxJJ0rKweEll4t13YcQIpxklqZxZvKQycf/96dHiJUnly+IllYn+/WHDDWGTTXInkSQtK4uXVAamToUnnkijXSHkTiNJWlYWL6kMDB4Mc+Y4zShJ5c7iJZWBvn1hnXVgu+1yJ5EkLQ+Ll1TiPv8cHnoIjjgiHRUkSSpf/jMulbgHHoCZM+HII3MnkSQtL4uXVOLuvTdNM+64Y+4kkqTlZfGSStgXX6Rpxh//2GlGSaoE/lMulbAHHoAZM5xmlKRKYfGSSti990LbtrDTTrmTSJIagsVLKlFffAEPPug0oyRVEv85l0rU4MFOM0pSpbF4SSXq3nuhTRunGSWpkli8pBL05ZdfTzM2bpw7jSSpoVi8tHi1tbzXrh27hsDk9daD2trciSre4MEwfbrTjJJUaZrkDqB8pk2DN9+EsWPhrbfS47hxsPrqsMUWsPnmsP1btaz2m25cOm0aw4BLJk3ium7d0hN07Zo1fyW7915Ye2340Y9yJ5EkNaQQY8ydYbFqamri6NGjc8eoGKNHwzXXwF13paNo5lllFVh/ffjwQ5g0Kb1vBRoxkwX/jDQPgelz5xYpcXX58kto3RpOOAGuuy53GknS0gohjIkx1tT3MUe8qsTMmdC3L/zjHzByJKy4Ivz0p7DrrvCd78B3v5tGuub55BP43/9gg10j5wADgGlAS+Aw4KoyKOzl6sEHnWaUpEpl8aoC990HP/85TJ4MG20EV18Nxx2XRrgWZrXVYJddgA4daDVhAjOA5sAMoBXQZMUOjBuXRsjUsO6+G9Zaq+71lyRVFBfXV7CpU+EnP4EjjoB27eCRR+CVV+D00xddur6hRw/eb9SI7sAIoDvwbmjEr2b2YIstoF+/gsWvSp98AoMGQefO3s0oSZXI4lWhHn0UNtsM+vSBiy+G4cNh772XYQf0rl3pd9ttXNuhA1uGwLUdOjDg9tu4bGxXNt00bXdw7rnw1VcF+TKqTt++MGsWHHts7iSSpEJwcX2FmTEDzjknLZ7/3vfg9tuhpt7lfctv5kw480y44QbYc89U8tZcszDXqha77goffAAvvwwh5E4jSVoWi1pc74hXBfnsM9hvv1S6zjwTnn22cKULYIUV4Prr4cYbYehQ2GYbGDOmcNerdOPHw1NPpdEuS5ckVSaLV4WYMgV23x2GDUv7m/7tb9CiRXGu/dOfpuvGmBaEP/VUca5bae68Mz26PZokVS6LVwV4+23YeWd46SUYMAC6dCl+hpoaGDUKOnSA/fdPI2BacjGmaeGdd4aOHXOnkSQVisWrzL32WjpE+b33YMgQOOCAfFnatIHHH4f11ktTnsOG5ctSbp59Fl591UX1klTpLF5l7L//TUfKzJgBTz6ZRktym1e+2rVL5es//8mdqDzccQc0a+amqZJU6SxeZWriRNh337TAfdgw2Hrr3Im+1rYtPPEErLNOymj5WrQ5c9IdoQcemDaulSRVLotXGfr00zSl+OWX8NBDaTf6UjN/+dpvP3jhhdyJStdjj8H776fNbiVJlc3iVWZmzUqblr76ajoKaPPNcydauHXWgX/9C1q1SkXxnXdyJypNd9yRRrr22y93EklSoVm8ykiM8H//l8pM795p09JS164dDB6cRukOPBA+/zx3otLyxRfQvz8cdVSaNpYkVTaLVxm5+GK47Ta46CI4/vjcaZbcllvCPffA//4HxxyT1jQp6d8fpk1zmlGSqoXFq0zcfnsqXiecAL//fe40S2/ejvoPPph21S+Dk6qK4tZbYf31YccdcyeRJBVDk9wBtHgvvQQnnwydOkGvXuV7nEz37vDWW3DVVbDBBvCLX+ROlNfrr6dp48suK9/fU0nS0rF4lbgvv0x7O7VqlbYcaNo0d6Ll88c/wrhx8Ktfpbsxc274mtv110OTJnDSSbmTSJKKxanGEnfaaekOxtratDlpuWvUKK1T22qrdLTRa6/lTpTH9Olwyy1w+OGV8fsqSVoyFq8SdsstaQ3Q734He+yRO03DadkyLSpv1gwOPRQ++yx3ouK7+2745BM49dTcSSRJxWTxKlEvvZS+KXfqVJ6L6RenQwe491544w047jiYOzd3ouK67jrYZBPYZZfcSSRJxWTxKkFffpn2dVp5ZbjzTmjcOHeiwujUCf7yF7j/frj00txpimfMGHjmmXSzgYvqJam6uLi+BJ11FrzyCjzySDp6p5Kdfjo8+2zam2zrreHgg3MnKryePdN063HH5U4iSSo2R7xKzMMPp13pf/1r2Guv3GkKL4R0d19NDRx7bLqRoJJNnZpGMbt0gVVWyZ1GklRsFq8S8umn6Uig738/jQBVi+bNoV8/aNECDjusshfb33ZbuqPxlFNyJ5Ek5WDxKiFnnw3vvpvuZmzePHea4lpvvXSn3xtvpN35K3Fn+xjTNON228EPfpA7jSQpB4tXiRgyJE0xnnNO+sZcjTp1gj/9KW01ccUVudM0vCefTFOpbiEhSdUrxDIYWqipqYmjR4/OHaNgPvsMNtsMVlwRnnuu+ka75hdjWv90991pvdvee+dO1HCOOgoeewzeeSdNq0qSKlMIYUyMsaa+jzniVQLOOSd9M7755uouXZAW2/fuDZtuCp07p+OFKsFrr8F996U1fJYuSapeFq/MHnssHXz9q1/BDjvkTlMaVlwxTTd+9VU6UmfatNyJlt9ll8EKK6TfZ0lS9bJ4ZTRtWhoB2WgjuPji3GlKywYbpPMpX3gBfvaz8l5s//rraQuJ006DtdbKnUaSlJPFK6M//AHGj08jXk4/LeiAA9KO9n36wJVX5k6z7OaNdp19du4kkqTcLF6ZvP56KhPHHgu77po7Tek67zw4+mg491wYPDh3mqX3+utp5O7UU2HttXOnkSTlZvHKIEb4+c/TQvo//Sl3mtIWAtx0E2y1VVps/8oruRMtnR490mjXOefkTiJJKgUWrwz69oVHH01TUG3a5E5T+lq2hAED0nTswQfDJ5/kTrRk3ngD7rgj7VLvaJckCSxeRff55+kQ7K239tiYpdG+fTpWaMKENPU4Z07uRIs3b22Xo12SpHksXkV28cXpWKDrroMmTXKnKS877ZSO3Hn00VReS/lOxzffTGu7TjnFUU1J0tf81l9EL74If/tb2h7BPbuWzUknpXVef/4zrLtuWnRfii67DJo2dbRLkvRNFq8iiTHd2bbKKmkbCS27K6+E995Ldzy2bZsO1S4lw4fDbbelUTlHuyRJ87N4FUnfvjB0KFx/Pay5Zu405a1Ro3S80gcfpNHDtdaC/ffPnSqZNi0VwfXWg4suyp1GklRqir7GK4SwXgjhiRDCyyGEl0IIZxY7Q7HNmAG/+Q1svnkqClp+zZqlxfZbbglHHgkjR+ZOlJx/frqb8aaboFWr3GkkSaUmx+L6OcCvYoybADsAp4UQNsmQo2iuvjod9vyXv0DjxrnTVI6VV4YHH0zTeQcckA6izqK2Fjp2JDZqxJl/68hNe9ayxx6ZskiSSlrRi1eM8b0Y47N1P/4ceAVYt9g5iuWDD9JC6wMPhD33zJ2m8qy9NjzySJp+3G23dANDUdXWQrduMGECIUY6MoET/tMtvV+SpG/Jup1ECKEjsDVQIhNFDe/CC2H6dLjqqtxJKtcGG8ATT6Qf77orjBpVxIuff35a2DWfMH1aer8kSd+SrXiFEFYC7gPOijF+Vs/Hu4UQRocQRk+ZMqX4ARvAiy+mA7BPOQU23jh3msq26aYwbFi6a3SPPb4uYgU3ceLSvV+SVNWyFK8QQlNS6aqNMfar73NijL1ijDUxxprWrVsXN2ADiBF+9atUBC68MHea6vCd76Ty1aED7LcfDBxY+GvOWad9/R9ov5D3S5KqWo67GgNwI/BKjPEvxb5+sTz0EAwZAr//PayxRu401WOddeDf/4YttoDDD0/bThTKG2/Ar2b2YBotv/mBli3T6diSJH1LjhGvnYCfALuHEJ6veyuRXZgaxpw5cPbZsOGGadNUFdcaa8C//gWdOsFPfwqdOzf8wdrPPw8/+hHcSVcmX9IrDbOFkB579YKuXRv2gpKkilD0DVRjjMOAUOzrFtPNN6djbfr3T/tNqfhWXhkefhj++Me0kenQoXDLLQ1zZ+nQoXDQQekajz4K3/leV/idRUuStHgekt3Apk1L3+h33BEOOSR3murWpEm6uXDEiFSS9toLzjwz3WW6rAYPhr33TttY/Oc/8L3vNVxeSVLls3g1sH/8A959F664Is08Kb9ttoFnn4Uzzkib2X7/+3D55en3aUnEmBbtH3NMKtObbJJ+7vp5SdLSsng1oI8/TgdgH3gg7Lxz7jSaX4sW8Pe/p6nB9ddPI2HrrZemDO+/H2bPXvDXTJsGvXvD1lun389HHkkjZk88AWV4o60kqQR4SHYDuuIK+OyzNJqi0rTnnuntzTfTeYq33