{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# PDE session 1\n", "## Finite differences using python" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this session we will use python to compute the derivative of a dependent variable $u$ as function of an independent variable $x$.\n", "\n", "The dependent variable $u$ could be interpreted as the temperature, a displacement or any other scalar variable of interest. In this python notebook we are concerned with how this variable evolves along a 1D bar of length 2 meters. We will compute the gradient of $u$ using backward, forward and centered finite differences.\n", "\n", "The independent variable $x$, the dependent variable $u$ and a reference derivative $du/dx$ are stored in a text file. The reference derivative will be used to determine the accuracy of the various finite difference schemes.\n", "\n", "You should carry the following tasks in this notebook:\n", "\n", "0. Import the necessary python modules\n", "1. Import the data needed in this session\n", "2. Split the data into the independent variable $x$, the dependent variable $u$ and its derivative $du/dx$ using array slicing\n", "3. Plot the dependent variable $u$ and its derivative $du/dx$ using a subplot (i.e. one plot per quantity)\n", "4. Write a function, called backward, which computes $du/dx$ using a backward finite difference where the inputs are the dependent variable $u$ and the independent variable $x$\n", "5. Write a function, called forward, which computes $du/dx$ using a forward finite difference where the inputs are the dependent variable $u$ and the independent variable $x$\n", "6. Write a function, called centered, which computes $du/dx$ using a centered finite difference where the inputs are the dependent variable $u$ and the independent variable $x$\n", "7. Plot the derivatives computed using the functions or questions 4,5 and 6 and plot them alongside the reference data in a subplot (i.e. one plot per method)\n", "8. What can you comment upon the results plotted in question 7?\n", "9. Write a function, called abs_error, which computes the absolute error between the reference derivative $du/dx$ and its numerical estimation\n", "10. Plot the errors obtained with the three different finite difference approximations using a subplot (i.e. one plot per method), what can you say about your results?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 0**\n", "\n", "We first start by importing the necessary modules for our notebook" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 1**\n", "\n", "Next, we need to import our dataset which is stored in the file named `data_1.csv`. This file should be stored in the same folder as this python notebook.\n", "\n", "To load this data file we use the package `loadtxt` from `numpy`. We will look a bit more closely to the import of data in a dedicated notebook. For the time being we will skip the first row of the text file and use a , as a delimeter. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "data = np.loadtxt('data_1.csv',delimiter=',',skiprows=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Question 2" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "x_value = data[:,0]\n", "u_value = data[:,1]\n", "du_dx = data[:,2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Question 3\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.subplot(1,2,1)\n", "plt.plot(x_value,u_value)\n", "plt.title('u_value')\n", "\n", "plt.subplot(1,2,2)\n", "plt.plot(x_value,du_dx)\n", "plt.title('du/dx')\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Question 4 backwards" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def backward(u,x):\n", " du_dx_num = np.zeros_like(u)\n", " du_dx_num[1:] = (u[1:]- u[:-1]) / (x[1:] - x[:-1])\n", " du_dx_num[0] = np.nan\n", " return du_dx_num\n", "\n", "#print(backward(u_value,x_value))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def backwards(u, x):\n", " n = len(u)\n", " du_dx_num = np.zeros(n)\n", " du_dx_num[0] = 0\n", " for i in range(1,n):\n", " du_dx_num[i] = (u[i] - u[i-1]) / (x[i]- x[i-1])\n", " return du_dx_num\n", "\n", "b = backwards(u_value,x_value)\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Question 5 forward" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def forwards(u, x):\n", " n = len(u)\n", " du_dx_num = np.zeros(n)\n", " for i in range(n-1):\n", " du_dx_num[i] = (u[i+1] - u[i]) / (x[i+1]- x[i])\n", " return du_dx_num\n", "\n", "f = forwards(u_value,x_value)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Question 6 Central\n", "\n", "6. Write a function, called centered, which computes $du/dx$ using a centered finite difference where the inputs are the dependent variable $u$ and the independent variable $x$\n", "7. Plot the derivatives computed using the functions or questions 4,5 and 6 and plot them alongside the reference data in a subplot (i.e. one plot per method)\n", "8. What can you comment upon the results plotted in question 7?\n", "9. Write a function, called abs_error, which computes the absolute error between the reference derivative $du/dx$ and its numerical estimation\n", "10. Plot the errors obtained with the three different finite difference approximations using a subplot (i.e. one plot per method), what can you say about your results?\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def centered(u,x):\n", " n = len(u)\n", " du_dx_num = np.zeros(n)\n", " for i in range(1, n-1):\n", " du_dx_num[i] = (u[i+1] - u[i-1]) / (2*(x[i+1]- x[i]))\n", " return du_dx_num\n", "\n", "c = centered(u_value , x_value)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Question 7\n", "\n", "7. Plot the derivatives computed using the functions or questions 4,5 and 6 and plot them alongside the reference data in a subplot (i.e. one plot per method)\n", "8. What can you comment upon the results plotted in question 7?