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Created March 17, 2022 10:54
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ベクトル・行列からはじめる最適化数学 10章練習問題 10.16 共分散行列ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "ベクトル・行列からはじめる最適化数学 10章練習問題 10.16 共分散行列ipynb",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyNLyKG6XH0ISTncpFbBqGV5",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/hotchpotch/bb98b791778a9da91598e4ffb6efad3c/-10-10-16-ipynb.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"source": [
"# 10.16 共分散行列"
],
"metadata": {
"id": "VXNmdaYQfJQt"
}
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "y0iEOTTMfCcN"
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n"
]
},
{
"cell_type": "code",
"source": [
"size = 270\n",
"a = np.linspace(0, size, size+1)\n",
"sin = np.sin(np.radians(a))\n",
"sin_minus = -np.sin(np.radians(a))\n",
"sin_n = sin + np.random.randn(size+1) / 20\n",
"sin_minus_n = sin_minus + np.random.randn(size+1) / 20\n",
"\n",
"\n",
"plt.plot(a, sin_n)\n",
"plt.plot(a, sin_minus_n)\n",
"\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 282
},
"id": "bDT8PC_RfcFm",
"outputId": "0edc3ea2-8398-4312-9607-e0e35970a71e"
},
"execution_count": 2,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f19e3e1f6d0>]"
]
},
"metadata": {},
"execution_count": 2
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"plt.plot(a, sin)\n",
"plt.plot(a, sin_minus)\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 282
},
"id": "DpFDSk1Kh_Uj",
"outputId": "597c2d9e-7316-4bbb-c698-814a921df59b"
},
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f19e3e11150>]"
]
},
"metadata": {},
"execution_count": 3
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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uNB5J9wjc0NwN6bz82yaub1OHe6/SDmPeYNSVjbguvjavzNrE/E3pdsfxHiu/gCXvQue7IOE2u9N4LC0Ebmbz/qPcP3kVretG8OrAeO0r4CVEhFcHtqFlnSrcN2k1KRlH7Y7k+Xb+BT89CBdcCd1fsDuNR9NC4EYOH89jxBcrCA8OYMItCTrhiZcJDfJ3vK9+jJiYSPaJfLsjea6sXTDlZoisD4O0mWh5aSFwE4VFhvsmryI9O5cJtyZQKyLE7kjKBepUDeWDmzuwJ+sk90xaSYEOXX3u8nNgyi1WC6EbJkOoNqQoLy0EbuL1OZtZtPUAz/ZpSdt6Ve2Oo1woIa4az/dtxaKtBxg3e4vdcTzPLw/BvtXQ70OI0sH9nEELgRuYnbyf8Qu2MbRjPYbqNJM+YUjHWG7sHMsHv29jVvJ+u+N4jqTPrYHkLn0Iml1rdxqvoYXAZqmZx/jv1DXEx0TwdO+WdsdRFeip61sQHxPBQ1PXsP2ADkNxRruT4JeHoeHVOpCck2khsNHx3ALu+iqJAH/hvZva68lhHxMc4M97N7XH31+4+6skTuQV2B3JfR0/AFNvhcq1YMDH4Kf/V5xJC4FNjDGM/m4tKRnHeOeG9sREhtkdSdkgJjKMt4a2Y3P6UR7/fr32PC5NYYHVc/h4pjXfcFg1uxN5HacUAhHpISKbRSRFRMaUcv9wEckUkdWOy4hi9w0Tka2OyzBn5PEEny7ewU9r9/HQNU25pHGU3XGUjS5vEs1/rramuvx62S6747ifBc/D9t/hutehTlu703ilcje+FRF/YDzQDdgNrBCRmaVMOTnFGHNPicdWA54CEgADJDkee7i8udzZql2HeemXjXRrUZO7L9fhBhTce1UjVqUd5tkfN9CqboS2HDtly2z48w1rmsl2N9udxms5Y4+gE5BijEk1xuQBk4E+Z/nYa4A5xphDji//OUAPJ2RyW9kn8rnnm1XUighh3MA22nNYAdbsZm8OaUt05WD+/VUSWSd02Gqy98D3d0LNVtDjZbvTeDVnFIK6QFqx27sdy0oaICJrRWSaiNQ7x8ciIiNFJFFEEjMzM50Qu+IZY3jkuzWkH8nhnRvaEREWaHck5UaqhgXx3k3tyTyWyyO+PlJpYQF8NwIKcmHQ5xCoHSxdqaJOFv8IxBlj4rF+9U881ycwxkwwxiQYYxKio6OdHrAifLFkJ7OS0xndo5kOK61K1aZeVUb3aMbsDel8sWSn3XHs8/tY2PUXXP+mdhqrAM4oBHuAesVuxziW/R9jzEFjTK7j5sdAh7N9rLdYvyebF37eyNXNajDi0gZ2x1Fu7F8XN+DKptG88PNGkvdm2x2n4m1bAH+Ms84JxA+2O41PcEYhWAE0FpEGIhIEDAVmFl9BRIoPqN8b2Oi4PgvoLiKRIhIJdHcs8ypHc/IZ9c1KqlcKYtwgPS+gTs/PTxg3qA2R4YHc+80qjuf6UP+Co+kwfSREN4Wer9idxmeUuxAYYwqAe7C+wDcCU40xySLyrIj0dqx2n4gki8ga4D5guOOxh4DnsIrJCuBZxzKvYYzh0enr2H34JG/f0I7I8CC7IykPUL1SMG8OaceOg8d54of1dsepGEWFMH0E5B61zgsE6dSsFcUpY7caY34Bfimx7Mli1x8FHi3jsZ8CnzojhzuasiKNn9bu4+FrmtIxTjvCqLPXpWF17r2qMW/N28rFjaIY0CHG7kiu9efrsP0P6P0u1Ghudxqfoj2LXSg18xjP/LiBixtV1/4C6rzcd3VjOjeoxhMz1rMt85jdcVxndxIseAlaDdD+AjbQQuAi+YVF/GfKaoID/XhtUFv8/PS8gDp3/n7CW0PbERzgx/2TV5FX4IXzF+Qesw4JVakDvV4HPYdW4bQQuMibc7ewdnc2Y/vH6yQzqlxqRYTwUv941u85whtzvXD+gt/GwOEd0H8ChGqPajtoIXCBZakHeW/hNoYk1KNHq1p2x1FeoEerWgxJqMcHv29jWepBu+M4z4YZ1vwClzwA9S+yO43P0kLgZNkn83lgymrqVwvjyetb2B1HeZEnr29B/WphPDh1DdknvWC+4+w9MPM+qNMOrii1LYmqIFoInMgYw+PfryPjaC5vDW1HeLBOqK2cJzw4gDeGtGX/kRyemuHhTUqLiuCHu6AwDwZ8Av463IqdtBA40fer9vDT2n080K0JbXT0SOUC7WIjue+qxvywei8zVntwJ/wl71pNRXu+DNW1RZ3dtBA4SdqhEzw5I5lOcdW4S5uKKhcadWVD2sdW5X8/rGdP1km745y7fWth3rPQ/Hpod4vdaRRaCJyiwNFUVAReH9IGf20qqlwowN+PN4e0o6jI8OCU1RQWedAopXknrFFFw6Pg+re1qaib0ELgBB/+kUrSzsM837eVTjmpKkRs9TCe7t2SZdsP8dGiVLvjnL15z8CBzdD3fZ1y0o1oISinDXuP8ObcLfSKr02ftqVOpaCUSwzsEMO1rWvx2uzNrN/jAaOUbv8Dln0Ane6EhlfanUYVo4WgHHILCnlw6moiQoN4vk8ru+MoHyMivNC3NZFhQTz07RpyCwrtjlS2nCPwwyio1hC6Pm13GlWCFoJyeHveVjbtP8rLA1rrqKLKFpHhQYwd0JpN+4/y1tytdscp26zH4Mhu6PchBOnhU3ejheA8rdx1mPcXbmNwQgxXN69pdxzlw65qVpPBCTF88Ps2Vu46bHecf9oyy+o9fPF/oF5Hu9OoUmghOA8n8wp5aOoaakeE8sR12ntY2e+J61pQOyKUh6au4WSeGx0iOnEIZt5rTUB/xRi706gyOKUQiEgPEdksIiki8o93W0QeFJENjsnr54lI/WL3FYrIasdlZsnHuqOXf9tE6oHjvDownsoh2iNS2a9ySCCvDIy3PpezNtsd5//7+b9WMej3AQQE251GlaHchUBE/IHxQE+gBXCDiJT8mbwKSHBMXj8NKD4H3UljTFvHpTdu7q+UA3z+1w6GXxTHRY2i7I6j1P+5uFEUt3apz6eLt7PUHQamW/8dJE+HK0ZDrdZ2p1Gn4Yw9gk5AijEm1RiTB0wG+hRfwRizwBhzwnFzKdYk9R7naE4+D09bywVR4Yzu0czuOEr9w5iezahfPYyHp63hmJ1zHR/db+0N1E2Aix+wL4c6K84oBHWBtGK3dzuWleV24Ndit0NEJFFElopI37IeJCIjHeslZmZmli/xeXrupw3syz7JuMFtCA3ytyWDUqcTFhTAa4PasPvwSV78ZaM9IYyxRhXNP2kdEvLXwRfdXYWeLBaRm4EE4NVii+sbYxKAG4E3RaTUgXqMMROMMQnGmITo6OgKSPt38zamMzVxN3dd3pD2sZEV/vpKna2EuGrccekFfLNsF79vseFH06qvYOssq79AVOOKf311zpxRCPYA9YrdjnEs+xsR6Qo8DvQ2xuSeWm6M2eP4mwosBNo5IZNTZZ3IY8z0dTSrVZn7u+oHW7m/B7s1oVGNSoyetrZi5y7ISoPfHoW4S60exMojOKMQrAAai0gDEQkChgJ/a/0jIu2AD7GKQEax5ZEiEuy4HgVcDGxwQianevbHDRw+nsdrg9sQHKCHhJT7Cwn05/XBbcg8lsszPyZXzIsaAz/eB6YI+rwLfto63VOU+50yxhQA9wCzgI3AVGNMsog8KyKnWgG9ClQCvi3RTLQ5kCgia4AFwFhjjFsVgvmb0pm+ag//vqIhLetE2B1HqbMWH1OVUVc0ZPrKPczZkO76F1z1FWybD92egcg417+echoxxoOGsHVISEgwiYmJLn+d7JP5dH/jd6qGBvHjvZcQFKC/cJRnySsoove7f3LoeB5zHriciDAX9Xs5shfGXwi1WsGwn3RvwE2JSJLjnOzf6Lt1Gi/8vIEDx/J4dVC8FgHlkYIC/Bg3qA0Hj+fx3M8u2tk2Bn56wJp2svc7WgQ8kL5jZfhjSyZTE3cz8rILiI/RaSeV52pVN4K7Lr+AaUm7Wbg548wPOFfrvoUtv8HVT+i0kx5KC0EpjuUW8Oj0dTSMDuf+q7WVkPJ8917VmEY1KvHo9HUczXFiK6Kj6fDrIxDTCTrf5bznVRVKC0EpXvplI3uzT/LKwDaEBGorIeX5QgL9eXVgPOlHcnjxl03OeVJj4Jf/WtNP9hkPfvp/xVNpISjhr5QDfL1sF7df3IAO9bXjmPIe7WIjGXHpBUxavovFKQfK/4QbfoCNP8KVj0J0k/I/n7KNFoJiTuQVMHr6WuKqh/Hf7k3tjqOU0z3YrQkNosIZ/d1ajpdnLKLjB+Dnh6BOO+hyr/MCKltoISjmld82k3boJC8PiNexhJRXCgn055WB8ezJOskrv5XjENGvoyEn2zokpGMJeTwtBA4rdhxi4pIdDOtSn84XVLc7jlIu0zGuGsO6xDFxyU6Wnc9w1Zt+hvXT4LKHoWZL5wdUFU4LAdaMY49MW0tMZCiP6PDSygc80qMpsdXCeOS7tec2o9nJw1afgZqt4dIHXRdQVSgtBMAbc7ew/cBxxvaPJzxYd3OV9wsLCuDlAfHsPHiCcbPPYUaz3x6zzg/0eRf8dXY+b+HzhWDVrsN8vCiVGzrFcrHOOKZ8SJeG1bn5wlg+XbydpJ1nMen91jmw5hu45AGo09b1AVWF8elCkJNfyMPT1lKrSgiPXauHhJTvGdOzOXUiQnlk2hpy8k9ziCgnG368H6KbweWPVFxAVSF8uhC8PW8rKRnHeGmATkKvfFOl4ABe6t+abZnHeXPu1rJXnP0EHN0Hfd7TSei9kM8WgnW7s/nwj1QGdYjh8iYVP+OZUu7isibRDEmox4Q/trEmLeufK2xbACsnQpd7IKZDxQdULueThSCvoIiHp62hengQ/+vVwu44Stnu8euaU6NyCA9PW0NuQbFDRLnHrMlmqjeCKx+zL6ByKZ8sBOMXpLBp/1Fe7NfadeOzK+VBqoQE8mL/VmxJP8a781P+/x3znrGmn+wzHgJD7QuoXMophUBEeojIZhFJEZExpdwfLCJTHPcvE5G4Yvc96li+WUSucUae09mw9wjjF6TQt20durao6eqXU8pjXNWsJv3b1eX9hdtI3psNOxbD8gnQ+U6IvdDueMqFyl0IRMQfGA/0BFoAN4hIyeMttwOHjTGNgDeAlx2PbYE1x3FLoAfwnuP5XCK/0DokVDUskKeu1x6RSpX05PUtqBoWxP+mLsfMvMeacvLqJ+2OpVzMGXsEnYAUY0yqMSYPmAz0KbFOH2Ci4/o04GoREcfyycaYXGPMdiDF8XwuseLrp+mVMYHn+rQiMjzIVS+jlMeqGhbE831bce2BT5FDqdaMY0HhdsdSLuaMQlAXSCt2e7djWanrOCa7zwaqn+VjARCRkSKSKCKJmZmZ5xXUL3sXdwX8SM+Inef1eKV8QY+IXdwe8CvfFHZlS1g7u+OoCuAxJ4uNMROMMQnGmITo6PNr7nnhyHeQiBiYMQryTzo5oVJeID8HZozCVK7Le4HDePjbNRQUFtmdSrmYMwrBHqBesdsxjmWlriMiAUAEcPAsH+s8wZWR3m/DwRRY+JLLXkYpj/X7WDiwBf8+bzG6TwJrdmfz8Z/b7U6lXMwZhWAF0FhEGohIENbJ35kl1pkJDHNcHwjMN8YYx/KhjlZFDYDGwHInZCpbw6ug/a3w1zuwO8mlL6WUR9m7Cha/DW1vhkZduS6+Nte0rMnrc7awLfOY3emUC5W7EDiO+d8DzAI2AlONMcki8qyI9Has9glQXURSgAeBMY7HJgNTgQ3Ab8AoY8w5jIl7nro/D5Vrw4x/Q0Guy19OKbdXkAc/jIJKNeCaFwAQEZ7r24rQQH8embaWwiJjc0jlKk45R2CM+cUY08QY09AY84Jj2ZPGmJmO6znGmEHGmEbGmE7GmNRij33B8bimxphfnZHnjEIi4Lo3IXMT/PFqhbykUm5t0TjISLb+X4RW/b/FNSqH8NT1LUjaeZiJf+2wL59yKY85Wex0TbpDmxtg0euwb43daZSyz761sOg1iB8CTXv84+5+7epyZdNoXpm1iZ0Hj9sQULma7xYCgGtehPAoa5e4IM/uNEpVvMJ86xBpaDXoMbbUVUSEF/u3JtDPj9HfraVIDxF5Hd8uBGHV4Lo3IH0d/PmG3ShNCNYAAB2RSURBVGmUqniL34T966DXa9b/hzLUjgjl8V7NWZp6iK+X76rAgKoi+HYhAGjWC1oNtM4VpCfbnUapipOxEX5/BVr2gxa9z7j6kI71uLRxFGN/2cjuwycqIKCqKFoIAHq+Yp1A/uHfUFhgdxqlXK+wwPq8B1eGa8ed1UNEhJf6twbg0enrsFqAK2+ghQAgvDr0Ggf7VsNfb9udRinXW/Iu7F0J175qnSc7SzGRYYzp2YxFWw8wNTHtzA9QHkELwSkt+0Hz3laP48zNdqdRynUObIUFL0Kz66Bl/3N++E2d69O5QTWe/2kj+7NzXBBQVTQtBMX1es0aaXHGKChyfb82pSpcUaH1+Q4MhV6vg8g5P4Wfn/DygHjyi4p47Hs9ROQNtBAUV6mGdb5g9wpY+r7daZRyvmUfQtoy6PkyVD7/iZniosJ5+JpmzN+UwQ+rXTc8mKoYWghKaj0ImvSE+c/BwW12p1HKeQ5ug3nPQuNrrM5j5TT8ojjax1bl6ZkbyDiqh4g8mRaCkkSsvgUBwTDjHijSIXiVFygqgpn3gn8gXP/meR0SKsnfT3hlYBtO5hfyxA/r9RCRB9NCUJoqteGal2DXX7DiY7vTKFV+iZ/AzsXWgHJV6jjtaRvVqMSD3ZowKzmdn9ftc9rzqoqlhaAsbW+EhlfD3Kfh8A670yh1/g7vhDlPWUOwt7vF6U8/4pIGtImJ4MkZyRw8pqP5eiItBGURgd5vg/hZu9S626s8kTHw433W5/n6t51ySKikAH8/XhnYhqM5+Tz94wanP79yPS0EpxMRA92fg+1/QNJndqdR6twlfQ6pC6Hbs1C13pnWPm9Na1Xm3qsa8+OavcxK3u+y11GuoYXgTDoMhwaXwewnIUt7UioPcngHzHocGlwOHW5z+cvdfUVDWtSuwuPfryfrhI7m60nKVQhEpJqIzBGRrY6/kaWs01ZElohIsoisFZEhxe77XES2i8hqx6VtefK4hAj0fgdMEcy8Rw8RKc9QVGQNry5+0Gc8+Ln+N1+gvx+vDIwn60QeT8/UARw9SXk/HWOAecaYxsA8x+2STgC3GmNaAj2AN0WkarH7HzbGtHVcVpczj2tExsE1z1u72NqKSHmC5R/Czj+hx0suPSRUUqu6Edx7VWN+WL2XX7UVkccobyHoA0x0XJ8I9C25gjFmizFmq+P6XiADiC7n61a8DrdZrYjmPKkdzZR7O7DVau3W+Bpod3OFv/y/r2xI67oRPP7DejKPaisiT1DeQlDTGHOq7O8HTttnXUQ6AUFA8W/SFxyHjN4QkeDTPHakiCSKSGJmZmY5Y58HEejzrtUh54d/61hEyj0VFsAPd0NAiKPVm/NbCZ1JoL8frw9uw7HcAh2LyEOcsRCIyFwRWV/KpU/x9Yz1bpf5jotIbeBL4DZjzKnuuo8CzYCOQDVgdFmPN8ZMMMYkGGMSoqNt2qGoUgd6vgppS+Gvd+zJoNTp/PW2NVZWr9egci3bYjSuWZmHuzdlzoZ0vlupYxG5uzMWAmNMV2NMq1IuM4B0xxf8qS/6jNKeQ0SqAD8DjxtjlhZ77n3Gkgt8BnRyxka5VPxgaH49LHgB0rXNtHIj6cnWMOot+kCrAXan4V+XNKBTXDWemZnM3qyTdsdRp1HeQ0MzgWGO68OAGSVXEJEg4HvgC2PMtBL3nSoignV+YX0587ieCFz3JgRXge/v1EnvlXsoyIPv77Jm2jvP4aWdzd9PGDeoDYXG8Mg0nfTenZW3EIwFuonIVqCr4zYikiAip5rXDAYuA4aX0kz0axFZB6wDooDny5mnYoRHwfVvwf61sOjspvlTyqUWjbM+j9e9eU4zjrlabPUwHu/VnD9TDvD1sp12x1FlEE88kZOQkGASExPtjmH9Als7FUbMgbod7E6jfNXeVfDR1dYQ6v0/tDvNPxhjGPbZClZsP8Sv919KXFS43ZF8logkGWMSSi7XnsXl0WOsdULu+7shX4+BKhvk51g/SCrVhJ5j7U5TKhHhlQHxBPoL//12DYV6iMjtaCEoj9CqVq/jA5thvmcc1VJeZt6zkLnJ+hyG/qNjv9uoFRHCs31akbTzMB8tSrU7jipBC0F5NboaEm6HJeNhx592p1G+ZNt8WDoeOo2Exl3tTnNGfdrWoUfLWrw+ewub9h+xO44qRguBM3R/DqpdANPvhJNZdqdRvuDEIatjY1RTa2RRDyAivNCvFVVCA7l/0mpy8rVTprvQQuAMQeEw4CM4th9+ekAHplOudWqOgeMHrM9dYKjdic5a9UrBjBsUz+b0o7z82ya74ygHLQTOUrcDXPEoJE+HtVPsTqO82eqvYeOPcNX/oHYbu9Ocsyua1mD4RXF8tngHCzeX2gdVVTAtBM50yQMQexH8/BAc2m53GuWNDqXCr6Mh7lK46F6705y3MT2b0bRmZR76dq1Ob+kGtBA4k5+/1Y5b/GD6SGsAMKWcpbDA+lyJP/R93/q8eaiQQH/euqEtR3LyGf3dWh2YzmZaCJytaixc9zrsXg6LXrM7jfImi8ZZA8pd93qFzjHgKs1qVWFMj2bM3ZjBN8t32R3Hp2khcIXWAyF+KPz+MqQttzuN8gZpK+D3V6D1YOvz5SWGXxTHZU2iee6nDaRkHLM7js/SQuAq174KEXXhuxGQo22mVTnkHIHpd1jDoPfyrrGt/PyEcQPjCQsK4P7Jq8grKDrzg5TTaSFwlZAq0P8jyE6DXx+xO43yVMZYTZKzdkL/Cdbool6mRpUQxvZvTfLeI7w2e7PdcXySFgJXir0QLnsY1kyyBqdT6lyt+grWT4MrHoP6F9mdxmW6t6zFjZ1jmbAolT+22DADoY/TQuBqlz1iNSn98T9wIMXuNMqTZG6GXx6GBpfBpQ/ancblnujVgiY1KvPAlNVkHMmxO45P0ULgav4BMOBjCAiGb4dbo0UqdSb5J63PS1C4dYjRg5uKnq3QIH/evbEdJ/IKuX/yah2ltAKVqxCISDURmSMiWx1/Sx3+UEQKi01KM7PY8gYiskxEUkRkimM2M+8TURf6fQDp62DWY3anUZ7gt0chYwP0+9DWuYcrWuOalXm2T0uWpB7knflb7Y7jM8q7RzAGmGeMaQzMc9wuzUljTFvHpXex5S8DbxhjGgGHgdvLmcd9NbnG6gma+Amsn253GuXOkr+HpM/govs8YlRRZxvYIYb+7ery1ryt/LXtgN1xfEJ5C0EfYKLj+kSseYfPimOe4quAU/MYn9PjPdLVT0FMR/jxfmuoAKVKOrwDZt4HdRPg6iftTmMLEeG5vq1oEBXOfyav5oAOQeFy5S0ENY0x+xzX9wM1y1gvREQSRWSpiJz6sq8OZBljTo3DsBuoW9YLichIx3MkZmZ6aKsC/0AY8Ik1sfi3t0GBfsBVMfk51nkBBAZ+Yn1efFR4cADjb2xP1sl8HpiyWie+d7EzFgIRmSsi60u59Cm+nrEGCynr3arvmCfzRuBNEWl4rkGNMROMMQnGmITo6Ohzfbj7iKwPfd6Dfath9hN2p1Hu5Lcx1vzD/d6HyDi709iuee0qPHV9CxZtPcD7v2+zO45XCzjTCsaYMg9Siki6iNQ2xuwTkdpAqWPKGmP2OP6mishCoB3wHVBVRAIcewUxwJ7z2AbP0/w66Hw3LHsf6nXyqiED1Hla/Y11XuDi/0CzXnancRs3doplaeohXpu9mTYxVbmkcZTdkbxSeQ8NzQSGOa4PA2aUXEFEIkUk2HE9CrgY2ODYg1gADDzd471W9+cgtgvMvBfSk+1Oo+y0f53VezjuUrhK9xKLExHG9m9NoxqVuHfSSnYfPmF3JK9U3kIwFugmIluBro7biEiCiHzsWKc5kCgia7C++McaYzY47hsNPCgiKVjnDD4pZx7P4R8Igz6H4Mow5Wad4tJXncyCKbdYE88P/NTqd6L+Jjw4gA9u7kBBoeHfX6/UKS5dQDxxHPCEhASTmJhodwzn2LkEJl4HjbrB0G/AT/v4+YyiIphyE2ydDcN/toYkUWWanbyfkV8mMbRjPcYOiLc7jkcSkSTH+dq/0W8du9XvAt1fgC2/wp86f4FPWfwmbP4Fuj+vReAsdG9Zi1FXNmTyijQm6/wFTqWFwB10vhNaD4L5L0DKPLvTqIqwbT7Mfw5a9ofOd9mdxmM82K0plzaO4skZyaxJ08OpzqKFwB2IwPVvQY0W8N3tVqci5b0ObrP6kUQ3g97vWO+/Oiv+fsJbQ9sRXTmYu79K0vmOnUQLgbsICochX4Ipgkk3Qu5RuxMpV8g5ApNusOa1vmESBFeyO5HHqRYexAc3d+Dg8Tzu/mqlTmbjBFoI3En