AIPPADNm6dy1qTJ129Tp8Lnn6c7JHv1gi5dYMUVc38FkqRyFmKMuTMsVk1NTRw9enTuGIs0aVK6i/Hoo9M3c5WHOXPS1h///jfMmpV+Pu+tefNUtnbayWljSdKSCyGMiTHW1PcxR7wayEUXwdy5cPHFuZNoaTRpkqYbDzoodxJJUjVwjVcDeOWVtIXEaaelbZwkSZLqY/FqAOedByutlB4lSZIWxuK1nEaOhAED4JxzYM01c6eRJEmlzOK1nC64ANZaC37xi9xJJElSqXNx/XJ48kl47DH461/dZkCSJC2eI17LKEb43e9g3XWhe/fcaSRJUjlwxGsZDRmSjo3p2TPt9yRJkrQ4jngtgxjT2q6OHeGnP82dRpIklQtHvJbB/ffD6NFp765mzXKnkSRJ5cIRr6U0d25a27XRRnDssbnTSJKkcuKI11K65x548UXo0ycdNyNJkrSkHPFaCnPmwIUXwmabwVFH5U4jSZLKjWM2S+GOO+D116FfP2hkZZUkSUvJ+rCEZs+GSy+FH/wADj00dxpJklSOHPFaQrffDmPHwsCBEELuNJIkqRw54rUEZs+Gyy6DbbaBAw/MnUaSJJUrR7yWwK23wrhxcPXVjnZJkqRl54jXYsyalUa7tt0WDjggdxpJklTOHPFajFtugQkT4LrrHO2SJEnLxxGvRZg1C3r0gO23h/32y51GkiSVO0e8FuGmm2DiRLjhBke7JEnS8nPEayFmzkyjXTvsAPvskzuNJEmqBI54LcRNN8GkSXDjjY52SZKkhuGIVz1mzoTLL4cf/hD22it3GkmSVCkc8arHzTc72iVJkhqeI17fMmtWGu3aYQdHuyRJUsNyxOtbbr4Z3n4b/vlPR7skSVLDcsRrPvNGu7bfHvbeO3caSZJUaRzxms+tt6Z9u66/3tEuSZLU8BzxqjNvl/rttoN9982dRpIkVSKLV20t77Vrx14rBO6dsB7X71LraJckSSqI6i5etbXQrRuXvvMOw4CbmcRW13VL75ckSWpgIcaYO8Ni1dTUxNGjRzf487Zo1IgZ9Xz9zUNg+ty5DX49SZJU+UIIY2KMNfV9rKpHvMbGSBegZd3PWwJdgXFlUEYlSVL5qeri1bZDB1oBM4DmdY+tgDYdOmTNJUmSKlNVFy969OD9Ro3oDowAugOTGzVKtzdKkiQ1sOrex6trV/oBnH8+TJzIte3bp9LVtWvuZJIkqQJVd/GCVLIsWpIkqQiqe6pRkiSpiCxekiRJRWLxkiRJKhKLlyRJUpFYvCRJkorE4iVJklQkFi9JkqQisXhJkiQVicVLkiSpSCxekiRJRWLxkiRJKhKLlyRJUpFYvCRJkorE4iVJklQkFi9JkqQiCTHG3BkWK4QwBZhQ4MusCXxY4GuUO1+jRfP1WTxfo0Xz9Vk8X6NF8/VZtGK9Ph1ijK3r+0BZFK9iCCGMjjHW5M5RynyNFs3XZ/F8jRbN12fxfI0Wzddn0Urh9XGqUZIkqUgsXpIkSUVi8fpar9wByoCv0aL5+iyer9Gi+fosnq/Rovn6LFr218c1XpIkSUXiiJckSVKRWLyAEMK+IYTXQghvhhB+mztPqQkh3BRC+CCE8GLuLKUohLBeCOGJEMLLIYSXQghn5s5USkIIzUMIo0IIL9S9PhfnzlSKQgiNQwjPhRAeyJ2lFIUQxocQ/hdCeD6EMDp3nlIUQlg1hNA3hPBqCOGVEMIPc2cqFSGEjev+7Mx7+yyEcFaWLNU+1RhCaAy8DuwFTAKeATrHGF/OGqyEhBB2Ab4AbosxbpY7T6kJIbQF2sYYnw0hrAyMAQ71z1ASQgjAijHGL0IITYFhwJkxxhGZo5WUEMIvgRqgVYzxwNx5Sk0IYTxQE2N0j6qFCCHcCgyNMfYOITQDWsYYp2aOVXLqvu+/A2wfYyz0HqELcMQLtgPejDGOjTHOAu4CDsmcqaTEGJ8CPs6do1TFGN+LMT5b9+PPgVeAdfOmKh0x+aLup03r3qr7f3zfEkJoBxwA9M6dReUphLAKsAtwI0CMcZala6H2AN7KUbrA4gXpG+Tb8/18En7T1DIKIXQEtgZGZo5SUuqm0Z4HPgAejTH6+nzT34BfA3Mz5yhlERgSQhgTQuiWO0wJWh+YAtxcN2XdO4SwYu5QJeoYoE+ui1u8pAYSQlgJuA84K8b4We48pSTG+FWMcSugHbBdCMEp6zohhAOBD2KMY3JnKXE/ijH+ANgPOK1uCYS+1gT4AdAzxrg18CXgmuVvqZuCPRi4N1cGi1ea511vvp+3q3uftMTq1i7dB9TGGPvlzlOq6qY+ngD2zRyllOwEHFy3hukuYPcQwh15I5WeGOM7dY8fAP1Jy0T0tUnApPlGk/uSipi+aT/g2Rjj+7kCWLzSYvoNQwjr1zXhY4CBmTOpjNQtHr8ReCXG+JfceUpNCKF1CGHVuh+3IN3I8mrWUCUkxnhujLFdjLEj6d+fx2OMx2aOVVJCCCvW3bhC3fTZ3oB3Wc8nxjgZeDuEsHHdu/YAvMFnQZ3JOM0IaWiyqsUY54QQfg48AjQGbooxvpQ5VkkJIfQBOgFrhhAmARfGGG/Mm6qk7AT8BPhf3TomgPNijA/mi1RS2gK31t1J1Ai4J8bolglaGmsD/dP/cWgC3BljfDhvpJJ0OlBbN4gwFjgxc56SUlfa9wJOzpqj2reTkCRJKhanGiVJkorE4iVJklQkFi9JkqQisXhJkiQVicVLkiSpSCxekiRJRWLxkiRJKhKLl6SqEkLYNoTw3xBC87od0V/y7EhJxeIGqpKqTgjhMqA50IJ0vt0fMkeSVCUsXpKqTt2RKs8AM4AdY4xfZY4kqUo41SipGq0BrASsTBr5kqSicMRLUtUJIQwE7gLWB9rGGH+eOZKkKtEkdwBJKqYQwnHA7BjjnSGExsDwEMLuMcbHc2eTVPkc8ZIkSSoS13hJkiQVicVLkiSpSCxekiRJRWLxkiRJKhKLlyRJUpFYvCRJkorE4iVJklQkFi9JkqQi+X/SPqHbYkYBswAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percent Error: 0.8492%\n"
     ]
    }
   ],
   "source": [
    "# Output: [1, 3, 4.20134833, 5.72175047, 6.07329955, 5.5815012, 10]\n",
    "_x = [0, 1, 2, 3, 4, 5, 6, 7]\n",
    "_y = [1, 3, 2, 6, 4, 8, 5, 10]\n",
    "_X = [0, 1, 2.5 , 3.25, 4.5, 5.75, 7]\n",
    "\n",
    "cubic_spline_test_2 = my_cubic_spline(x = _x,\n",
    "                                      y = _y,\n",
    "                                      X = _X)\n",
    "print(cubic_spline_test_2)\n",
    "\n",
    "# Check accuracy\n",
    "f = CubicSpline(_x,\n",
    "                _y,\n",
    "                bc_type='natural')\n",
    "\n",
    "x_new = np.linspace(min(_x), max(_x), 100)\n",
    "y_new = f(x_new)\n",
    "cubic_spline_2 = f(_X)\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.plot(x_new, y_new, 'b')\n",
    "plt.plot(_x, _y, 'ro')\n",
    "plt.plot(_X, cubic_spline_test_2, 'k*')\n",
    "\n",
    "plt.title('Cubic Spline Interpolation')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()\n",
    "\n",
    "# Calculate Percent Error\n",
    "cs_error_2 = round(\n",
    "                np.mean(\n",
    "                    (cubic_spline_2 - cubic_spline_test_2)/cubic_spline_2)*100,\n",
    "                4)\n",
    "\n",
    "print(f\"Percent Error: {cs_error_2}%\")"
   ]
  }
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