\n", "9. Write a function, called abs_error, which computes the absolute error between the reference derivative $du/dx$ and its numerical estimation\n", "10. Plot the errors obtained with the three different finite difference approximations using a subplot (i.e. one plot per method), what can you say about your results?\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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erzft1xFCaH7NdHH2xz/+EcuWLcPUqVNx//3347nnnsOaNWtw+umnO26nPzdPGGi4g4qj0eiQ97322mvo7OzE5z//+bxe8+WXX1Z3h3300Uc4+eST8/p6lLstW7akjAS3bt0KWZYxadIk/P3vf0coFMLTTz+dMuIcvONq6tSpAICNGzdi2rRpGV8vGAzimWeewemnn46zzz4br7zyypDd1QsWLEA4HMaf//xn7Nu3T+10P/vZz2LdunUYOXIkjjzySIwcOVL9nMceewynnXYa7r///pSv1d7ejvr6+qw/B+Uw3C1btgz5u08//XTI+/x+P84//3ycf/75kGUZ3/rWt3Dvvffihz/8YdafAWWn/D7S/ew3b96M+vp6TRutJkyYgAkTJmDdunXYvn17SizdeOONePTRRxGNRlOWgmiN+2zPv3HjRgghUtrYdN8PABxzzDE45phjcPPNN+P111/HKaecgnvuuQc/+9nPNL8mGaOhoQFVVVXYuHHjsB8zdepUdHd3qxU6I+RyacBjjz2GKVOm4PHHH0/5/FtuucWw57IKK3YaNDQ0oLS0NGtHpVTV2tvbUz5GqcQle/bZZzFz5syU3WjDdYhNTU1py8wHDhzA9ddfj7POOgvnnXcebrrpprSvRdZQttgr7rjjDgDAOeeco44yk0eVHR0deOCBB1I+56yzzkJlZSVWrlyZclTK4M9VVFdXY/Xq1WhsbMSZZ56pTuUqTjrpJJSUlOC2225DbW2tmvgtWLAAb775Jl555ZWUCgsQGxEPfq1HH30U+/bty/ozAGKVxDlz5uAPf/hDyhTGmjVrsGnTppSPbWlpSXnb4/Gouy7THWdB+iX/PpLbpo0bN+L555/XNbhcsGABXnrpJbz99ttq3MyZMweVlZX4xS9+gdLSUsybN0/9eK1xn8nnP/957N+/H4899pj6vt7eXtx3330pH9fZ2YlIJJLyvmOOOQYej4exZBOPx4MLL7wQf//739POKgghcMkll+CNN97A6tWrh/x9e3v7kN+pFspAZXBfnEm6WH3rrbfwxhtv6H59u7Fip4HX68XixYvx5JNPYvfu3erI85NPPkkJxqqqKtTX1+PVV19NWRf3f//v/x3yNVetWoXzzjsv5X1nnHEGSkpKcMcdd+Css85SRw2Dt3srrrrqKsiyjPvvvx9erxezZs3ClVdeiTVr1lhyzRml2rFjBy644AKcffbZeOONN/DHP/4RX/7yl3HsscciGAyqlalrrrkG3d3d+N///V80NjbiwIED6teoqqrCb37zG3z961/HCSecoJ4ltmHDBvT29uIPf/jDkNetr6/HmjVrcOqpp+KMM87Aa6+9hrFjxwKILTKfN28e3nzzTfUMOyBWZenp6UFPT8+QxO68887Df/3Xf+FrX/sa5s+fj48++ggPP/wwpkyZovlnsXLlSpx77rk49dRTccUVV6C1tRV33HEHZs2ahe7ubvXjvv71r6O1tRWnn346xo0bh127duGOO+7AnDlzMGPGDF0/fxrer371K5xzzjk4+eSTceWVV6rHnVRXV+u6emnBggV4+OGHIUmSOjXr9Xoxf/58rF69GosWLVIXoAOxgYqWuM/kqquuwp133onLL78c7733HkaPHo2HHnoIZWVlKR/30ksv4brrrsOSJUtw5JFHIhKJ4KGHHoLX6x0ynUfWufXWW/H8889j4cKFuPrqqzFjxgwcOHAAjz76KF577TV8//vfx9NPP43zzjsPy5Ytw7x589DT04OPPvoIjz32GHbu3KlppiCZMrj49re/jcWLF8Pr9eLf/u3fMn7Oeeedh8cffxxf/OIXce6552LHjh245557MHPmzJQ2yxHs2o7rNBs2bBDBYFBMmDBB/OIXvxA/+9nPhhx3IkRsizYAceWVV4q7775bXHbZZWLevHkp26O3b98uAIiXX355yOusWLEi5biTK6+8Mu1xJ7///e8FAPHggw+q7/vjH/8oAIi77rrLtJ8DDaUcEbFp0yZx8cUXi8rKSjFixAhx3XXXpRxZ8vTTT4vZs2eLYDAoJk2aJG677Tb197hjx46Ur/n000+L+fPni9LSUlFVVSVOPPFE8ec//1n9++TjThRbt24Vo0ePFjNmzBBNTU3q+7///e8LAOK2225L+XjluIht27alvL+/v19873vfE6NHjxalpaXilFNOEW+88YZYuHChWLhwofpx6Y7VSPa3v/1NzJgxQwQCATFz5kzx+OOPi6VLl6Ycd/LYY4+Js846SzQ2Ngq/3y8mTJggrrnmGnHgwIGMP3Ma3nC/lxdeeEGccsopakydf/75YtOmTSkfo8Rycvwk+/jjjwUAMWPGjJT3/+xnPxMAxA9/+MMhn6M17idOnCjOPffctK+7a9cuccEFF4iysjJRX18vbrjhBvHcc8+lHHeyfft2ccUVV4ipU6eKYDAoamtrxWmnnSZeeOGFbD8yMtmuXbvE5ZdfLhoaGkQgEBBTpkwR1157rXq8SFdXl1ixYoWYNm2a8Pv9or6+XsyfP1/8+te/FuFwWAiROKrkV7/61ZCvj0HHj0QiEXH99deLhoYGIUnSkCPJ0n0NWZbFrbfeKiZOnCgCgYCYO3eueOaZZ4a0Weler9AwsdPhlVdeEfPmzRN+v19MmTJF3HPPPWpDqOjt7RVXXnmlqK6uFpWVleKSSy4Rhw8fTgmEO++8U1RXV4uBgYEhrxGNRsVPfvITtVNdtGiR2Lhxo5g4caKa2O3Zs0dUV1eL888/f8jnf/GLXxTl5eVi+/btpvwMiIiIqHBJQujYSkKG+PznP4+Kigr89a9/tftRiIiIyEW4xs4GixYtGrKuiYiIiChfrNgRERERuQSPOyEiIiJyCSZ2RERERC7BxI6IiIjIJQp684Qsy9i/fz8qKyt54K7DCCHQ1dWFMWPGpFwIXsgYb87lxHgDGHNO5sSYY7w5l554K+jEbv/+/Rg/frzdj0F52LNnD8aNG2f3Y2jCeHM+J8UbwJhzAyfFHOPN+bTEW0EndpWVlQBi30hVVZXNT0N6dHZ2Yvz48erv0AkYb87lxHgDGHNO5sSYY7w5l554K+jETikVV1VVMQgdyknlfsab8zkp3gDGnBs4KeYYb86nJd6csTCAiIiIiLJiYkdERETkEkzsiIiIiFyCiR0RERGRSzCxIyIiInIJJnZERERELsHEjoiIiMglmNgRERERuQQTOyIiIiKXYGJHRERE5BJM7IiIiIhcgokdERERkUswsSMiIiJyCVMTu7vvvhuzZ89GVVUVqqqqcPLJJ+Mf//iHmS9JRYzxRlZivJHVGHOkhamJ3bhx4/CLX/wC7733Ht59912cfvrp+MIXvoCPP/7YzJe1VVQWeGNbC7r6B+x+lKJTjPEGAFsOdWF7U7fdj1F0ijXe9rb1YuO+DrsfoygVY8x1hyJ4fVszIlHZ7kdxDEkIIax8wdraWvzqV7/ClVdemfVjOzs7UV1djY6ODlRVVVnwdPm74ZEP8NT6/RhbU4rnv/tZlAd8dj+SLQrld+f2eHvmw/247k8fwOuR8OerPoMTJ9fa/Ui2KJTfnZ54AwrnubXasKcdF939OiKywK+XHIuL542z+5FsUyi/Oze3cf0DUSy+/VXsaunFOUePwt1fmWf3I9lGz+/OsjV20WgUjzzyCHp6enDyySen/ZhQKITOzs6UP06yp7UXT2/YDwDY196Hp9bvt/mJilcxxJsQAne8uBVArFJ836vbbX6i4qUl3gDnx9zdL29DRBbx/98Ki+sClKQY2rhnPjyAXS29AIB/bDyIbZyZ0MT0xO6jjz5CRUUFAoEAvvGNb+CJJ57AzJkz037sypUrUV1drf4ZP3682Y9nqOc3HUJyO/fS5sP2PUyRKqZ429Pah08Pdalvr9vShAFOV1hKT7wBzo65cETGy/9KtGnbmnqwt63PxicqTsXUxq3++GDK22vZp2piemI3ffp0rF+/Hm+99Ra++c1vYunSpdi0aVPaj12xYgU6OjrUP3v27DH78Qz1zo5WAMDiWSMBAO/vbuOI1mLFFG9v7WgBAMydUIOashKEIjI+3u+sEbnT6Yk3wNkx99G+dvQPyKgt9+PY8TUAgHd3tdr7UEWoWNo4WRZ4d+fQPpWyM30BmN/vx7Rp0wAA8+bNwzvvvIPf/va3uPfee4d8bCAQQCAQMPuRTCGEwLu7YkH31c9MwppNh9DaE8bhrhBGVgVtfrriUSzxBgDv7ozF22em1KGmtARrP23Ch3vbMSfe6ZL59MQb4OyYeycebydMGoGxNWXYsKcdG/Z04Itzi3ednR2KpY3b3tyDtt4BBEs8uPSE8Vj98SF8cqAr+yeS9efYybKMUChk9cuarqUnjObuECQJmDdxBKY2VAAANrGCYiu3xhsA/OtwrJE7ekw1jhhZCQDY3tRj5yMVPVfH26HkeIu1b9ubGW92c2vMbT4Y6ztnjK7C7HE1AICdLT3oCUVsfCpnMLVit2LFCpxzzjmYMGECurq68Kc//Qkvv/wyVq9ebebL2mLb4diiznEjSlHq92JaYwW2HO7GzhY2fFYppngTQmDroVjMTWusUI/X4eJi6xRTvAHA1sOJeKst9wMAj9mxWDHF3LbDsb5zWkMF6isCGFFWgrbeAexu7cWM0YW/o9dOpiZ2hw8fxuWXX44DBw6guroas2fPxurVq3HmmWea+bK22Bpv4JRK3YTaMgDA7tZe256p2BRTvB3uCqErFIHXI2FSfRk6+mKJHSt21immeBNCqIndESMrUF0aS+z2tfehfyCKYInXzscrGsUUc2qf2pjoU9t6O5jYaWBqYnf//feb+eULSvLoAgDGxRO7PUzsLFNM8bYlXq2bWFuGgM+LyfXlAID9HX0IR2T4fbwt0GzFFG/7O/rRG47C55Ewsa4cPo+EyoAPXaEI9rT2qksByFzFFHNqhTipT92wt4N9qgZs/Q2ijC6mNaZW7Pa08jgAMt62QaPZ+go//F4PhAAOd/Xb+WjkQspSk0n15SjxeiBJEkbXxDaFHexkvJGxZFmo0/xD+1QmdtkwsTPI3niwTayLVU7GjygFAOxpYxCS8fa1xwYMSmMnSRJGVsd2vx3sYEdLxhocbwAwqjrWxh1gvJHBmrpDCEVkeD0SxsX70vEj4okdz07MiomdAYQQasOnBKFyxElvOIpu7uIhgynxNqamVH3f6Cp2tGSO/Wq8JY5uGh1v4ziQIKMp7duoqiB83liaMrIqNnDljER2TOwM0NoTRigiQ5ISCV15wIdyf2xB8WFOVZDB9sVHrWOTOtqR1bH/P8R4I4Mp8ZY8kFDijVOxZLQD7bGYSh5INFbG/v9wp/uOdjEaEzsD7I8HYUNFIGXRemM8yTvcxUAkYykVlLE1iamx0fGOlhU7Mto+Nd6SKsTVrNiROZT2bXR1It4a4xW75u4QojJvdMqEiZ0B0k2LAUBDpVI6ZmJHxglFompMJY9oR3FqjEySLrEbxYEEmSRdn1pX7ockAbIAWnrYp2bCxM4A+9M0egDQqCR2nKogAymJW8DnUQ+KBRIDiaZuNnpknKgs1JhL7mgbKhIVFCIjJfrUxMDV5/WgrlzpUxlzmTCxM0C6hcVAYk1AEyt2ZKDk6okkSer76+JJXltP2JbnIndq6gohIgt4PZI6WAWAuopEvAnBqTEyzv6O9LNgSvyxT82MiZ0BhgtCTsWSGdSNEyNS421EPLFrZWJHBtrXHjuyKXmHIgCMKIvFW0QW6Oznzn8yzv72oRViILlP5SxYJkzsDLAvHoTJCz2BxIiWHS0ZSdn1qqypU6gVu94wZC4uJoMc7IgNTJXNEopgiVfd+c82jozSPxBV42nMsH3qgOXP5SRM7AzQHK/IKefsKJQRbXsvGz0yjjIN0Tg43uKJnSyg3h1LlK+meHVkcLwBQC0Hr2QwpX0L+DyoKk299ZR9qjZM7PIkhFADsaFycGJXAgBo62UnS8ZRNkfUV6TGW4nXg8pgrCFsYUdLBhku3gCgtoyJHRnrcFJ/mryGGEjuUxlvmTCxy1NnXwThqAxgaMNXU5aYGiMyynADCSAxHcuOloyixlu6xE6NN64jJmMo8ZZuIJHoU1ksyYSJXZ6U0Wxl0IdgiTfl75TRRVd/BJF48keUL20dLRM7MkZzdyyW0g0kauPHT3DNExlFOT4nXbxxKlYbJnZ5ylQ9qS4tUf+/nWueyCCZYo6JHRktc7zF2jhW7MgomeKNy5u0YWKXJ6Vil6564vN61OSOIwwyQm84gp5wFEC2xI4dLRkjc2IXex/XdJJRMvWpygYx9qeZMbHLk7Ijtj5NowckRhicqiAjNHfFGrRgiQcVAd+Qv1emKrgrlowgyyLL1FisfetkvJFBMvWpI5LW2PFQ7OExsctTptEFwA0UZKym7tjRE+l2jAFAVanS0fLAWMpfe98AIvEzEZXrnJIx3shomfrUmvhAIspDsTNiYpenTNMUQGJEy9IxGSHTxgkAqIofd8KKHRlBibcRZSXw+4Z2F1XBWPvGeCOjZOpTgyVelMY3KbJPHR4Tuzw1Z6nYjeD2bDJQtoGEWkHpZ7xR/rLHW2wgwXgjIwiRmPpvzFIsYZ86PCZ2edLa0Xax4SMDMLEjK2VaXwckdv5zjR0ZoTsUQf9A+nNhFexTs2Nil6dsHa1yE0AX1wOQARLrT4Jp/16ZGuOaJzJC9qn/WLz1hKM8q5PypsRbRcCHUr837cewT82OiV0eZFmo2/yHraAEOaIl42QbSFRzaowM1JSlYqd0sgA7WspfpsOwFUqfyord8JjY5aGtN4xofMeYcn7YYBxdkJGa4g1fXUX6eEseSMgyjwOg/ChHT9QNU7HzeT0oj1dWuIGC8pW4Tix9+wYk+lTOSgyPiV0elNP9a8pKUOJN/6OsDCauFSPKV1s85uqGGUgo609kAfSEGXOUn9b4zsPhBq5A0jo7VlAoT8rB6umO1lFUsmKXFRO7PCiJXW2ZhtEFg5AMoCR2I4bpaIMlXvVYCp7zRPlSdh5mauN4lh0ZRTnIf7j2DUjuUxlvw2Filwel0dMShKzYUb7CERldoVgcZexoua6TDJJtIAEkxRsHr5SnNrVCXDLsx3AWLDsmdnlQgnCEltEsGz3Kk3Igp0dKTH+lo54txsSO8qQkdpmmYhlvZBRlFixzn8pZsGyY2OVBnYrNOLqIBWF3KMLF7JSX1qSBhMcz9DoxBW8DICPorRAz3ihfbRrWdHKNXXZM7PLQpmV0EQ9CwcXslKdWDdNiQPJidsYb5U6pEHs9UsqxJoNxVoKMoqWN4/Km7JjY5UGtoGQIwoDPgxJvrLrCjpby0daTfSE7kHwcADtayl2iQlySpULM4yfIGO1aNuswscuKiV0e2jTsipUkiaVjMoRyFMCIDFP/QOzUdgDoCbHho9xpWe8EAOWMNzJIq4Y1nZXcrJMVE7s8tGrYFQtwhEHGUI4CyNToAYmOtptT/5SHNg1HTwBJ8cbEjvLQF46ibyAKQNsu7K7+CITguvV0mNjloU3D5gmAiz3JGFp2YQOs2JEx1MOJNU79cw0x5UNp3/xJt5mko8RbVBZqIkipmNjlQcvmCYBXoJAxtExTAMmJHRs9yl3iDLvMA9dyv1KxY7xR7lqT4k2Shl/TWeb3whtf88k+NT0mdjlKOQpAY0fLqQrKh9aKHafGyAhcY0dW0tq+SZKkVvTYxqXHxC5H7X2Jw2KVOf/hKA1fL6cqKA9qxS7DBdkAUB6IN3pc00l50HKmGJA0cGW8UR60zkgA7FOzYWKXI2VhcU2Ww2KBpI6WUxWUBy27sIGkqVg2epQH7RW7WPvGih3lQ8v1dQrOSmTGxC5HiUYvc7UOSKxB6WUQUh5aNVZQ2OiREfRW7HrC3KVIuWvVcIadQpmK7WWxJC0mdjnS2ugBSWtQWEGhHPWFo+gfkAFkH9FyVywZQe9xJ7IAdylSznKp2LFPTY+JXY60TlMAsV08AHcpUu5a4ocTZzsKAEhezM54o9y1apz6L/N7oWxiZJWYcpU4Xif7LFiZn21cJkzsctSmY6EnKyiUr0T1JPNRAEDq1Jgsc2qM9Es9LDZzRytJEirY0VKe9FTsKriuMyMmdjnSck+sooxlY8pTq8ajAIBEYicE0MupMcqBstSkxCup8ZRJOXfGUp707Ipln5oZE7scad2hCCSPLtjJUm6UeKvLctQJAARLPFA2anNES7lIXmqSrUIMJO/8Z7xRbrSeYwdwFiwbJnY50npPLJC0HoCjC8qRnjWdkiRxZyzlRc/mMIAdLeVHCKEuN9FUsVPWrYdZLEmHiV2OtN4TC7DRo/yxoyUr6RlIANylSPnpCUcRjsZ3/euo2PEIsfSY2OVI6WhrdOyK5Zk7lKtcO1pW7CgXejaHAYw3yo8Sb6UlXpRm2fUPJGbBeOh/ekzscqRvjR0P8KT86K3Y8cgTykdiqUn2GQmAFWLKj54D/4HEmk5eKZYeE7sc9A9E1bl9PbtiZQH1kFkiPVq6te/CBoBKtYIyYNozkXvpGbgCvC+W8qPnlAkgcZsTBxLpmZrYrVy5EieccAIqKyvR2NiICy+8EJ9++qmZL2mJ9vho1uuRUBXMfhRAWUmitMw1KOZxa7wBSRU7zVOxvJ/YbG6ON90dbYBTY1Zwa8zlOvXPzRPpmZrYvfLKK7j22mvx5ptvYs2aNRgYGMBZZ52Fnp4eM1/WdHqPAvB4pKTbJ5jYmcWt8QYArT36psZ4P7H53BxvujtaP6fGrODWmNO/hpj9aSbZy015eO6551LefvDBB9HY2Ij33nsPn/3sZ818aVMl1jtp62SB2AijNxzlmicTuTXehBBo17nGrlTtaBlvZnFrvAH6O1rGmzXcGnO5ryFmYpeOpWvsOjo6AAC1tbVWvqzh9DZ6QGJEy6lY67gl3jr7I4jErwbTGnNKhZiXslvHLfEG6O9olV2KTOys5ZaYU2cktFbs/ImpWG5IHMrUil0yWZbxne98B6eccgqOPvrotB8TCoUQCoXUtzs7O616PF30NnoARxhWc1O8KdW60hIvgiXZjwIAgFK1o2W8WUFLvAHOiLnkw2K1rrFLDCQYb1ZxUxun51xYIDEVG5UFQhFZc7tYLCyr2F177bXYuHEjHnnkkWE/ZuXKlaiurlb/jB8/3qrH06VVx2XFinJekm0pN8VbW6/2E9kVZZwas5SWeAOcEXPJh8Vq3azDqVjruamN07tZR6kQAyyWpGNJYnfdddfhmWeewdq1azFu3LhhP27FihXo6OhQ/+zZs8eKx9OtTeeZO0DSYk9WUEzn1nir0RFvagWFHa3ptMYb4IyYU+ItWOLRdFgswHizmtvauHadu/69HgmlJRxMDMfUqVghBK6//no88cQTePnllzF58uSMHx8IBBAIBMx8JEOoh3fqWGNXxqlY07k13nKZ+mejZz698QY4I+ZyWUPMCrE13NrGKWvstNzkpCgPeNE3EOVtJ2mYmthde+21+NOf/oSnnnoKlZWVOHjwIACguroapaWlZr60qfTuUASACh6oaDq3xlurWrHT09HG4o0VFPO4Nt569Sd2pSXcPGEFN8acECLndevN3WH2qWmYOhV79913o6OjA4sWLcLo0aPVP3/5y1/MfFnT5bLGrpS7FE3n1nhTDsSuzWEqtpeL2U3j3njT38kmpmIZb2ZyY8x19kcQje/617PcRJmVYJ86lOlTsW7UlsNUBRcXm8+t8aZUUPRU7Bhv5nNtvKnTYrkMJGLHT2g5uJ30c2PMKQOJMr/2Xf8A27hMeFdsDlp1LvQEEteK9XN0QTrlV0FhvJE+ucSb0skKAYQivA+btMtlTSeQaOPYpw7FxE6nvnAU/QOxhkvr9U5A0lQsO1rSqS2fCgrjjXTKZ00nwJgjfZSlJnr6UyBpKpbxNgQTO52URZ4lXgkVAe0z2UHuUqQcteWymJ2bJyhH6kJ2HQMJr0eC3xfrTngoNumRa8WOferwmNjplDya1bOOhFc8Ua5y2TGmTP2HozIiUU6NkXZ6b51QcPqfcpFL+wawT82EiZ1OiR2K+oKQZWPKRfL1Trp2jCUdLNvLho90yKVCDCQGE6ygkB65xhv71OExsdMpsUNR53oAji4oB73J1zvpGNEGfB54PbGKMhs+0iPnCopyCDunYkmHthwO/AeSlpuwTx2CiZ1OicuKObog8ylT/36fR40hLSRJYgWFdMu1QgxwKpZyox4fluPmCbZvQzGx06lN52XFijKOLigHyVP/es8GS5zzxAoKadOTY4UYYEdLueFxJ8ZjYqdT4nBivVOxyo4xBiFp15bj1D/ACgrp15ZjhRhgvFFu2nOcig1y4DosJnY6cT0AWSnX9U5AIuY4mCCt2pIOX9dbIS5T440dLWmn3k2scyq2TL1SjLv+B2Nip1O+O3jCEVm9F48om1yur1PwkGLSSx245jSQSFwrRqSFEEK96UR/sYT3Ew+HiZ1OrTlunihLOn6CVTvSqjXHU9mB5HOe2PCRNrkuNQE4FUv6dYciGIjGCh05J3bsT4dgYqdTe44j2oDPA2Vmg1MVpFWuo1mAi9lJv1w3hwG8lJ30U/rTYIkn5exNLdi+DY+JnU6tOY5oJUlSA7E/zDUBpE0u93YqWEEhvfKq2JVwTSfpo86A5dG+9TPehmBip0P/QFQt++Y0olVGGJwaI43U405ymIrl5gnSq7U3/46Wa55Iq8Su/3z6U7ZvgzGx00EJQp9HQmX8lHU9SllBIZ3yafi4eYL0MmTzBOONNMpv1z/70+EwsdMheVpM71EAAG+fIP3aDJiqYAWFtDJiFzYXs5NWrTnecgIk+tMQT5oYgomdDvlMiwFs+Ei/XM9NBFhBIf3yqdixQkx6tedRsVPOTQR4+8RgTOx0yGchOwAEuYuHdEhd05nLYnauQSF98tk8wTWdpFc+fWrAl0hfGHOpmNjp0JbHwmKAFTvSJ3lNZ0UOazqVgUSI8UYaCCFyPoAdAILxjpbxRlol7sLWP5DweJJOmmDMpWBip0NbT+7TFAAXe5I+6tE65Tmu6VQvyebxOpRd30AUoUgsVvLZPMFOlrRKbuNywUOK02Nip0NiNJvbGrvSEt4XS9olLsfOLd4CPjZ6pJ3Syfq9HpTrPCwWSNocxngjjfKpEAM8pHg4TOx0yPU6MUWpP/bjZsWOtMi70WMFhXRoT7q+LpcKcbCEFWLSx6g2jn1qKiZ2OuQbhMouHo5oSYt8jp4AEmueGG+kRWu+8ZZUsROCx09QZrE1nbnfhQ3wPuzhMLHTIXGPYm5BGOQ5dqRDvo2eMpoNsYJCGuQ7cA2WJLoTZa0e0XB6w1GElTWd+Q4meE1nCiZ2OqibJ/LcFcv1AKSFkRUUomzUCnGeA1eA0/+Unbqm0+dR+0a9En0qK3bJmNjpYNRCTzZ6pEU+1+0AjDfSpzWPw7ABoMTrgc8TW5vHdXaUTfLmsFzWdAJs44bDxE6j/oGoWmnLd2s2RxekRUt3fokd1zyRHu15DlwB7owl7VqNiDfOgqXFxE4jZXTh9UioCuo/LBZgo0f6tMSnKuoqAjl9vrLmSQiueaLsErcA5DYVCwABriMmjdryPGUCYJ86HCZ2GrX0hAAYUzZmo0datHTHYq4uz4odwA0UlJ2S2NXnOJAAEkc69UfYxlFmzUr7lk+8sU9Ni4mdRkqjV1eeT6PHc55IGyFEIuYq8l/zxBEtZaNM/ecabwAQjB+K3c+OlrJQZyTyqdjxrM60mNhpZEijV8JzxUibzr4IInJsXZwRUxVs+CgbZVbCkMErK3aURWt3/okdd/6nx8ROIyPKxsoVT+xkKRulk60M+NS4yUWADR9pIMv5V4iBRMWO54pRNupAIq8+NT71z1mwFEzsNDKibBxk9YQ0UuKtNo9OFkha88SYowza+wYQLxDntUsxyKkx0qg5z13/APvU4TCx00gpG9cbMBXbzx2KlEWLAdMUQFIFhQ0fZaBs1KkuLYHfl3u3UMrlJqRRYrOOAYkd+9QUTOw0UsrGtfmsP4kHYTgiQ5Z5rhgNz4h4A3itGGljxIwEwAoKaddi4K5YxlsqJnYaNRuyeSLp+AmOMCgDIyrEACt2pI0Rm8MAdrSkTf9AFD3xndP5TcXGUpgQ4y0FEzuNlAqKEWVjgB0tZdZiwOGdANc8kTZG7IgFkit2HLjS8JT2rcSb+4H/AHfFDoeJnUaJrdm5N3xej4QSr3KXIgORhpfvrROKoI9rnig7oyp27GhJC2Uatrbcn/OB/0DSunUOJFIwsdOgL5xUNjZoaoyJHWWS760TCh6KTVokKnb5JnbchU3ZtRhw4D/AI8SGw8ROA6XR83s9qAzkXjYGEueKsaOlTIw4UwzgQIK0SVTs8tysw4odaWB0hZjtWyomdhokB2E+ZWOAdymSNkatseOVO6RFi1EDiRLuwqbsDJ+R4GbEFEzsNDCqegKwgkLZJd8CkM+F7AAQUM4V492dlEHymqd8sGJHWrQavIaYR4ilYmKngXqdWJ7rAQCWjim7zv4BROONVD63AADsaEmbFg4kyEJGHB8GpJ40wVmwBCZ2Ghh1eCfAXTyUndLoVQZ9ed0CAPD4CcouEpXR3jsAwICpMfUmAHayNLxWwzbrJCV2bONUTOw0SJyQbURix4odZWbUNCzAA2Mpu9beWLxJElCTZ4VYPe6EFTvKwKhdsTxCLD0mdhoYdaYYwAoKZWfUeieAx09QdsrmsNoyP7yefDeHxTdPcDE7ZaDGHIslpmBip4FRF7IDDELK7nBXLLFrMHAgwTV2NJxWg3ZgA0lX2LFiR8MQQqApPnitN3TdOgcTCiZ2GjQbORXr43EnlFlTPLFrrOJmHTLf4a5+AEBDpQFT/zzOibLo7I8gHK/oGtPGMeYGY2KngVJBaawM5v211I6WI1oahtrRGrjGro+jWRrG4U6lfTOwQsz2jYbRFG/fKoO+lM0PuVKPEGPMqUxN7F599VWcf/75GDNmDCRJwpNPPmnmy5kiKgt1zZMxDZ8yumBHazQ3xBtgTsUuxIqdKdwQc+rAtcq4gWuI54qZwhXxZuBAAkgqlrBipzI1sevp6cGxxx6Lu+66y8yXMVVLdwiyADyS0ZsnGIRGc0O8AUlr7IyYGuMaO1O5IebUgYSB8QZwA4UZXBFv3ca1bwCPEEsnv4tPszjnnHNwzjnnmPkSplM62bqKQN47xgAmdmZyQ7wByR2tERUU7oo1kxtizsg1dqnnikXVXbJkDFfEW6dx7RvAPjUdrrHLQmn0DC8bc3RBaURloW7WMbKjZcWOhmPkGmKvR4LfG799gjFHabBPNZ+pFTu9QqEQQqGQ+nZnZ6eNTxNj/HoAVlAKRSHGW0tPbOpfkow+XkeGEAKSlH/VmXJXiDHX1Gns1FigxINwVGYbVwAKMt4MXEMMsGKXTkFV7FauXInq6mr1z/jx4+1+JENHs0DSOU8MQtsVYrwpjV5deQA+b/7/PJOnwrjmyX6FFnN94Si6QhEAxnW0XNdZOAot3gBj1xADiSPEGG8JBZXYrVixAh0dHeqfPXv22P1IibKxwaOLEMvGtivMeDOn0QN4BEUhKLSYU9q3YIkHlQFjJnBYQSkchRZvgLFriAHu/E+noKZiA4EAAgFjOjSjmDYVy63ZtivEeDNyhyIA+LwelHglDEQFY64AFFrMJXeyRk3Tl3LNU8EotHgDkmfBjO5TGW8KUxO77u5ubN26VX17x44dWL9+PWprazFhwgQzX9owiQqKMaMLXspuHjfEW5PBFTsgNv0/EI2wYmcCp8ec0Z0skOhoGW/Gc3q89Q9E0dE3AMC4No596lCmJnbvvvsuTjvtNPXtG2+8EQCwdOlSPPjgg2a+tGGMXugZ4GjWNK6KNwM72kCJF12hCGPOBE6PucOdxi41AZLaOFaIDef0eFN2/Pt9HlSXlhjyNQNM7IYwNbFbtGgRhHDu6eNCCMM7Wu6KNY/T4w0w9kwxhRJzIXa0hnN6zBm9OQzgOmIzuSXeGioChk3987iToQpq80Shae8dQDgaCxbjTsnmjjEa3iGDD+8E2PDR8IzerAMkNuywYkeDHTb4aB0gaeqffaqKiV0GSqNXU1aCgM+YE9Q5mqVMDnbEKnaja4xL7ALsaGkYhzqNrxAH2MbRMA529AEARlcbOHD1cSp2MCZ2GRyIB+EoAy7HViij2XBURpSXZFOSqCxwMN7RGtrwsaOlYRyIDyTG1pQa9jVZsaPhKPE2iu2bqZjYZaAE4RgDG73UA2PZ8FFCc3cIUVnA65EMnorlGjsaSgiBA+3GV1ACvJSdhqH2qdVG9qkcSAzGxC4DMxq9YNKULhs+SrY/Hm+NlQF4PcZd/aUsI+CIlpJ19kfQEz+SZLSBHa3SxnEgQYMps2BGLjXhVOxQTOwy2NdufMXOk3RJNgORkqnr6wwcSAA8FJvSUzrZEWUlKTMJ+eLUGA1nf7vSxhnXp/IIsaGY2GVwwISFnkBiqoK7eCjZfnXjhHGNHsARLaV3wIROFkjarMN4oyRRWaibdcYYWbFjfzoEE7sMzFhjB/AuRUpPnfo3cLMOkBhIsIJCyfbHB65GdrJAUsWOVzxRkubuECKmrCFmfzoYE7thCCHUNU9GLvQEkg8pZsNHCQc6zanYKWvsOBVLycyq2PEQdkrHrDXEnPofiondMNp6B9QR58hqYy9RLlUDkQ0fJRxQBxLmVFA4kKBk+01YyA4kDSTYvlESs9YQK/0pjxBLYGI3DGV0UV8RMOxwYkWQdylSGgdNOOMJSKx54i5FSqZU7IyekVCn/jkVS0lMW0Nckkhj2MbFMLEbhpLYjTV4NAskL2Znw0cxUVngUPymE/PWdDLeKMGszWFc80TpmDYjwSPEhmBiN4wDHeasPwGSdsWG2fBRzMHOfkRlgRKvhPoKY6f+uUuRBhNCmLY5LBFv7GQpQZ36N7hPTT5CjDtjY5jYDWOfMrowuNEDOBVLQ+1u6QUAjBtRZujCYoC7FGmopq4QQhEZHgkYafAu7ES8sX2jhN2tsTZuQm2Z4V87wA07KZjYDWNXSw8AYEKtiYkdR7QUtyfe6I03odHjLkUaTOlkx9SUwu8zthtg+0bpKIPXCXVmtHGc/k/GxG4Yu1tjFbuJdeWGf+1SdrQ0SGI0a8LUP68Uo0FMrZ5wsw4N0tE7gM7+CABg/AjjY66Ug4kUTOzSEEJgd7xiZ04FhcedUCozO9pgCTtaSrUrXj2ZaGL1hAMJUijtW0NlwNDr6xRqG8c+FQATu7Rae8LoCUchScB4M6diueaJ4sxN7DiapVSWTP1zIEFxZrZvANetD8bELo1d8SAcXRU0/Aw7AAhylyINYmZHq+5SZKNHceZOxcbazIGo4IGxBADY1aqsWTcpseMRYimY2KWhLPI0o5MFgAAXelKS7lAELT1hAGZP/bPRoxhl8Dqx1vg1xDwwlgbbY3LFjrtiUzGxS0MZzZqx/gTgOU+USmn0RpSVoCpYYvjX59QYJesLR9EUPwzbzIodwDaOYsyeig2wYpeCiV0aiYXFxo9mAW7NplQ7m82dpuDdnZRM6WSrS0tQXWb8QMLrkVDijZ3FyIodAYk+1axZMB7plIqJXRo7W0xeD8DNE5RkW1M3AGBqY4UpXz/57k4huOap2G2Px9ukenMGrgDXPFFCXziqHvg/tcHkYgkHEgCY2A0hhMCWQ10AgGkmdbQcXVCyrYfjiV2DWfEWa/SEAMJRdrTFTom3aSbFG8A1T5SwrakbQsSWmtQZfF2iItGnsn0DmNgN0dQdQmd/BB4JmGzSiDbo4zl2lLCtKVYhNmsgEUi6WYANH21REjuT4g1IOhSbsxJFT5mRMDPe2KemYmI3yNZDsSCcWFeuVjqMxrs7SSHLIjEVa1IFxe/1QIpfP8s1T6RU7I4ws6NlxY7itlkwkGCfmoqJ3SBbTJ4WA9joUcLBzn70hqPweSTTdmFLkpQ0omXDV8yiSQMJKyp2bONoq8kDV4B96mBM7AZRR7MjzR9dcFqMlHibVF+OEq95/xy55okAYF9bH0IRGX6fx7QdikDyNXZs44qduobYgood27cYJnaDbDkc3zhhxeiC02JF71+HzI83IGkNCjvaora1KRZvU+rL4fVIpr0OO1oCgIGojJ3NsaNOzN2sw2JJMiZ2SYQQ2Hww1vAdObLStNfhNAUpPt7fCQCYNabK1NfhVAUBwKZ4vE0fZV77BiQ27HDqv7htOdSNcFRGVdCHcSOMv3ddwWsTUzGxS7K3rQ/tvQMo8Uo4cpQVRwHwXLFi9/H+DgDATJMTO57MTgCwcV8ssTtmbLWpr5NYzM6OtphtTGrfJIkVYqswsUuidLJHjqxMuRbHaMm7bTk1Vrz6B6LqUSezxpjd0SprntjwFbONFg0kuI6YgESF2PT2jdd0pmBil0QZzR5tehAmJXYMxKK1+WAXorJAXbkfI6vMObhTwTUo1N4bxt622A0AZne0ifuwOZAoZhv3xQYSR4+1aiDBeAOY2KVQRrNHjzO30SvxSlDWLXNNQPH62KJpCoAdLSWqJxNqy1Bdavwdscl4rhjJssCmAxZV7BhvKZjYxQkh1NGF2QvZJUniCIPwwe52AOavdwLY8BGwYa817RvA43Uodn5dbziK0hIvpph4LzHAzWGDMbGL29nSi+buMPw+D2aONr/hY0dL7+1qAwCcMKnW9NfiQILe3dkKAJg3cYTpr6Vu1uGMRNF6Jx5vcyfUwGfiGZ0A+9PBmNjFvb2jBQAwZ1yNaVeJJQtyaqyoNXWFsKM5tnHiuAlWdLQ8DqCYybLAu5YOJHjcSbF7d2cs3o63It54hFgKJnZxb++IN3qTze9kAe4aK3ZKtW76yEpUl5m73glgR1vsthzuRkffAMr8XkumYtWOlhWUoqVU7E6YZH6fmjwVyyPEmNip3t4Zq9idOLnOktcLcGqsqL25PRZvx1vQ6AHJHS3jrRi9FZ+RsGJaDEissQuxfStKe9t6sbetDx4JmGvFjES8P5UFMBBlYsfEDsD2pm7sae1DiVeyZP0JwMWexe6VfzUBABYc0WDJ6wVYsStqr3wai7f5U+steT1W7Iqb0r4dN2EEKgI+019P6U8BDl4BJnYAgJc2HwYAnDi51pIgBJLXPLHhKza7Wnqwo7kHPo+EU6ZZUyFO3BXLRq/Y9A9E8c9tzQCA049qtOQ1uVmnuK3dHEvsFk23ZuDq93qgnBjFmGNiBwBY+2kssTttujWNHsCGr5itjQ8kjp80ApVB89fXAVzTWcze3N6C/gEZo6qCOMrkO2IV6l2xHLgWnVAkitfjA4lFFvWpkiTxfuIkRZ/YtfaE8db22CJPq0azQFIFhYld0XnmwwMAgDNmjLTsNXmuWPH6x0cHAQCnHdVo+kHYCvX4CcZb0Xn50yb0hqMYVRW0ZKOOgsWShKJP7J75cD8issDRY6swpaHCstdNrLHj6KKY7Gntxbu72iBJwHmzx1j2uompWMZbMekfiGLVR7GBxBfmWBdvHEgUr6fW7wMAXDBnjGUDCSD5yBO2cUWf2P3t/VgQfmnuOEtfl6OL4vTkB7F4O3lKHUZVBy17XXa0xWnNpkPoCkUwtqYUJ1pwnpiCA4ni1NE7gBc+iS01sXIgASQVS7iOuLgTu/d3t2HDnnaUeCWcf6zVQcjjJ4pNOCLjoTd3AQCWHG/tQCLAAzyL0oOv7wQAfOm4sfB4LKyecCBRlB5+exfCERkzRldZcoNTssT0PwcTRZ3Y3ffKdgDAhXPGoqEyYOlr8/iJ4vP0hv043BVCY2UA5x5jz2iWFZTi8d6uVry3qw1+rwdf/cxES187wGmxohOKRPGH+EDi66dOtnQaFuDZsMmKNrH7YHcbnvs4tqj4qs9Osfz1eWBscekfiOI3a/4FAPjaKZPh91n7T49T/8VFCIHb/vEpAODCuWPQWGXdtD+QPJDgTQDF4oF/7sShzhBGVQUtnwEDkq7pZJ9anIndQFTGLU9/DAC4eN44HDnSmiMAkvH4ieJy19qt2Nfeh9HVQSybP8ny11fPTWS8FYUn1+/D2ztbESzx4DtnHGn56/MmgOKyr70Pd760FQBw0+Lplg9cAfapyYoysfvlc5vx4d4OVAZ9+I+zp9vyDFyDUjxe39qMu9bGGr2bz52JUr/X8mdQ159wKtb1tjV14+YnNgIArl00DWNqSi1/hoCPNwEUi1Akim//+QN0hyKYO6EGX5o71pbnYJ+aYElid9ddd2HSpEkIBoM46aST8Pbbb1vxskMIIXDX2q3433U7AAC/ung2GiutnaJQcA2KeQol3oDYRdhXP/QeZAFcdNw4nDt7tC3PwXPFzFNI8ba9qRtf+d1b6AlHceKkWnxz0VRbniPgS9wEwHXExiqkeOsLR3Htwx/gvV1tqAz48NtL51q6SScZN4glmJ7Y/eUvf8GNN96IW265Be+//z6OPfZYLF68GIcPHzb7pVPsae3FN/74Hn61Orbu5KazjsTZR9vTyQKpa1DIOIUSb33hKO54cQsuu+9NdIciOHlKHX7+xaMtfYZkAa4/MUWhxFskKuNPb+3GBXf+Ewc6+jG1oRx3/ftx8HntmZRJvgmAHa1xCiXeAODdna344v/9J1745BD8Pg/u+eo8TKgrs/w5FNwglmD6xaj/8z//g6uuugpf+9rXAAD33HMPnn32Wfz+97/H8uXLTXlNIQQ6+yPY3dKLDXvb8dLmw3j1X02IyAIlXgn/3+dnYNkpk015ba24mN0cdsQbAPSGIzjQ0Y+P93fize0teGbDfnT2RwAA584ejV9dPFv9ndtBee2BqEBUFvDaNKp2G7viLRSJ4nBnCJsOdOKdHa145sMDONjZDwA4YdII3PXvx1m+03+wgM+L/gGZg1cD2RVvUVmgpTuE7c09eH93G1ZvPIgNezsAAPUVftz55ePwmSnW3Hs9HPapCaYmduFwGO+99x5WrFihvs/j8eCMM87AG2+8MeTjQ6EQQqGQ+nZnZ+eQj7nlqY3YfLALUVlgQBaIyjIiUYGILBCJyghFZLR0hxGODs3aT51Wj+XnHIWjx1Yb9B3mrtBvnugJRbD5YBe2Hu5CU1cIzd1hdIciCEdkDETl2H9lASEEhAAEBG4+dyZmWHx2UTIz4u2Rt3fj6Q37IQsRXwgup/wMwhEZ3aGImsQlGzeiFN9fPB0XHGvtCezpKPEGxJKCMr/pYzpdIlEZ25t7sPlgFw529KG5O4yO3gGE4z/nUERGRJYhC6gx96XjxuJLx1l7HmAyvfEGZI+59Xvacds/NsfbNzn232isbVPe19kXQUffwJCvPaKsBNedfgQuP3kiSmyq1CULlnjQ0VeYbZwsC+xp68UnBzqxr70fzd0htPWEY7GW9G9ciTdZCMwYVYWbz5tp2zObEW/hiIxlD7wNIRBv44T67y0cjf0MQgMyWnrCiMqpm2B8HglLjh+HG8+cbvsgAij8xK6lO4RPDnRhR3M3mrvDaOkJoTccxUBUIByJ/TcS71Pl+E7yh7/+mZxey9TWvbm5GdFoFCNHpt6JOXLkSGzevHnIx69cuRI/+clPMn7Njfs78d6uNk2vX1vux6wxVThuwgicf+xoTGu0fvfrcIIFuB5gICrj6fX78fgHe/Hm9tYh/5CzSdfZWMmMeNvd2ovXt7Voev0yvxdTGyowb+IIfG5GI+ZPrS+Yypiy/gSIdbRlfhsfJsm7O1vx8Fu78cInh9CVJjnO5PhJI0x6Km30xhuQPeY6+wbwxnZt8VbilTC1oQLHjqvBaUc14LSjGlN+z3ZLbNgpnDZuy6Eu/OGNnVj98SE0dYWyf0ISve2h0cyINwCa2zePBIyqCuLY8TU4aXItzjt2DOor7E/oFMEC3Pnf0TuAP761C3/fsB+bD3ZZ9roFNWxfsWIFbrzxRvXtzs5OjB8/PuVjvnPGEejoG4DPI8Hn8cDrlVDi8cDrkVDilVDi9aCuwo/6ioCtU1/ZBArs5ol3drbipkc3YFdLr/q+kVUBHDmyEqOqgqivDKAqWAK/zwO/V4Lf54HP44HHA0iQIEnAVAvv2jWClng7b/YYTB9VCY8kwSPFY8znQcDrgd/nQYnXgzK/FyOrg6gM+GyvzA1H+fcxEBUF0dEe7uzH8sc/wkubE2uDyv1eHDW6CuNHlKKuIoARZSUI+LyxmPN54PNI8HpiseaRJEwfVTgDNa2yxdxRoyvxfy6bG2/fJPi8sXYu+b+VAR8aK4OoKi3ceAMK64idnlAEP31mE/7y7h4ox+r5fR5MH1mJiXVlqK8IoLbcj2CJB36vB36fFyXeWLx5pFjMNRRQEqNVtnjzeST89t/mQJIkeCTAK0nqvzd/UhtXXxFAfYXftjWbWhTSAcVCCPz57T1YueoTdIViA1ZJAibVlWNqQwUaqwKoL/ejPOBDSfzn7Pd54JUSbZwkSRBC5PRv3NTErr6+Hl6vF4cOHUp5/6FDhzBq1KghHx8IBBAIZP7Hs+CIBkOf0S7BArp54k9v7cbNT34EWcTWS3ztlMk495jRmFRfbvej6WJGvM0cU4WZY+ybXjZS0OfFQDRie0e7+WAnvvK7t9HcHYLPI+Gi48ZhyfHjMHfCiIKpcGqhN96A7DHXWBnEBTYc7mqGQqnYHersx7//7i1sPdwNAFg8ayS+fNJEnDylzpbz1nJlRrx5PBK+MMee40mMVihHOkVlgf/824d47L29AICjRlXiilMm48yZIzGi3JqpElOj2u/3Y968eXjxxRfV98myjBdffBEnn3yymS9d8AplPcDj7+/FD56IJXVfnDsWa29ahGtPm+a4pA5gvGUTKIBznnY29+Cy+95Ec3cI00dW4h83LMBtF8/G8ZNqHZXUAYy3bIIFcKRTR+8ALrvvTWw93I1RVUE8cvVncO9Xj8fCIxscldQBjLdsCuEcOyEEfvD4R3jsvb3wemIbNVd9ewEuOWG8ZUkdYMFU7I033oilS5fi+OOPx4knnojbb78dPT096q6eYqUmdjaOLjYf7MQPnvgIAHDlqZNx87kzCnpqRwvG2/CU9Vd2jWj7B6L41sPvo613ALPHVeOhK09CdWmJLc9iFMbb8AI2H+kkhMD3H9uA7c09GFtTikeu/gzG19p3HIcRGG/DS1zTaV+f+pd39uAv7+6BRwLu+vJc245UMz2xu/TSS9HU1IQf/ehHOHjwIObMmYPnnntuyALQYqMs9AxHZMiysPxQR1kW+M/HPkT/gIxF0xvw/33e+UkdwHjLxO4R7d0vb8OmA52oK/fjvq8e7/ikDmC8ZWL3IexPb9iP5zcdgt/rwT1fmef4pA5gvGVi9yzY4c5+/PSZTQBi16rZeU6uJZsnrrvuOlx33XVWvJRjBJI2doQisuXXTP3t/b3YsLcDFQEffnnxbNtOCzcD4y09O09m39feh3te2QYA+K8vHI1R1fbc+GIGxlt6dk7994WjWLkqtlP0+tOn4Zhx9h9xZRTGW3rKZh27bte57blP0ROOYs74Gnzjs/bc+KJw1iIDFwkm36VocSBGZYE743eXXn/6NNuuVSNr2Xky+32vbEMoIuPESbX4/DHpF3qTuwRtnPr/yzu7cbCzH2NrSnHVZ6dY/vpkvUTFzvp4293Siyc+iG2W+PEFs2wvlDCxs4nPGzu+AbD+yJPVHx/ErpZe1JSV4KsnT7T0tck+dk1VtPeG8dd3Y43etz93hCum/Ck7u6b+o7LA/f+M3Qf+jYVTCvrYKzKOGm82rOn83WvbIQtg4ZENmDO+xvLXH4yJnY3sGmE89MYuAMBXPzOx4G4gIPMkpiqsjbfH3tuLvoEoZoyuwinT7L12iKxj1xq7V/51GHta+zCirAQXzxuf/RPIFewauPaGI+rRJlcXSHWYiZ2N7BjR7m/vw5s7YieNX3I8G71iYte5Yk+u3wcA+PKJ41mtKyJBm3bFPvHBfgDAhXPHWr52mexj1zWdazYdQm84igm1ZZg/tTAGrkzsbGTHYvanN+yHEMCJk2tdsUuMtLOjQrz1cBc27uuEzyPh3NnuOHiXtLEj3rpDEazZdBBA7FxOKh52bQ574oPYwPXCuWMLZuDKxM5Gdixmf/bDAwCAC11y2jhpl7jiybqG75l4vC08sgG1Fh7QSfazY5fii58cQv+AjCn15ThmrHt2wlJ2yTdPCGHNvb4dfQNYt6UZAHDhnMIZuDKxs5HVawKaukL4aF8HAODMmTz3qNjYceXOy582AQAWz+JO2GJjR7y9Eo+3s2aNKpjqCVlDKZQA1sXca1uaEZUFpjVWYEoB3ZXOxM5GVk9VvPqvWKN39NgqNFQ670Jryo/V54q19YSxYW87AGDhdHfc8UzaWb2GWJYFXt0Sa+MWMd6KTvLuZ6s2iL386WEAwKIjCyvemNjZyOrFxS/HE7uFBRaEZA11DYpF8bZuazOEiF2CPbKKZyUWG6vjbdOBTjR3h1ER8OG4CSMseU0qHCVej3rftBUxJ4TAK0qfWmADCSZ2NgpauNhTCIHXt8bWAiw8stH016PCow4kLBrNruNAoqhZHW9Kte7kqXXw+9i1FaOgheuItx7uxuGuEIIlHpwwqdb019OD0W+jgIXbs3e29KKlJwy/z4Njx3NRcTGy+pLs93a3AQA+M6UwjgAgaynXJlpVsXt/F+Ot2AUsXN70bjze5oyvKbhDsJnY2cjKit178SCcPbZanSKh4hIosW6XYmtPGNubegAAcyfUmP56VHgSu7DN72SFEGobdxzjrWhZWbFT4u34iYVVrQOY2NnKytGFEoTzJnLtSbGysmL3QbxaN7WhHDVlPOakGFl5IPaO5h609Q7A7/Ng1hjOSBQrK0+aeL+A+1Qmdjay8m6793a1AijMICRrWNnocSBBQQuvFFPi7dhx1VxfV8QS0//mxlxLdwjbm2MzEoW4UYf/AmxkVUfbE4pgy+FuAMDcAgxCsoZ6YKwFFbv1e9oBFGajR9aw8ngdxhsB1h2x82H8PNipDeWoLisx9bVywcTORlaNaDcf7IIQQGNlgOfXFTF1aszkRk8IgU0HOgEAR/P0/6Jl5QHFn8TjbRbjragpfarZMbdpfzzeCnTan4mdjaw6x05p9GaMrjL1daiwWVVBOdjZj/beAXg9EqY1Fs5p7GQtZSF7OCJDls274kmWBTYf7AIAzBxdadrrUOGzqmJX6H0qEzsbJSoo5o4uCj0IyRpWjWY3H4h1slMbygvuGACyTiDpdx+Omhdzu1t70RuOIuDzYFJduWmvQ4XPqlmJRJ9amAMJJnY2sn50UZhBSNawKt6UadijRnEgUcyCSZsYzIw5pX07cmQlfF52acXMims6+wei2BHfODGzQIsl/Fdgo6AFB3imTlMUZhCSNQIWrelkhZgAwJd8xZOJMfdJvH3jwJWsGLx+erALsgDqyv0Fu2adiZ2NrDjAM3maYnI9pymKWfLxOkKYt+aJFWJSWHFgLAcSpLDifuLkeJMkybTXyQcTOxsFLDjuZGv8mJMpDRWcpihySrwJYd6ap3BExs6WXgDA9FFM7IqdFbMSShs3fSTjrdhZcU2nEm9HjCzcjWHs6W1kxZViylqAKQ2s1hU7pWIHmNfw7W7tRVQWKPN7MaoqaMprkHOYveYpHJGxuzU2kJjSULgdLVnD2j61cOONiZ2NghaMLrY3x0YXUzkNW/T8Xg+UmQOzdo0pjd7k+vKCnaYg65h9xM6etsRAYmRVYa53IutYsXlCuXGikPtUJnY2suIuxW1NhT+6IGtIkmT6odg74gMJruckwPwKyvYmDiQowexrOp1SIWZiZyMrRheciqVkZjd8TpimIOuYPSvBgQQlM/scO6dUiJnY2cjsmye6+gfQ1BUCwIaPYkpN3rCjVogZbwSg1G/urIQ6kGC8EZL7VHMGEk6pEDOxs5EyTTEQFYiacOWOEoQNlQFUBgvvomKyntlV4uQ1dkRmT8VyqQklM3/qP3HKRCFjYmej5OuWzAhEjmZpMDOP2EmpEHPqn8CBBFnLqngr9D6ViZ2NAiZfuaMs8pxYV2b41yZnMvNk9l3x8+vqK/yoYoWYYO6u2J5QRB1ITCrwjpasYfYubKf0qUzsbOTxSPB7lcXsxo8w9rbFgnDciMIOQrKOOlVhSrz1AQDGMt4ozswKyr72WLxVBX2oLuVAgsy/eUJp4wq9T2ViZzMzRxiJICw1/GuTM6kVu7AZ8aYMJBhvFKMMJPpMad9i8caBBCnM3IUdlQX2tzujT2ViZ7OgiWuenDK6IOuYecXTPoc0emQdM6f+93HgSoOY2Z8e6uxHRBbweSSMLPBbdZjY2cysEYaTRhdkHQ4kyEpmHsLOGQkaLHGOnXlLTcbUlMLrKdyjTgAmdrZTpiqMPlDRSaMLso6ZUxVqR1vDjpZiLIk3DiQoLhjfkBiOyoYfIeakpSZM7Gxm1tSYk0YXZJ2Aiec8OanhI2uYWyFmvFGq5CPEjK4SO6lCzMTOZupJ2QaPaNnoUTpm7VLs6BtAV38EADCWMUdxZh4Y66SOlqyRktiZ1qcWfoWYiZ3NzK7YsdGjZKUmxZuykL2u3I8yv8/Qr03OFfSbM5DoC0fR0hMG4IyOlqzh9Ugo8cZmqIq5T2ViZ7PE1Fjxji7IOmbtUmSFmNJR1jwZPpBoj8VbZYBn2FGqoGl9qnPWdDKxs5lZHa1y9MRYLmSnJGbtGkscTsx4owSzpv73MN5oGGZcmyjLAgc6nBNzTOxsZlbF7mBHPwBgdDV3xFKCWQOJg51KvBV+o0fWSQwkDI63ePs2hgNXGsSMNq6lJ4yBqIAkAY2VAcO+rlmY2NnMrI72UGfsDsWRTOwoiVlrOpWOdhSP1qEkpg0k4vHGo5xoMOUOdiOLJYfiA9f6igBKvIWfNhX+E7qcGR1tdyiC7lBshyI7WkqmVIj7DL5STKnYcSBByZT2zegrxZSOlu0bDWZGn+q0gSsTO5uZcdyJEoSVAR/KA9yhSAlmHRjLjpbSMWshuxpv1YU/LUbWMmP6Xx24OqR9Y2JnMzPOeTrE6gkNw4zRrBAiaWqMHS0lqAOJSBRCGHcTwMH4UpNGh3S0ZB0zBq9OG0gwsbOZGSezO61sTNYxY1dsZ18EoUjs6zllREvWUHYoChG75skorBDTcMwoljitT2ViZzMzRhdOKxuTdcxYzK7EW01ZScrJ70RKvAHGtXGhSBSt8cOJndLRknVMKZY4rE9lYmczZURr5L12Tisbk3VMGc2yekLD8Hs9kOJXVRu15ulwfBrW7/OgpoyHE1OqgLJuPWLGVKwz2jgmdjYz4wBPp5WNyTqlyhVPRjZ6PHqChiFJUuIaO4PauORpWEnJGoni2KcysbOdGVfuHHJY2Ziso1TsorLAgEFrnhLTFKwQ01BGb9hhvFEm6qyEQfHWF46isz92fJhTNiSaltj9/Oc/x/z581FWVoaamhqzXsbxTBldOKxsbBTGXHaBlDVPxjR8xbqQnfGmjTp4NSjeivVwYsabNkavI1b60zK/F5UOOT7MtMQuHA5jyZIl+OY3v2nWS7iCckq2UetPIlEZTV2xNSjF1tEy5rIL+BJrnoyeGnPKaNYojDdtjB68Hmb7ZvejFDSjr+lMnoZ1ytS/aennT37yEwDAgw8+aNZLuILRO3iau8OQBeD1SKirKK6pCsZcdpIkIeDzoH9ANnxEW2wdLeNNG6MvZVc72iIbSDDetEkc+m/sjISTKsQFVVcMhUIIhULq252dnTY+jTUS60+MGV0o1bq6cj+8HmeMLuxSjPEGxGLOyMROvZfYQQ2fXYox5pSO1qhrxZSOlocTZ1ec8WbsGjulT22odE6hpKA2T6xcuRLV1dXqn/Hjx9v9SKYzej1Ac3csCOuLrFqXi2KMN8DYa55kWahnijHmsivGmDP6iJ1EG+c35Ou5WVHGm8FnwzqxT9WV2C1fvhySJGX8s3nz5pwfZsWKFejo6FD/7NmzJ+ev5RTJU7FGXLnT1O280UUmZsZcMcYbkHrNU77aesOIyrG4rXNBR8s2znhG34fd3B0bSDQ4qKMdDuPNeEYvb1L61PpK57RvuqZiv/e972HZsmUZP2bKlCk5P0wgEEAg4Px/rHooo1lZAANRAb8vv+lTJ44uMjEz5oox3gBjGz6lk60pK0GJt6AmAHLCNs54Rk6NhSMyOvoGALijjWO8GS9geIXYeTMSuhK7hoYGNDQ0mPUsRSn5+IlQJAq/L7/OsbkrHoQOGl1kwpgzXsDAXYotLhtIMN6MZ+RAQpn293kkVJc6/9YJxpvxggbfPNHswDV2pm2e2L17N1pbW7F7925Eo1GsX78eADBt2jRUVFSY9bKOoxw/IUSso63Mcz2wUrFzwzSFXow5bYw8V6ypiNc7Md60MXLNk9K+1VX44SmyzWGMN22MP2nCeX2qaYndj370I/zhD39Q3547dy4AYO3atVi0aJFZL+s4Rh8/4bapWD0Yc9qYMRXLeGO8DcfIqbEmtm/q24y39Iw8N1GWBVocuDnMtEUxDz74IIQQQ/4wAIdSAjFkwBoUZWu2k4LQKIw5bUoNPGKnmAcSjDdt1PuJjajYKcc5Md4Yb8NITMXm35+29w04cnOY81c7u0DAZ/xUhVvW2JHxjDzAs7mreKdiSRsj7+5MVIgZb5SekTdPKIUSp20Oc86TuphRU2MDURltve7ZMUbmMHYqtngrdqSNkWd1OnG9E1nLjHhzWvvGxK4AGHVgrLJjzCMBI8o4oqX0jFyDUsxr7EgbdamJkTMSjDcahtKfRmSBSDS/mHPqYdhM7AqAUSMMpWxcWx7gdWI0rICBVzwlpv7Z0VJ6Rl4pxqUmlI0ykADyX0fs1DXrTOwKQMCgAzydOrogaxl1xZMQAi1c80RZGDn138IKMWURSDoLNt+Yc+qMBBO7AmDU1Jh61Q6rJ5SBUfHW2R9BOD7V4bSGj6xj5HEnnIqlbDweST3oP//EznmHEwNM7AqCcmBsvtuz2eiRFkbdFavEW0XAlzL9QZTMqAOKo7JQ1xE76egJsl6iT+UaO7KJYRU7Hj1BGiQWs+eZ2DHeSAOj7opt7QlDFoAkAbXcHEYZGDX979RiCRO7AmDU5gmnBiFZy6gKilPXn5C1jNoVq7RvtWV++Bx0phhZz7hiiTPbOP7rKACGVVDY0ZIGRm2e4ECCtODAlaxmxCHsQgi09Dhz1z8TuwKg3jyR53oArj8hLYJ+g3dh8+gJyqDU6GkxxhtlETDgtpOuUAQD0fh1YuXOijkmdgXAqPUASmJX67AgJGsZdSC2UiGuK3fWaJasFTTobuIWxhtpZMRyk9Z4vJX5vY7bHMbErgAYkdgJIdDaGwtE3jpBmRg1NdbGCjFpoAwkorLAQB43AXDgSloZ0ac6uT9lYlcA1KnYPEYXveEowvERMRs+ysSohcVObvjIOspNJ0B+HW1bLxM70iZgwKxEm4MHEkzsCoAho4t4EPp9HpT5nVU2JmsZNfXv5IaPrBPweSDFbzjM51oxpY0bwXijLIyYlXByvDGxKwBGrEFRRrN15X5IEu+JpeEZNhXbOwCAFTvKTJIkdVYinyNPlHjjGXaUjRFnJyb3qU7DxK4AGNHRtvRwWoy0UdY8RWSBSI5rnoQQnBojzYyoErepFZQSQ56J3MuQzRM9zh24MrErAEpHm8/1J5wWI62Sd3jlWiXu7I8gKseOAqgpY0dLmRmxE7uNazpJo0Sfms9UbPxAbAcOJJjYFQAjDih28noAspYyLQbkXkFRBhJOPAqArJfv/cSyLBJTsWzjKAsjbjtRK3YOjDcmdgXAiKlYdVqM1RPKwuNJrHnqC+cWc9wRS3ooHW2u8dbFCjHpYGyf6rw2joldATBia7Yyuqjl4Z2kgbJzOteGr53r60gHJd5y3RWrdLIVAZ/aXhINx8g1nU5s45jYFYB8pymA5CDkaJayU6556s21YufgaQqyXqk/v4qdWiFm+0YaGHE2bKuDB69M7AqAkefYsaMlLUrzraCou7DZ0VJ2pSU+AEbEG9s3yi6Q53EnkaiM9l7nDl6Z2BWAQNLWbCFETl+j1cHrAch6hlVQGG+kgRJvuVeIGW+kXb7Fkva+AfX/a0qdN3hlYlcAkncV5nrkSRsrdqRDmUEVFCdOU5D1yvLsaHlmIukRzHMqVmnfqktL4PM6L01y3hO7UDBpMXAu27NjRwE495Rssl6+FRT1TDHGG2mQiLdITp/PW05Ij3wrdkqF2Kn9KRO7AlDileCJ3wKWy5qAzv4BxE8CQA0bPtKgVD1+IseOtofXO5F2eQ8kuDmMdFDPsct1BszhA1cmdgVAkqS8DlRUrhOrDPjg9/FXStnle/wEdymSHvlOxXJzGOmhnDSR66H/Tr5ODGBiVzDUAzxzCESuryO9ggZVUJza8JG1DJv6Z7yRBvn0p4CzrxMDmNgVjMS5YvqnxjiaJb3K8rgJIHlNJxezkxbcFUtWKvZzOpnYFYiyPI6f4MYJ0iufqdiu/kjSmk5njmjJWvnfdMJ7Ykk7Jd5CEVm9ik4PJ18nBjCxKxhleYxonb4egKyXz1RsK693Ip3yqaAkV4i5ppO0KPP71P/PZfDa6vDjnJjYFQh1qiKXNXa93DFG+pTlsQYlMfXPeCNtSuMdbS4zEsm7/jl4JS2CJR5I8ZMmclne5PSlJkzsCkSZ2vDpD8KWbq6xI33yuXmCGydIr1IDBhKVAR9KHHhYLFlPkqSkI530x5zT+1T+KykQ+Swudvp6ALKeUkHJabMOdyiSTmV5HFDs9DPFyB75LG9yep/KxK5AlOWxBsXp6wHIeompWP3nJrY7fJqCrJdfhdjZOxTJHmXq4FVfzPUPRNXPcWrMMbErEOWB3NegOH09AFkv0dHmcrwON+uQPnlNxarVE67pJO1yPWlC6U99HglVQV+Wjy5MTOwKRD5TsTzHjvQqzeO4E17vRHopnexAVGAgqq9KzAPYKRdKG9ejc/Ca3J9Kyg4Mh2FiVyDKcjygOByR0dUf+xynrgcg6+VzbqJSQeG9xKSV0skC+gcTXNNJuci5YueCe7CZ2BWIXCt2ynonjwRUlbKCQtrkc65YG9d0kk5+rweeePFDf0fLeCP9SktyW2OXGLg6tz9lYlcgcl3o2RY/kb26tARejzPLxmS95KlYIfSdzM57O0kvSZKSjnTKrY1jvJEeue7EdsNAgoldgUhc8aQzCHkUAOVAqdgJEbt2R482Xu9EOQjmWCXmmk7KRb6bJ5zcpzKxKxC5TsXysFjKRfKVO3piLioLdfqfN0+QHrkOXrnGjnKR621OiT7Vue0bE7sCkfvogtMUpJ/XI8Hvi/3z17OYvbMvcb1TTSljjrRLtHHcFUvmK+Y+lYldgcj1lOzEeifnji7IHokrd7RXUJTqSWXApyaGRFoEc9j5H5UF2vuc39GS9cpyvF3HDWuI2TIXiFx38HA0S7nKpYLS7oL1J2SPshzOTuzsG4Cyt8fJuxTJernu/G9zwVITJnYFoizHmwDcUDYme5TmUEFp5fVOlKNcLmVXKsRVQR9KvOyuSLt8z7Fzcp/KfykFoixpoaee4yc4FUu5ymVxsbpDkfFGOuWyQcwNR0+QPXLekMipWDKKEoR6j59ww9ZssocymOjPoYLCeCO9cpmK5XWJlCt1jZ2OeAtFomoi6OSYMy2x27lzJ6688kpMnjwZpaWlmDp1Km655RaEw2GzXtLRcj1+op1TsQAYb7nI5VwxHq8Tw3jTL5epWDdUT4zAeNMvl+VNSn/q9UioCvqyfHThMu3JN2/eDFmWce+992LatGnYuHEjrrrqKvT09ODXv/61WS/rWMrxE+GIjN5wRPPUQ6sLztwxAuNNv3wqKMU+NcZ4069UuXlCV7xx4Aow3nKRy1Ss0r7VlJZAkpx7k5Npid3ZZ5+Ns88+W317ypQp+PTTT3H33XczEIdR5vciHJE1j2gjURmd/VzMDjDecpFbBYUdLcB4y0UuuxSVXdjFfusE402/XDZPuGVpk6Vr7Do6OlBbW2vlSzpKmc6GryP5KIDS4m740mG8ZVaaw/3E3KwzPMZbZrlMjakVlCIfSKTDeMusLIcjxBI7Yp3dvlk2ibx161bccccdGUcXoVAIoVBIfbuzs9OKRysYekvHSvWkKuiDj0cBpGC8ZZfYia29o+W5ielpiTeguGMup12xvZz6T4fxll1p0lITWRbweLJPrbplTafubGD58uWQJCnjn82bN6d8zr59+3D22WdjyZIluOqqq4b92itXrkR1dbX6Z/z48fq/IwcrD+g7KbsYDotlvJlHibeekP6bJ9za0ZoZb0Bxx1yFEm85VOyc3tEOh/FmnvKAV/1/res6212S2Omu2H3ve9/DsmXLMn7MlClT1P/fv38/TjvtNMyfPx/33Xdfxs9bsWIFbrzxRvXtzs7OogpEvWtQimGagvFmnop4w9cT0hZvUVmgw+XXO5kZb0Bxx5wykOjWGG9AYpeiWwcSjDfzBH2JxK43HFXjLxNls06Nw9d06k7sGhoa0NDQoOlj9+3bh9NOOw3z5s3DAw88AI8nc4EwEAggEAjofSTX0LvYU230HL4eIBPGm3kSHa22CkpHEVzvZGa8AcUdc+XqQEJ/hdjpa56Gw3gzj8cjobTEi76BqI4+VTmA3dkDCdPW2O3btw+LFi3CxIkT8etf/xpNTU3q340aNcqsl3U0vZcWt7qkbGwExpt+FTqnYpUKcSWvd2K85UBvvEWicqJC7NKKnVaMt9yU+WOJndZ1xG5ZY2daYrdmzRps3boVW7duxbhx41L+Ts+VWcVE7xVPbtmabQTGm37lfn0dbbvL19fpwXjTL68KcZHv+me85abU7wV6dCxv6nXHQMK0YfeyZcsghEj7h9LTO6Jtd8nWbCMw3vRTN09wTadujDf9KgKJ4ye0/Jy46z+B8ZYb3X2qS6b+i/tfS4Ep17mYnfd2Uj70rnlSj55weKNH9lDWEEdloek+bB51QvnSu/PfLYNXJnYFRO9UhVu2ZpM99MZbm0umKcge5Un3YWuJuVaemUh50rMTOxKV0dUfi0unDyaY2BWQSiUI+/V1tG7doUjmSp6m0DQ11uOOHWNkD49HUqt2WioobtmhSPZJ9KkDWT+2Pb5RR5KAaoev6WRiV0DKdR7g2cYL2SkPSrzJAugfyD41xgoK5UtPlVg9U4yJHeVIXW6iYR2x0p9Wl5bAq+GWikLGxK6AKBWULg0VO1kW6giDU7GUC+VuYkBbR6tOxTLeKEeJKrGGjlZdY+fs6gnZpyIQix0tfaqb2jcmdgVEzw6erv4IonJs+oxTsZQLj0dCuY6pMXa0lC89G3ZYIaZ8VeQSby7oT5nYFRA9O3iUTrbc70Ug6eoUIj30TI21uWTHGNlH2UChJd64OYzypadPdVO8MbErIBXB+FSsjsSOnSzlQ0+VuJXHT1CedMVbj3s6WrKHvj7VPWs6mdgVED27FHnGExlB64adqCwS1zu5oOEje+iqECt3YbONoxzpGUi4aakJE7sCkrxLsS/LtWJtPTzqhPKnrHnKds5TyvVOjDnKUbmOzRNuWvNE9tAz9e+mpSZM7ApIWYkXUnyXdbZAZMWOjKB1RKt0spVBH0qK/Honyp26mD1LhTgSldHZzwOxKT/KVGyxVYjZQheQ2C5FbSPaNhct9CT7aF1c3M6BBBlAa7ylVIgdflgs2SeXqVg3VIiZ2BWYCo23T/DWCTKC1qkxt9yhSPbS2tEqnWxV0AcfK8SUI639KeCuDYn8F1NgEmuesjR83DFGBqjQuHlCnfrnQILyoPXuTuXWCVaIKR+JzWFRyHKWDYku6lOZ2BWYCo27xlp5nRgZQOviYvVUdsYb5UHrVKw6LcZ4ozwo/SmQefAaTbrJyQ19KhO7AqMs9szW8LXEE7u6CucHIdlH600AbhrNkn20bp5gvJERgiUe9d7XTMtN2nrDEAKQJK6xIxNoraC0dIcAAPUVAdOfidxL765YN4xmyT5a27dWbg4jA0hS4trETDHX0p2INzes6XT+d+AyWrZnR6Kyq8rGZB9laizbJdluuiCb7FOucTF7u3r0hPOrJ2SvymAshjImdj2xQolb+lMmdgVGSwWlrXcgqWzsjkAke1THj5LozNLRtsYbPjdMU5B9EvE2kPHjlAqKG3Yokr20LDdR4q2OiR2ZQUsFpUXtZP3q+gGiXFQpHW1flo42PhVbX8mpf8qdEm/9AzJCkeHXPCltXAOXmlCetPSprS5bs87ErsBUBjUEoctGF2Sfqni8ZUvsmrtiHS1jjvJRGfCpt+t09g3fxjXH1xC7paMl+yhTsV0ZqsTKmvW6cncMJJjYFRhlqqIjQ0fbzIXsZBAl3rpCEUSHOeepLxxFTzhWXWHFjvLh8UiojFdQMk3HKlNj3BxG+SrGPpWJXYGpKY0FVkdfeNiPaeWOWDJIVdJ1TcMtaFemxfxej9opE+WqKktHK4RIrHlixY7yVKMhsWtVBxLuiDcmdgVGy+iCZ9iRUUq8HpTFjwMYLuaakxo9SeKaTspPdZZ1nZ39EYSjMgAOXil/2vpUZerfHfHGxK7AaCobd7urbEz2qgpm3qmorj9xSaNH9lLibbg2Tom3ioAPwRKvZc9F7qSnWOKWPpWJXYHREoStLhtdkL2qSmPTq8N3tKwQk3GUeBvuiB3OSJCRNCV2nIolM1VrOA7AbWfukL2yTY01cU0nGShbvCk7sBlvZIRsazoHorL6d7XcFUtmqAwmjgMYLhDVM3eY2JEBsk/FsoJCxlHjbbjEju0bGShbxU65l9gjJTZaOB0TuwKTchzAsIvZecYTGSdbw6csLK53yWiW7JXt9gmu6SQjZa0QJ61Z97jkwH8mdgWoumz4jjYckdW1KW45TJHslbh9Iv2aJ2UgUV/JgQTlL9vUmBJvDRy4kgGS+1Mhhp7VmZgBc09/ysSuAGWqoLT1xoLQ65HUjyPKR7aONrGm0z0NH9mnOstAIjH1z3ij/CnxNhAV6BsYum5dmZFwy45YgIldQcqU2B3uVBYWu6dsTPZSrxUbZmqsmWvsyEDchU1WKvd71TvVM/WpjVXuGUgwsStAamLXOzQID3X2AwBGVgUtfSZyr6oMa1BkWajH6/BCdjJCts06zT3cFUvGkSQpY7HEjX0qE7sClAjCoVMVh7piQdjIOzvJIMpOsNY0A4nW3jBkAUgSMMJFUxVkn5r4midlbdNgTV2JWQkiI2QqlhyOx5ub+lQmdgUo05qnRNnYPaMLspeylkmpzCU72BEbSNSVB1DiZXNB+VPWanb1RxCOyCl/1xuOoCu+OcxNFRSyV6Y+VanYualPZUtdgEaUxUaqykaJZIdZsSODKeeFKRdhJ1MavVHVjDcyRnVpibrmaXAbpwwkyv1eVAa5OYyMMSJeJU7fp7JiRxZQ1pYo2/6TKRU7jmbJKLXxKa+ecBT9g3aNHVTWn1Qy3sgYHo+kdrQtgwYTB1243onsl+hT0yR2Low5JnYFSFlbki4IucaOjFYZ8MEfn2ZtGbTu6VC8gjKy2j2NHtlPmY5tGTT978aF7GS/4Yol3aEIesKxwayb+lQmdgWIFTuykiRJ6hlOLd2DO9rY26MYb2QgJd4Gb6BQ440DCTLQcMUSpVpXEfChPH7jkxswsStA9epi9jBkOXFSdlQWarLnptEF2U85M2xwxU6ZGmNiR0aqG6ajVdbYceBKRlL61OEGrm7rT5nYFSBlNBuVBdqTdvE0d4cgi9hlxTyVnYyUqNgNrqBwKpaMp27YGWYqdpSLDosl+w03C6ZsRmxgYkdm8/s86rk7yYG4r70PQKx64uWtE2Sg4TpaVuzIDLXliVmJZGq8cSBBBhquQqz0qWNrSi1/JjMxsStQiTUBSYldWywIx40os+WZyL3q0uwa6x+Ioj1+oCcTOzKS0tE2dQ2zWYfxRgZSKnZtvWFEoomzExN9KhM7skC67dl740E41mVBSPYbGZ/6UtY4AYnRbJnfq97vSWQEJXFTpl4BYCAqqxW7MS6roJC9asv9kCRAiNhtOgq39qlM7AqUMud/OKnh29vWC8B9owuy3+jqWEwd6OhT37e7NRZvE2rLIEmc+ifjjI5PtSbH2/72PsgCCPg8rlvMTvbyeiT1iB3lZAkguU911ywYE7sCpcz5KyMKIFFBYWJHRhtTE+to97cnBhJ7khI7IiMpFbnm7jBCkdg5YhxIkJmUqpzSpwohXNunMrErUEqgKYEHJJWNa9jRkrGUit2hzn5E40fs7G5hYkfmGFFWgoAv1v0o0/+7OZAgE42rSe1TW3rC6B+QIUmJ9s8tmNgVKGV0oSzujMpCraCMr3VXEJL9GisD8EhAJOmsRLWjrWNHS8aSJEmt2ilV4t1q+8Z4I+MN7lN3xQeuo6qC8PvclQq567txEaUqp4wu9rX1IRSR4fd5XLcegOzn83rUBe374zHHjpbMNHidHaf+yUxj1YpdLM62He4GAExtqLDtmczCxK5AKaOLjr4BdIci2HK4CwAwpb6cZ9iRKcbHBww7W3oQicrY3twDAJhcV27nY5FLqfEWj7Mth2Id7eR6xhsZb+ygqVilT53WyMROlwsuuAATJkxAMBjE6NGj8dWvfhX79+838yVdoyLgU8+y297Uja3x0YUbg9AojLf8TBsZi62th7uxs6UX4YiMMr+XFZRhMN7yc4QSb03dCEWi6kDiqNGVdj5WwWK85WdSfawd29HUA1kWru5TTU3sTjvtNPz1r3/Fp59+ir/97W/Ytm0bLr74YjNf0lWOGlUFANh8oAufHnLv6MIojLf8TGtIJHabD3YCAI4cWQkPK8RpMd7yM7UxEW9bD3cjKgtUl5bwMOxhMN7yM6muHH6fBz3hKPa29eFfh9yb2Jl66uh3v/td9f8nTpyI5cuX48ILL8TAwABKSkrMfGlXOGpUJV7b2oxPDnZi/e52AMDscdX2PlQBY7zlR6mgfHqwC5PqOgAAM1g9GRbjLT9HxDvUHc09eH9XG4BYm8ejTtJjvOXH5/XgyJEV2LivE69sacK+9j5IEjBrTJXdj2Y4y46Tb21txcMPP4z58+cPG4ShUAihUOLwwM7OTqseryDNGB0LuBc+OYQ9rbF1AXPHj7DzkRyD8abfMWOrIUnAzpZe/H1DbIrnhEm1Nj+VM2iJN4Axl2xsTSnqKwJo7g7hnle2AwBOnMx404LxlpsZo6qwcV8n/vfVWLxNH1mJyqD7kmLTN0/853/+J8rLy1FXV4fdu3fjqaeeGvZjV65cierqavXP+PHjzX68gnbKtHoAUJO6maOrMCJ+WTulx3jLXU2ZHzPi0//742eLnTy1zs5HKnh64g1gzCWTJAmfmRJL5JQF7Yy3zBhv+Tn1iFifquz4nz+13s7HMY3uxG758uWQJCnjn82bN6sf//3vfx8ffPABnn/+eXi9Xlx++eUQQqT92itWrEBHR4f6Z8+ePbl/Zy4wqjqI4ybUqG9fOHeMfQ9jE8abtc47drT6/5+ZUuu6gzuzMTPeAMbcYOfNTsTbmOogTppcXIkd481ai45sRGmJV33brX2qJDJFRRpNTU1oaWnJ+DFTpkyB3z+0srR3716MHz8er7/+Ok4++eSsr9XZ2Ynq6mp0dHSgqsp98+BabNrfiev//D7G15bh7n+fh1K/N/snFQCjfneMN2v1hCK45qH30NQVwm8vm6Nu4Cl0Tow3gDEnywI3PboB7+xqxa1fPAYLjmiw+5E0M+J3x3iz3pMf7MOtqz7BJcePx02Lp9v9OJrp+d3pXmPX0NCAhobc/vHJsgwAKXP+lNnMMVV48XuL7H4M2zDerFUe8OGPXz/J7sewDePNWh6PhP+5dI7dj2Ebxpv1Lpw7FhfOHWv3Y5jKtM0Tb731Ft555x2ceuqpGDFiBLZt24Yf/vCHmDp1qubRBZFWjDeyEuONrMR4Iz1M2zxRVlaGxx9/HJ/73Ocwffp0XHnllZg9ezZeeeUVBAIBs16WihTjjazEeCMrMd5ID9Mqdscccwxeeukls748UQrGG1mJ8UZWYryRHrwrloiIiMglmNgRERERuQQTOyIiIiKXYGJHRERE5BJM7IiIiIhcgokdERERkUswsSMiIiJyCSZ2RERERC7BxI6IiIjIJZjYEREREbkEEzsiIiIil2BiR0REROQSPrsfIBMhBACgs7PT5ichvZTfmfI7dALGm3M5Md4AxpyTOTHmGG/OpSfeCjqx6+rqAgCMHz/e5iehXHV1daG6utrux9CE8eZ8Too3gDHnBk6KOcab82mJN0kU8HBDlmXs378flZWVkCQJQCxrHT9+PPbs2YOqqiqbnzA/bvle0n0fQgh0dXVhzJgx8HicMeOfLt4Ad/+enMgt8Qa4u41zy/cBuCfmGG/OkG+8FXTFzuPxYNy4cWn/rqqqyvG/PIVbvpfB34dTRrGKTPEGuPf35FROjzegONo4t3wfgPNjjvHmLLnGmzOGGURERESUFRM7IiIiIpdwXGIXCARwyy23IBAI2P0oeXPL9+KW72M4bvn++H04g1u+P7d8H4C7vpfB3PK9ueX7APL/Xgp68wQRERERaee4ih0RERERpcfEjoiIiMglmNgRERERuQQTOyIiIiKXcHRi9/Of/xzz589HWVkZampq7H4cXe666y5MmjQJwWAQJ510Et5++227H0m3V199Feeffz7GjBkDSZLw5JNP2v1IpnNqzLkh3oDiizmnxhvgjphjvDkH4y3B0YldOBzGkiVL8M1vftPuR9HlL3/5C2688UbccssteP/993Hsscdi8eLFOHz4sN2PpktPTw+OPfZY3HXXXXY/imWcGHNuiTeg+GLOifEGuCfmGG/OwHgbRLjAAw88IKqrq+1+DM1OPPFEce2116pvR6NRMWbMGLFy5Uobnyo/AMQTTzxh92NYxkkx58Z4E6K4Ys5J8SaEO2OO8Va4GG+pHF2xc6JwOIz33nsPZ5xxhvo+j8eDM844A2+88YaNT0ZuxHgjqzHmyEqMt6GY2FmsubkZ0WgUI0eOTHn/yJEjcfDgQZueityK8UZWY8yRlRhvQxVcYrd8+XJIkpTxz+bNm+1+THIRxhxZifFGVmK8FR+f3Q8w2Pe+9z0sW7Ys48dMmTLFmocxQX19PbxeLw4dOpTy/kOHDmHUqFE2PVVxc3PMMd4Kj5vjDWDMFRrGW/EpuMSuoaEBDQ0Ndj+Gafx+P+bNm4cXX3wRF154IQBAlmW8+OKLuO666+x9uCLl5phjvBUeN8cbwJgrNIy34lNwiZ0eu3fvRmtrK3bv3o1oNIr169cDAKZNm4aKigp7Hy6DG2+8EUuXLsXxxx+PE088Ebfffjt6enrwta99ze5H06W7uxtbt25V396xYwfWr1+P2tpaTJgwwcYnM48TY84t8QYUX8w5Md4A98Qc4209AMabVQyLN2M36Fpr6dKlAsCQP2vXrrX70bK64447xIQJE4Tf7xcnnniiePPNN+1+JN3Wrl2b9ue/dOlSux/NNE6NOTfEmxDFF3NOjTch3BFzjDfGm5WMijdJCCF0JJREREREVKAKblcsEREREeWGiR0RERGRSzCxIyIiInIJJnZERERELsHEjoiIiMglmNgRERERuQQTOyIiIiKXYGJHRERE5BJM7IiIiIhcgokdERERkUswsSMiIiJyCSZ2RERERC7x/wMljdknB0hfGQAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.subplot(1,4,1)\n", "plt.plot(x_value,du_dx)\n", "plt.title('du/dx')\n", "\n", "plt.subplot(1,4,2)\n", "plt.plot(x_value, b)\n", "plt.title('backwards')\n", "\n", "plt.subplot(1,4,3)\n", "plt.plot(x_value, f)\n", "plt.title('forwards')\n", "\n", "plt.subplot(1,4,4)\n", "plt.plot(x_value, c)\n", "plt.title('central')\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Question 8\n", "\n", "8. What can you comment upon the results plotted in question 7?\n", "9. Write a function, called abs_error, which computes the absolute error between the reference derivative $du/dx$ and its numerical estimation\n", "10. Plot the errors obtained with the three different finite difference approximations using a subplot (i.e. one plot per method), what can you say about your results?\n", "\n", "\n", "They look very similar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Question 9" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def abs_error(numerical):\n", " n = len(du_dx)\n", " error = np.zeros(n)\n", " for i in range(1,n-1): #Fjerner grenseverdiene for å passe på at alle 3 metoder fungerer altså dropper første og siste verdi\n", " error[i] = np.abs(du_dx[i] - numerical[i])\n", " return error\n", "\n", "#Forwards = f\n", "#Backwards = b\n", "#Central = c\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Question 10" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.subplot(1,3,1)\n", "plt.plot(x_value,abs_error(c))\n", "plt.ylabel('absolute error')\n", "plt.title('Central')\n", "\n", "plt.subplot(1,3,2)\n", "plt.plot(x_value, abs_error(b))\n", "plt.xlabel('X-value')\n", "plt.title('Backwards')\n", "\n", "\n", "plt.subplot(1,3,3)\n", "plt.plot(x_value, abs_error(f))\n", "plt.title('Forwards')\n", "\n", "\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 2 }