1hlZLosxN1iTlRfoB9ypFhdaMdQdTYPBE7TRWDq1jInhlYDzLdxziiR/W44mNXtyJFgJ30/Aq6DHWOok4/zm70yhnmv8cbJ0FPV+25hhQ5dKnbV3uubIRUxLT+GzxDrvjeDRttOyOOt1hDUH85+vWceQ2Q+xOpMpr7bfw5xvQ4TboOMLuNF7jwW5N2JpxlOd/3sAF0eFc0bSG3ZE8ku4RuCMRuPZVq6fpzHshbYXdiVR57FoKM0ZB/Yuh5yt6ctiJ/PyE1we3pWmtKtz7zSpSMo7ZHckjaSFwV/6BMPgLqFIbJt+gLYk81cFt1snhiBgY8hUEeOfcS3YKDw7g42EJBAf68a/PV+iw1edBC4E7C6sGN34Lhfnw1UA4ccjuROpcHD8IXw+09gBu+tZ6P5VL1K0ayke3JpBxNIfbJyZyMk+HoTgXWgjcXXQTq5lh1i7rl6XOeewZ8nOsPbnsPTB0ktUiTLlUu9hI3h7ajnW7s7h30iqd8/gcaCHwBPUvsuY8TlsK39+pzUrdXVER/HA3pC2D/h9CbGe7E/mM7i1r8XTvlszdmM7TM5O1WelZ0lZDnqJVfziyF2Y/DnNi4JoX7E6kSmOM9R4lT4euz0DLfnYn8jm3doljz+GTfPhHKnUjQ7nrct0bOxMtBJ6kyyjIToMl70KlmnDxfXYnUiX9MQ6WvmeNH3Tx/Xan8VmjezRjb3YOY3/dRI3KwfRvH2N3JLemhcCTiMA1L8KxdJjzBIRUgQ7D7U6lTlnxMSx4HuKHwDUvaTNRG/n5CeMGxXPoeC4PT1tLWFAAPVrVsjuW29JzBJ7Gzx/6TbDmL/jxP7Bumt2JFFjvw88PQZOe0Ge8zivhBoID/JlwSwLxMRHcN2kVi7Zm2h3JbZXr0yoi1URkjohsdfyNLGWdK0VkdbFLjoj0ddz3uYhsL3Zf2/Lk8RkBQVYfg/oXWSePt8yyO5Fv2zrXeh9iu8Cgz6w+IMothAcH8PnwTlwQHc7IL5JI2qlNsEtT3p8tY4B5xpjGwDzH7b8xxiwwxrQ1xrQFrgJOALOLrfLwqfuNMavLmcd3BIXBDZOhZiuYeitsX2R3It+0bYE1y1iN5nDjZAgMtTuRKiEiLJAvb+9MzSrBDP9sBcl7s+2O5HbKWwj6ABMd1ycCfc+w/kDgV2OMzkDtDCFV4Obp1iiW3wyBHYvtTuRbUhfCpKFQrSHcMgNCIuxOpMoQXTmYr0Z0pnJwADd/vIwNe4/YHcmtlLcQ1DTG7HNc3w/UPMP6Q4FJJZa9ICJrReQNEQku64EiMlJEEkUkMTNTj/X9n/DqcOsMawiDrwfC9j/sTuQbUhdaxbdaQxj2o/U+KLcWExnGN3dcSEigPzd+vJT1e3TP4JQzFgIRmSsi60u59Cm+nrF6bpTZe0NEagOtgeIHtB8FmgEdgWrA6LIeb4yZYIxJMMYkREdHnym2b6lcC4b/BFXrw9eDrcMVynVSf4dvHHsCw2ZqEfAgcVHhTBnZhfCgAG78aClrd+t0l3AWhcAY09UY06qUywwg3fEFf+qLPuM0TzUY+N4Yk1/sufcZSy7wGdCpfJvjwyrVsIpBtQuswxUpc+1O5J1S5jn2BBo4ikCU3YnUOYqtHsbkkRdSJTSQmz5exqpdh+2OZLvyHhqaCQxzXB8GzDjNujdQ4rBQsSIiWOcX1pczj28Lj7IOU0Q1tsYl2vSz3Ym8y/rvrCJQvRHcqkXAk9WrFsaUO7sQGRbELZ8sZ1nqQbsj2aq8hWAs0E1EtgJdHbcRkQQR+fjUSiISB9QDfi/x+K9FZB2wDogCni9nHhVe3fqSqtUaptwMSZ/bncg7rPgYpt0OMR2tPa9KenjS09WtGsqUOy+kZpVgbvl0Ob+u23fmB3kp8cRBmRISEkxiYqLdMdxb3nGYOgxS5sAVj8Hlj2hP1/NhjDVsxILnrc5igz7TJqJe5vDxPG6fuIJVaVk827slt3SJszuSy4hIkjEmoeRy7f7orYLCreGr29wIC1+Enx6wJk9XZ6+oEH4d7Rg2YigM+VKLgBeKDA/i6xEXcnWzGjwxI5lxszb73KilWgi8mX8g9H0PLnkQkj6zDhXl6lR+ZyX3qHWeZfmH0OUe6Pu+9hj2YqFB/nxwcweGdqzHuwtSeHjaWnILfOeHkw465+1EoOtTULk2/DYaPr0Ghn4DkfXtTua+snZZzUMzN0Gv16Hj7XYnUhUgwN+Pl/q3pmaVEN6at5UdB47zwS0diKpUZvcmr6F7BL6i80hrusSsNPjoStj5l92J3NOOxfDRVZC9G26epkXAx4gID3Rrwjs3tGPdnmz6vLvYJ4ak0ELgSxp1hTvmQ2gkTOwNSz+wToYq69/hr3dg4vXWUBEj5kDDq+xOpWxyfZs6TLvrIgqLDAPfX8L3q3bbHcmltBD4mqhGMGIeNLraOlQ09VbI8f5fPKeVexS+HQaz/wfNroU7FkB0U7tTKZu1jolg5j0X07puBA9MWcOY79aSk++d5w20EPii0KrWyKXdnrM6nX14GexZaXcqe6Qthw8ugY0/QrdnYfCX1mB+SgE1qoTwzR2d+fcVDZm8Io2+4xeTkuF9DS60EPgqEWuqy9t+hcJ8+KQbLHzZuu4LCgtgwUvwaQ9rsvnhP1tTS2pfC1VCgL8fj/Roxue3dST9SA693l7EZ4u3U1TkPYdVtUOZgpOH4ZdHYN1UqNMO+n3o3YdG0jfAzHthT6LVP+DaV3QIaXVWMo7kMGb6OuZvyqDLBdV5dVA8MZFhdsc6a2V1KNNCoP6/5B+sjmd5x+GSB6xLYIjdqZwnPwf+eBUWv2l98V/7KrQaYHcq5WGMMUxNTOPZHzcA8EC3Jgy7KI5Af/c/wKKFQJ2dYxkw6zFY9y1ENrC+LBt3sztV+RgDW+fAb2Pg0DZocwN0f0GHj1blknboBE/NTGb+pgya1arMc31b0TGumt2xTksLgTo3qQutydgPboXG3eHqp6BWK7tTnbv9663WQKkLrCG6e70ODa+0O5XyEsYYZm9I55mZyezNzuG6+No81L0pcVHhdkcrlRYCde4KcmHp+/Dn65BzBOKHwJWPWlNjuruD22DRa7BmEgRXgSvGQMLtEBBkdzLlhU7kFfD+wm18vGg7+YVFDO1Uj/uuakyNKu51aFULgTp/Jw7Bn2/A8glWq6JW/eGi+6B2vN3J/iljozVaaPJ08A+yvvwvewjC3HuXXXmHjCM5vD1/K5OXp+EnwoAOdRlx6QU0jK5kdzRAC4FyhiN7Ycl4a46DvGNwwZWQ8C9o0sPeX9qF+bDpJ0j81JqzOTAcOo2wBourVMO+XMpn7Tx4nAl/pPJt0m7yC4vo2rwmN3aO5bLG0fj72ddEWQuBcp6TWdaX7vKP4OheCKtuNcNsPRBqtwW/Cmg9UVRkNf9M/gHWT4Nj6RARCwnDocNtugeg3ELm0Vy+WLKDr5ft4tDxPGpVCWFAh7pc36YOTWtWRiq434pLCoGIDAKeBpoDnYwxpX47i0gP4C3AH/jYGHNqJrMGwGSgOpAE3GKMyTvT62ohcBNFhdYcvqu+hM2/QlG+Ncppkx7WCebYC537hXz8IOz80/rVv/lXOLLHOvzTqBt0GG4Nm+Hn77zXU8pJ8gqKmLcxnamJafy+JZMiAzGRoXRtXpMrmkbTvn4kVUJcP8y5qwpBc6AI+BB4qLRCICL+wBagG7AbWAHcYIzZICJTgenGmMki8gGwxhjz/pleVwuBGzpxCLbMgs2/WMUh/7i1vHpjqNcJajSHag2t+X4j6kJgWOm9eI2xxj46lgFZOyE92Truv38tZFjttgkMgwuugBZ9oWkP7QymPErGkRzmbcpg7oZ0/kw5QG5BESLQtGZl2sVWpVGNylwQFU5cVDi1qoQQEujntD0Hlx4aEpGFlF0IugBPG2Oucdx+1HHXWCATqGWMKSi53uloIXBz+TmwewXsXg5pK6zrJw78fR2/QGvMo6BKYIqsS2G+1cu5MPfv61auAzVbQGwXiLsU6rbXSWKUVziRV8DKnVkk7TxM0q7DrN51mCM5BX9bJ8jfjyqhgVQOCcDfT/hkWAL1q59f89SyCkFFTExTF0grdns30BnrcFCWMaag2PK6ZT2JiIwERgLExsa6JqlyjsAQaHCpdTnlxCE4lAoHU+DofsjJss415B0D8QO/AOtvaCRUqmldIupaexKhkfZti1IuFBYUwCWNo7ikcRRg9Us4dDyPHQePk5p5nMxjuWSfzOfIyXyO5hRQZAzBAc4//HnGQiAic4Fapdz1uDFmhtMTlcEYMwGYANYeQUW9rnKSsGrWJeYfP0aUUg4iQvVKwVSvFEyH+hXX4OGMhcAY07Wcr7EHqFfsdoxj2UGgqogEOPYKTi1XSilVgSpilKQVQGMRaSAiQcBQYKaxTk4sAAY61hsGVNgehlJKKUu5CoGI9BOR3UAX4GcRmeVYXkdEfgFw/Nq/B5gFbASmGmOSHU8xGnhQRFKwzhl8Up48Simlzp12KFNKKR9RVqsh9x9AWymllEtpIVBKKR+nhUAppXycFgKllPJxHnmyWEQygZ3n+fAo4MAZ1/Jc3r594P3bqNvn+dx1G+sbY6JLLvTIQlAeIpJY2llzb+Ht2wfev426fZ7P07ZRDw0ppZSP00KglFI+zhcLwQS7A7iYt28feP826vZ5Po/aRp87R6CUUurvfHGPQCmlVDFaCJRSysf5VCEQkR4isllEUkRkjN15nEFEdojIOhFZLSKJjmXVRGSOiGx1/PWYKb5E5FMRyRCR9cWWlbo9Ynnb8X6uFZH29iU/e2Vs49MissfxPq4WkWuL3feoYxs3i8gZp3K1m4jUE5EFIrJBRJJF5H7Hcq94H0+zfZ77HhpjfOIC+APbgAuAIGAN0MLuXE7Yrh1AVIllrwBjHNfHAC/bnfMctucyoD2w/kzbA1wL/AoIcCGwzO785djGp7Hm/S65bgvHZzUYaOD4DPvbvQ1n2L7aQHvH9crAFsd2eMX7eJrt89j30Jf2CDoBKcaYVGNMHjAZ6GNzJlfpA0x0XJ8I9LUxyzkxxvwBHCqxuKzt6QN8YSxLsWa8q10xSc9fGdtYlj7AZGNMrjFmO5CC9Vl2W8aYfcaYlY7rR7HmIamLl7yPp9m+srj9e+hLhaAukFbs9m5O/+Z5CgPMFpEkERnpWFbTGLPPcX0/UNOeaE5T1vZ423t6j+PQyKfFDud59DaKSBzQDliGF76PJbYPPPQ99KVC4K0uMca0B3oCo0TksuJ3Gmvf1GvaCHvb9hTzPtAQaAvsA16zN075iUgl4DvgP8aYI8Xv84b3sZTt89j30JcKwR6gXrHbMY5lHs0Ys8fxNwP4HmuXM/3UrrXjb4Z9CZ2irO3xmvfUGJNujCk0xhQBH/H/Dx145DaKSCDWl+TXxpjpjsVe8z6Wtn2e/B76UiFYATQWkQYiEgQMBWbanKlcRCRcRCqfug50B9Zjbdcwx2rDgBn2JHSasrZnJnCro9XJhUB2sUMPHqXEMfF+WO8jWNs4VESCRaQB0BhYXtH5zoWICNb84xuNMa8Xu8sr3seyts+j30O7z1ZX5AWrdcIWrLP2j9udxwnbcwFWa4Q1QPKpbQKqA/OArcBcoJrdWc9hmyZh7VbnYx1Lvb2s7cFqZTLe8X6uAxLszl+ObfzSsQ1rsb44ahdb/3HHNm4Getqd/yy27xKswz5rgdWOy7Xe8j6eZvs89j3UISaUUsrH+dKhIaWUUqXQQqCUUj5OC4FSSvk4LQRKKeXjtBAopZSP00KglFI+TguBUkr5uP8HxsIF146gHDQAAAAASUVORK5CYII=\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"plt.plot(a, sin_n)\n",
"plt.plot(a, sin_minus_n)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 282
},
"id": "T5Ev2xoyiAaa",
"outputId": "8ee3450a-4890-451f-a307-411f56548171"
},
"execution_count": 4,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f19e39408d0>]"
]
},
"metadata": {},
"execution_count": 4
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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XjD+j16UkJpBtS2Th2IxTfo3RIMi1JYYXjGUmm0lOTCAj2cyu2o7wdU26t1/vUII/4il/H7Y9BeMvjNSuOR6hDB37MYJvMMCYcyP1coYpKktnBPHH947Q6faHM1a2V3VQmpVMWXYKe+udON1+vqILb4EeojkeQggm59n4/JJSDAZx0jz7gUQIwTvfPI8vLh93Wq/LTbWwT68LFHpi+dS8IlbubqC6rRu3L4DTLTN26jrcuH0Blj7wLq/uiG3UEgxq4S8GxTBm4x9h90vw8t2xHaaOpWKN3Eavgg1x+S/h+qcHxr5BQgn+MOSR947w67cOUNnq4s8flKNpGo4eH39Ze5RrZxdw4WQZe/QGgozNSg7H34szkvjswhK+vKKMj8/pVaw0hpVfX87/XD1twD/LqWC3mHqt3j0ZeXZLuJBaaB7gC+eOxWgQPLamPJyKaTIK6h09+hNQD//aVhPzPv/YVsPSX6wOl59QDDPayqXAV22IZMo074ucP/S2bFYCUPmhLJMw+6bY+H0Iez7knDwNeSijQjrDkH9uq8EgBAlGA79edZDLZ+azv96Jxx/k0+eUhCcoQdasOac0gzf3NPCr62eRYDTw7VPInR/uhLx6myUhnJWTl2rh2tmFPL+lmuV6rf8p+XZ21TrYoxdW+7C8ldYuD+YEAzaLiQ3lbXj9QXbVOFgxOSc+H0ZxZmgaPHUtBLzQ0wZLvw6r7ofmA7J2jabB3z4hr73qdzLkYy+Ej/08vnYPIMrDH2b4A0EqWl04o0oB7693suloG2ajQS9kFplUKs1MZnxOCi/dvYQxx6xUHcmEFmX93ydnxUxC37l8HG5fkF++JWOxM4tS0TT44KBcRen2BVn883f55guya1YoxXOPqrQ5tDmwEv6wBPxRq8prt0FHpWxAArKsgTVLevRv3getRyLX/vseqN0Cy+6V6ZYjFOXhDzOq2rrxBTScPT6cbin4++qdbDzaxqziVCwmmfaYbjXR3u0LV6Ucbdx67ljOn5jD1GMWa03ItXHx1FxW7ZUlFZaUZfHMhire3tdIWXYytR09uH1B1h1uwdHjC/fv3VPn7HUPxRCifDU07QFXcyTDZu+/ZDcpa6bsLJUxDrInw+5/gBaUHj5I737DI+DplI1LRjDKwx9mhBp7uLyBcCXIrZXt7K51sCAqkyXXbiHJZOyVuz5asJiMvcQ+xP1XRlI5L56aS1F6Eh5/kFlFaTx352K+f/lkXN4AL26pRtMgzWpSgj/UaT0st6EGJZoGe1+RZQ8+9Thc/ZBcQJU9SYo9RKphZk2EO96FL74PJsux7zyiUII/zAiV/QWoaZclEt472Iw/qHFuVAOR0sxkJubZ4pphM1QpzrDy2xtmc/38IkxGA5+aJzMyJuXZmF2cxtWzpIf4+LoKAK6bU0RVW3f4iUoxBAkJfuth+MslsOsl6KiCyVfI+jaTLpPns6Pmr+p3yq29QNaiT85ipKNCOkOMdYdbcPsCXDild5bA9X/6MFwqAaC6TeaPaxosGJsRk0//k49Pxxc4/YVOo4VrZhdyzWwp7NefU8Tru+pYNkFO5OalWsKlo5dNyOL8Sdn8dd1RdlR3hK9RDCH8HinuAIdWySqX1Rvl8YRLYq8tWwH5s+RrmvfLMVvsSu2RjPLwhxiffWwjtz25hcNNsbXbO92+GLEH6PEFKEpPwmIycP+VU2O8+ayUxPDiKsWJyU9N4q1vnBcTArp8ej4zi1J56Ma5zBuTToJBsP5IaxytVPRJe0UkTNMWNRGbO6P3itmsCfDFD6B4gTxOzoaE3g16RipK8IcYqXqRsfv+tTtmvFFf/JOfauFzi8eExy+Zmseu/7m0V2Exxdnxvcun8MqXzyU1yURyYgJzS9JZd7gl3mYpjkfLoch+U1SO/cRLel8bIk3/GxpF3j0owR9yhGrabDzaRlNUS74Gh1z48+CnZ3Pjwojg25MSMJ3moiTFqRH9xLRkfCa7ah10dHtP8ApFXAjF742J4HHK5iI3vgBL7un7NemlcntsCYURjlKKOBMMaryyvRan20cwqNHR7eUCfYHPmoMRjzJU7yU/1YI9KTL1knqcBuGK/mfp+Cw0DdYqLz/+HH4HPF1Rx29DaomcfAW5SnbipZB0gpLXYcFXHr5iEPnTB+V87bntPLepik63n6AGS8oyyUpJ5P2DzQSCGq/uqKNWr+iYa7fEiLz9DMsVK06P2cVpZCSbeXOPaokYV5r2wTPXwQe/kMdVG2T9m0V3gVVPS07JO/n7hAQ/Do3E44kS/DjS0uXhwbflik+PL0i7Hi5It5pZPiGLNYea+c/ueu559iOe2VBFmtWExWQkyWQM94hVHv7gkGA0cOm0XN7d14jbF4i3OaOXfa/J7fa/Q8AHG/4gF1bN+3ykTn3KKZTASM6CG56FeV8YMFOHIkrw48jaQy149QYlbd3eiOAnm7hkWi7t3T4eWClTx1q6POEaOUII7LrQp1qV4A8Wl03Px+UN8MHB5nibMnrZ/28w2+SK2gP/gYq1shuVORmSdA/fdgoePsDkyyNPBaMEJfhxZGeNA4vJQGFaEu0ub4yHv2JyDqlJpnCuPcj88BAhz16FdAYPGWoz8+ymqnibMjpx1ED9Dlj2DUjJhfd+LlfWFi+U58Me/nEqXSoAJfhxZVdtB9MKUsmyJdLq8tLukis5061mEhOMXD1LTkKF6uFEV8G0W+TErQrpDB4mo4GbFo1h9YFmDjd1nfwFiv6lXha0Y+x5MO06WTsHIu0HwzF8Jfh9oQQ/TgSCGrtrncwoTCUz2UzbMR4+yMqOn1lQzD0XyqYludGCH/Lwk9Ri6cHkpkVjMCcYuPOpLayPytg52NjJV/6+jXaXSts8LQI+6DzFifBQvn3WBJh+ndxPypC1cCAi+Kca0hmFKMGPE+XNXfT4AswoTCXdaqbd5aWj24dByBruIGu+/Oy6mSwdn43FZGBSXqRsqz3JhMkoSDKdXlNwxdmRlZLIn26ehz+oce8LO9hb5+QHL+/ikgc/4LWd9Wyragfgtic28/Dqw3G2dhiw9Ql4aL4sdXAyWg5J792SCkXnyIYmpUsJ9+AMLaYKNTpR9EK5h3Fig14mYWZRKgcaO2l1eWnr9pJmNfdqGJ5tS2TTfRfF9JrNt1vI0xuRKwaXFZNy8F+pccdTW/jkH9cT1DQyk820urw0ON0EgxprDrWwv6GTL51fpv6PToSjWi6W6mqEtJITX9tyMOLNCwG3roxtKF52AXx1G2SWDZy9wxzl4ccBTdP4+8YqJufZGJ+TQrrVjMcfpK6jh/Q+sm7sFlOMcHztogk8e8eiwTJZcQwXTM6hMC2Jbm+Ax245h033XYTRIGhwuGnu8uANBKnt6GF/Q+fJ32w049H/fTobTnydpknBzxwfGbPlQVJ65FgIJfYnQXn4cWBLZTv76p387LoZCCHCPVfLm13k2E6tfr3NYsKmMnTihtEg+PG10zja0s3SCbKsbo4tkboONzXtkcyqt/c2MiX/+HX5FURWzIa6UvVFdyu4OyIevuKMUB7+AOHy+Pnlmwfo8fZepPPilmpSEhO4ZrbMwsnQBb+qrZs06+ip3DfcuWByLrctjcSL81MtNDh7wquic2yJPPL+Ef55TGN0RRTekOCfxMOPnrBVnDFK8AeINYdaeGj1YVbti81A8AWCvLmnkYun5mI1ywes6J6rxRmqpPFwJT81iXqHm1rdw3/2zkXMLErl3hd28PSHFXG1bcgSDun04eFXrocNf4SWA/JYCf5ZoQR/gAh5eVsrIjXsDzd18ec15Th6fFw+I1K0KTNK8K/Sc+8Vw4+8VAsNDjc17d2kWU2UZafw1K0LWT4xmx+9thePX5Vk6MXJYvib/wJv3Scbj5uSZZE0xRmjYvgDRMjL21wh0/Q8/gA3/2Uj9Q43tsQElk2ItFOL9vDnFJ+gwp9iSJOfaqHbG2BfvZOidPmkZk4wcOXMfD442Ex9h5vSUdpUvk+8J4nhO2sh6Ie9r0LOZDAoH/VsUP96A0Rth+w3u7/BSafbxwtbaqh3uPn+5ZN56rYFWKLy5+2WBJJMRu5WKXzDmlDpi21VHRSmRUJzRfp+6KlPEcXJPHxnrdz2tEHOlMGxaQSjPPwBorajh5TEBLo8ftYdbuEPqw8zf0w6dywb10vUhRDs/dGlcbJU0V/kR9U6KkyzRvZ1b7+2XQl+L06UpRMMgjNqPGfq4Ng0glEe/gBR297DpdPyyLUncu8LO6h3uPn6RRP79OCFEMq7H+aUZaeQbUukLDuZS6dF6rnkpyYhBNQoDz+WYAB8LkiwgNsBXlfseVcTBH2RY+XhnzX9IvhCiMuEEAeEEIeFEN89zvnPCyGahRDb9Z/b++O+Q5Vur5/2bh/jspP5/uVT6PYGmD8mnXPHZ8bbNMUAkmY1s/m+i3jnm+ezcFzk/9qcYCDXZlEe/rGE4vfZk+T2wWnQfBBe/jK8dBscWiXHQ7n32Urwz5azDukIIYzAw8DFQA2wWQjxqqZpe4+59HlN075ytvcbDtTpnlxRehJXzyqgudPDisk5yoMfxRSmJ4V/LxQ6oXDO7Jtgzs3wxrdg90uw/Rk5vudfcnvxj2X9+1HWjnAg6A8PfwFwWNO0ck3TvMBzwDX98L7DltBKy4K0JIQQ3L5sHGXZKXG2ShFPCtOS2FbVzrde3KEaoYcITdhaM+Cc22VRtB3PyrEx54Kmp7EWnQNzb46PjSOM/hD8QqA66rhGHzuWTwghdgohXhJCFB/vjYQQdwohtgghtjQ3D9+uQtVtMkMnlJqnUBSkJeHxB3lpaw0bytt6nQ8GteOuyh7RhEI6iXZZByd3BnTozWWW3iu3CZZR15VqIBmsSdt/A6Waps0EVgFPHu8iTdMe1TRtvqZp87OzswfJtP5nb72T1CRTTMMSxegmenFdqO/Bb98+xDee3877B5t5bnM1Sx94F18gGC8TB4/abdBRHfHwE/Wn37zpcptWAmUrZAcre2Gk/LHirOmPtMxaINpjL9LHwmia1hp1+Bjwi36475Blb52TaQV2FbNXhLlhQTGZKWbufWEHzZ0ePqpq58G3D2IQsnnK7OI0WV7Z4aY4w3ryNxyudDXDE1dKQZ/5aTlm1gU/Vxf8vJlgMMLSb4DfHR87Ryj94eFvBiYIIcYKIczADcCr0RcIIaJnW64G9vXDfYcc9Y4edtc62N/QyVRVIVERhc1i4rq5RaRbTTR1uvnlWwfISjFzzexCajt6whO6I35id91vZCpm9caokI7e2Cfk4efNkNslX4Xl3x58G0cwZy34mqb5ga8AbyKF/AVN0/YIIX4khLhav+weIcQeIcQO4B7g82d733jR0uXhkfeO0OXxh8c0TQPgtie2cOXv1+LxB5lWqARf0ZtsWyIVLd2sO9zKZxeOYUJuCh3dPg43S/Grc4xgwfd7Yctf5eSsqxkadsvxkODnzoBFX4KZ18fPxhFOv8TwNU17Q9O0iZqmlWma9lN97H5N017V97+nado0TdNmaZq2QtO0/f1x33jwzIZKHli5nyt/twan24emaVz5+7X8/p1DMX+sU/NT42ilYqiSbUsMt0GcnGcLl2CobpO/O7XtPbh9Ae58agu7ax1xs3NAaN4Hvm6Yf5s8PvKu3IZCOsYEuOxnkDEuPvaNAtRK29Nkf72caKpo7WbDkVYqWrvZU+dkW1U7Vr0+TrrVRFm2KpKl6E2OTRZYAyjNSu6VyVXb4ebD8lbe2tvIG7tO0hRkuKBpcHQN1G2Xx7M+IytfNu8DQ0Jsm0LFgKJq6Zwme+odnD8pm/cONHOwsZPGTtl8uaqtm8ZOD3edV8YXl48jwai+SxW9yY7qaFaamYyjxxdzvq6jhzUHWwDYXeccVNsGjJ0vwL/uBHuRTMHMHA9jl8HBlbISpkpuGDSU4J8Gjh4f1W093HBOCYebujjQ2IVfT6Mrb3GhaXJFZXS5Y4UimuwUKfh5dgtJZiOJCQZMRoEvIBuh10VN4O6pdaBp2vDO9tI0+PAhue+sgTFLZYnjax+BN76tvPtBRgn+abCvXnpcUwvsTMq1safOQWuXF7PRgFcX/nyVe684ASEPvzRLpl4aDIL81CSq2rqZNyadt/bKDmklGVaq2rppcLrJT2svrBwAACAASURBVJVhH18gSEuXJ3w8LKjaAA07IWuS7FqVP0uOWzPgk3+Jr22jEBV3OA326o/Y0/LtTMyzUd7swtHj47q5kYXFealK8BV9E2pSPzaqEUphmqymOSuq+c29F8uCYbtrnexvcLKrxsGzm6q48Ffv4/YNoxW55atBGODTz8jsnLIV8bZoVKM8/NNgS2UbeXYLOXYLk3JlKllxRhI3LRrDc5tldYl8JfiKExD28DMjgj8hN4V6Rw9LyjIZm5XMLz81kyn5dgwCdtV08NDqw/j8QeaOSaPbG6DBMYw6Z9V9JL377InwnUoVr48zSvBPkUBQY+2hFi6dlgfAtAKZZ/+5xaXhlZFmo4EMFb9XnICxWcnceu5YrpgZWYv47Usn8aXzx5OXamH1t84Pj0/Jt7PmcAt7ah1YTEZy7fLLosE5TARf02QZhYl6cx8l9nFHCf4psrOmA6fbz/KJssbPhFwb/7h7MbOL0zEaBHZLAmlW8/CeYFMMOAlGA/dfFdu5yWYxYbOYel27cGwmf113FIAuj5+9+hxSo3MIlxsIBmQIRwhw1EB3CxTMibdVCh0Vwz8JL39Uy+5aB2sOtSAEnDs+0nx83pgMjAYp8CWZVhXOUfQrC8fFVolsdHr07RAT/J4Oud34J/i/Mvj7p8HvgbptcrxgbvxsU8SgPPwoNle08eCqgzz+hXNITDDi8Qf49ks7KEhLwu2TXav6Ctn89NoZYfFXKPqDBaVS8ENpmyEaHJ7wfrfXT2KCMX6/exXr4Mkr4ZKfwpvfk1k4h96Ev14G7g4w2yB3WnxsU/RCefhRrD3UwvojrRxuknVN9tV34gtoVLZ20+j08L3L+26xNqs4jemFqpyCov9ITzazbEIWn5wX2z4i5OG7fQGm3v8mP3sjjrUIdz4PWlCKfYIFbn4ZPvEXcLXIHrWffRFM6sl3qKA8/CiaOuUf0uGmLqYVpLKjWj6qXjWrgLLsZOaWpMfTPMUo5OnbFgLw+s46nG4/yWZjWPBX728C4LWd9fzgyql9vseAEfDD/tfk6lmPE6Z/UubXz/gkTPu4XEWrFlYNKZTgRxGKkR7RPfwdNR1k2xL53Q2z1WSsIq4UZ1jZU+dkVnEaVXpHtZe3y7YTE/Nsg29QZwOs+RV0t8LH/wRVH8K5X4ucNxjlj2JIoUI6UYQ8p1Cp2h3VHcwqSlVir4g7xelWTEbB9MJUmpweXB4/q/fLNqBx6ZG77rew6c8w/mKYeg1c9VtV5XIYoDz8KEIe/uGmLuodPZS3uLh29vHa8yoUg8uVs/LJsSeSn2rBGwiyv6ETbyCIQUBrVxwEv2EXFM6Dm14a/Hsrzhjl4ev4AkFaXR4SDIKjLS4eW3MUAVw7Rwm+Iv5cObOAH10znVy9VtP+BpmTPyHHRkuXJ9yEZ1DQNGjcrbJvhiFK8HXkHw3MLk7DF9B4cn0Fl8/IH9n9RRXDjiy92uahRhl2nJCbgscfDNfYHxQ666GnPdKKUDFsUCEdnVA45zMLShifk0J5s4t7LpwQZ6sUiliyUuQ6kAMNshHPhBwbUE9rl5fkxEH6c27cI7fKwx92KMHXCU3YTsqz8Yl5RXG2RqE4PpkhD78p4uEDtLg8lGQO0tNoo96LNicOqaCKs0KFdHSadMHPsau8YcXQxW5JwGw00NLlITHBEG6ReOzEbU9/hXj8HnjtGxGvHmQFzNRiSErr+3WKIcmoE/yObi83/2Uj1Xouc4h6hxujQZCZrARfMXQRQoTDOpnJ5rDH39oVKbewsbyVmT98k1q9c9ZZ0bQXtvwVHlkCLYfA74Ujq1Vd+2HKqBP8DeVtrDnUwrv6KsUQ7x9sZnqBXdXDUQx5svSa+unJZjL12k6troiHv7miTZYEaXGd/c1cLZH9j56GyrVyVe2kK87+vRWDzqiL4YdKzO7XJ70ADjZ2sqfOyX9fpWKSiqFPSOQzks1YTEZSEhNiQjoH9Qye6C+BM8YlF3eRYIHmg+DrgYQkGHfe2b+3YtAZdYIf6kt7QM9jBvjXR7UYDYIrZxbEyyyF4pQJpWamW/XQToqZqjbpzfsDQQ42SmcmOsxzxoQEv3QpNO+H1kMwdjmYhlFfXUWYUSf4ob60Bxu70DQNTYNXPqpl2YSscPs5hWIoEwrphEp1f2x6Pn98/whXP7SWTref2nYZu2/rLw8/wSJX1R5+B9Bgzs1n/76KuDAqYvi1HT2sP9KCo8dHbUcPJRlWujx+atp72FTRRp3DzcfVilrFMCHk4YcE/2sXTmBMppXdtQ6OtrjwBoJAf4V0WiA5G7InAfpq3pJFZ/++irgwKgT/Fyv3c9sTW9hT6wDg2tkydHOgoZOXP6rFajZy8dTceJqoUJwyoSyddF3wk8xGXvjiYt755vmU6rn4RoOg0enm9ic3s7Wy/cxv5mqG5CzZiBzAaIb82WdlvyJ+jHjB1zSNjeVt9PgCvLW3EZD1cQwCdtY6eHtfExdOycVqHnXRLcUwJezhWyPd13LtFsZmJXP3+WVkpZiZXmBna2U7b+9r4u19jWd+M1czJOdA5njZq7ZgjmpoMowZ8YJf3dZDg76o6rWddWSlmBmXncK0glRe3FJNS5eHc8sy42ylQnHqzC5O4xNzi1h0TM9bgE+fU8Km719EYXoS7d0+AKpau3tdd8qEQjomC8y+EebecubvpYg7I17wNx5tDe+3dHmZkm8HYElZJvUO+UWwcJwSfMXwITkxgV9dPyu86OpYDMcsIKxsO8N8fE2LhHQArnkY5tx0Zu+lGBKMeMHfdLSNNKuJ/FT5GDpVF/xFulefa08Mxz0VipFCaEIXoLK1+9TKJzcfgLbyyLHHCQGv9PAVI4IRL/j7GpzMKExlYq5sAxfy8BeUZpBgECwcm6k6WilGHKGJXYBOt58OPbxzQh5eAL+bI3vVVq6HR/XyCUrwRwwjWvA1TeNos4uy7BQm6lUFpxZIwU9OTODPt8znW5dMiqeJCsWAkKGHdArT5AKpyrbTiOPveBb+/TVoOyKPk1XIc6QwolNTGp0eXN4AZdnJzCpOo9XlpSw7JXx+xeScOFqnUAwcmbqHf8HkHJ7eUMkT646yt97JhBwbD984R4ZqPF3w5JUcWvZbiibNI8mUDD4XvPoV+Sbnfh0q1kCuanQyUhhxgt/odPPj1/by/oFm5pemA1CWncLMojR+fb3KH1aMDqbk2Vk0LoObFo3h6Q2VvLy9DpArzH+/uwLD61+Hq38PTXt5/PkXGH9xKrf6XDDvC2DLlymYy78FKtw5ohhxgp+aZGJHTQfWRCOrD8g6IOOivHqFYjSQajXx3J2LAbh+fhGZKYnk2S3896t76KzaTqrbAYffBiBNc9DUpOfq506DBXfEy2zFADPiYvgWk5EPvr2Cu88rAyDZbCRXNTVRjGJ+8clZfOeyyeH5q6rKowBoR1YDkC0cuDr0cuFJ6XGxUTE49IvgCyEuE0IcEEIcFkJ89zjnE4UQz+vnNwohSvvjviewh0um5QHSu1dZOAoFTMyRmWrNDdUACIfcZgon3U59vYoS/BHNWQu+EMIIPAx8DJgKfEYIcWxh+duAdk3TxgMPAg+c7X1PiNdFQYqBS6bmct5ElVKmUIAM8+TYEsmiI2Y8Eye+LiX4o4H+8PAXAIc1TSvXNM0LPAdcc8w11wBP6vsvAReKgXK728rhV1Ng9z949Jb5fOtSlXapUISYmGsjWzhixrKEA7NX/xKw9i7XoBg59IfgFwLVUcc1+thxr9E0zQ84gF7JvUKIO4UQW4QQW5qbm8/MmvSxYMuFzX85s9crFCOYGYU2so4R/EzhJBXZJUt5+CObITVpq2nao5qmzdc0bX529hmGYoSA+bdC7Rao39G/BioUw5yvLcnCRADNJkuEHwnmkyE6yRSdaMLID9+q5vYnt8TZSsVA0R+CXwsURx0X6WPHvUYIkQCkAq0MFLM+I/tufvTMgN1CoRiOWNyyKbkouwCAjcEpGNAYK+rxJNh5cWstWyrb4mmiYgDpD8HfDEwQQowVQpiBG4BXj7nmVeBz+v4ngXe1U6rmdIYkpcH4C2Hfa/D0x+GFW8DvhfaKAbulQjGkWfNr2PoEdOn59rM/w3PznmNtcDoAZaKOloDsBNfR7aPHG4ifrYoB46wFX4/JfwV4E9gHvKBp2h4hxI+EEFfrl/0FyBRCHAbuBXqlbvY7k6+Ezjo48i7sfQW2/w0eWgA9HSd/rUIx0tjyOKz9DXTp+fYpeZROW0CLlgrAeEMdTf5IY/JQDwnFyKJfVtpqmvYG8MYxY/dH7buBT/XHvU6ZiZeCMIKmeyodlRDwyBKwJQsH1RSFIq4Eg9L5Cfrl3BZASg4LMmzcdukCeA8MaFjs2Vyam8ubexqpd/QwNisZTdPUOpYRxJCatO1XrBmw8C4w62UVQp5Ny8H42aRQDBZdzfDwIqhYK5uYBP1yfNeL8m8i0YbBILh04UxACvrU0kK+c9lkQNakWnuohbHfe4PK1jNsoKIYcoxcwQe47H/hgv8n90ONHVoO9L5O0+SPQjFSqN8BzfvgiSvAEZU13dMOi74UKYqWlAbXPCQLppUsIk9vFFTvcPPzlfsA2F3rBODOp7bw1IcVg/ghFP3NyBZ8iCwkaTkktwdWwgNjoXFP5Jo3vg1/G9yIk0IxoHQ1RPbX/15ux5wLY5bCef8Ve+2cm+Cb+2HBHVjNCaQmmahp7wkLfZfHh6ZprD7QxNpDLYP0ARQDwYirltmLJF3wu/Vf1NaQ8P9HVgYEqN8OzrrBt02h6E9qtkDNZlh0Nzjr5ZjJCgf06bVPPQEpJ+8BkZ9q4ZWPIpnVLV1e2rt9+AJauA+0YngyCjz8PlYOhmKaIMW+W+UeK4Y5L9wCK78LrUfkJG1SBhQvlM1ODCawZp3S2+TaLbi8ATKTzZiMguZOD4161k69o2cgP4FigBn5gp8UVRske0pkP+TRBwPQ2QD+HvCeRhs4hWIo8IclsOGPcj/kvW//u/Tw7QVQoDf9seWD4dT+3Nu7vQB885JJFKdbae7y0NTpAaS37/GrHP3hysgX/OhiUHNvhtvehryZ0Kk/8nY1RVI3uwdu8a9C0e/4PdC0B46+L4+NeuPy7X8HZ40U+Xxd8O0Fp/y237h4ItfNLeTT5xSTZUuM8fABGk4Q1tlS0Ub16fTPVQwqI1/wE+1g0KcqkrOh+Bz5y++sh8evgHd/ErlWCb5iOOHS56Wa9sYed9ZBw26w50PBHDlmzz/lt10xKYdfXz8bo0GQnZJIS5eHpijBr+voW/C/9tx2fvvOodP6GIrBY+QLvhCRCoAhb9+WL9MzK9fCzuci1yrBVwwnQokI7ZXgdcnf3ylX6Sc1sBVAWglkjof8WWd0i+ywh+8Jj50oju90+2hzec/oXoqBZ+Rn6YCM47uawapXZLYXyIksiJ28VRO3iuFEyKNHg8a94O6A3OnQtA9aD0uvXgj40kYwGM/oFlkpZjrdfqrbuynOSKK6reeEmTo93gAd3Urwhyoj38OHiGcfLfjHo2YTrLofAv7jn1co4k0wCHXb5X60g1K5Tm6tmVC6TO7b9bYUxoTIQqvTJNsm+0HvqXNSmplMmtVEXcfxPXxfIIg/qNHR4zujeykGntEh+EnHCL5Nj2earHJrLwIEbPkrrPstfPS0LLjmUyloiiHGgdfh0fOg+WAkpIOQJRRA/o5PuESOZZad9e2yUqTgN3d6yLFZyE9NorI1Minb4HDztec+oqLFRbdeYdPRrQR/qDI6BN+aDgmWKIHXPfxJl8ux1EIZ5w+Fd177usxpPvAG7HlZPiIrFEOBUImQ5n0ypCMMcgFh5Xo5npwFky+Hb+yGjHFnfbuQhw+QY09kxaRs1h1poaJF1tf567qjvLK9jluf2Bye2HX0yJW5iqHH6BD8mTfA8m9FHmtTi2UBqXHnw+wbYeJlEe8/c0Ikva2jGl6+G97/RTysVih6E1o/0lYuPfykDJl66dMLnIUWV6UW9cvtJuba+PicQpZNyOKSqbl8fkkpJoOBx9aW4/YFeHFLNeOykylvcfHvHdI2f1DDperpD0lGx6Tt2GXyJ0RiCnx9F1jSZG4+wMGVsgfX3JthyT3ws2Jo3A2+bll6QaEYCjj1kgetR2QhtOQsmYGzXe/uZu3VKvqssJiMPPjp2TFjV8zM57Wd9Swcm0l7t48fXjOde579KKaGfke3l5TE0SEvw4nR4eEfD2tG7MrD0B9K7nT5JGDPh+qNcqytHNyO3u+hUAw2oRo5bUdlGqY1KzblMnqh4QCxeFwmHd0+nlxfgd2SwCVTcwHCq3EByptdlDd3DbgtitNj9Ar+sYT+UPJmyK29ADqqIudVQ3TFUCAc0jkiBT85Uy8CKMCSCkbTgJswd4xc17Klsp2F4zKxmIyYEww0Rwn+f720k1uf2DzgtihODyX4IcacC2UXROqRhFLaQtSpsI4izgT8suxxgkWWBumokh5+YgpkTTjl4mhnS1m2TM8E6e0D2BITYjz8Bqebug63mrwdYijBDzH7Rrj5X5HjUOpmQpKc5D34JgRUupkijriaQAtC0Tny2O+WMXyAubfAtGsHxQwhBPNKpJe/uEwKfoolgdYuT8x13kAQZ49a0zKUUILfF6HUzdQiOPdrsgzD6/fG1ybF6CYUzpl0uSx3DJFsnCVfhQvvP/7rBoCrZxewaFwGk3JtAKQkJhA8jjPfrH8JHPtloIgPSvD7IlrwF9wBs26UOfnqEVURL0IZOqVL4VsH4bZVMuU4Dlwzu5Dn7lyMwSBTnfvKyGnu9LCzpoP5P32bPXUq8SHeKMHvi2jBByiaDx5nbH9QhaK/0TS5avZ4joVDF3x7gUwyKF4ACebBta8PogU/IzliU0uXh62V7WgaVLWqssnxRgl+X4QmbdNK5DbUDrFxb3zsUYwOarfKxuNH3u19rnqDrIDZz7n2/UGKRQp+gkGQlWImMUFKS0uXh331sjduuyq5EHeU4PdFchZc92eY93l5nKN3y2ra0+dLFIqzJvQE2XwgMvbmffDyl6D8PRh/wRkXQhtIQh5+kslISYaVJWWZGA2Cli4P+xs6gUgnLUX8UEvhTsTM6yP7llRILVEevmJg6WqW27YjsP73MgXzw4cBPcRTdkHcTDsRIQ8/yRxZmXvhr96n0enhgC74DlVFM+4owT8dcqdGugspFAOBq0luqzbC5sfkvilZ5tp3NcG4FfGz7QTYdA/fajZis8gMoqyURLZUtOHxBwFoV41R4o4S/NMhdzocWgWeLvkHqFD0N12Nctu4S27HnQ9TrpZrQep3DErphDMhWRd8iynSaCXblsj7B2X83mw0qBj+EEAJ/ukwZgms+aWssTP+wnhboxiJhEI6AMIINzwLZr2s98RL4mPTKZAS5eGHSE2Snv7E3BTSksw4eiIevsvjx+sPkp48NLKMRgtq0vZ0KF4o/whDzSZAxvRVoxRFfxEK6QDkTY+I/RDHZgkJfsSH9AVkKOe+K6aSmWKO8fC/9LdtzP/p29z/yu7BNXSUowT/dEhMgcK5kXZybeXwx6Ww+qfxtUsxcuhqhgy9U1WohMIwICVRevPRIZ3vfWwKD3xiBudNzCbNag73unX7Anx4pJVAUOOf22rjYu9oRQn+6VK6VOZKe12w8U+gBeCjv4FfLR1XnCWaJj38sctlzH7Sx+Jt0SmTYukd0inJtPLpc+Q6lnSriY5u2Qlra2U73kCQhWMz6PL46fKoejuDhRL806V4oWyFWLEOtj0NWROhpw32/TvelimGO55OWRAtY5xsUTj+onhbdMqkJEqhjxb8aNKsJvxBjZr2Ht4/2IzRILhyllzNHmqN2NTp5rOPbWBHdcfgGD0KUYJ/uhTMldt1v5Ft5a58ENLGwNYnIBgAv1dmU/ztehXbV5w625+FB0rlfqhE9zAiFNJJ6lPw5eTssl+s5tEPyplRmEpZVjIAjU4PgaDG157dzrrDrWyuaBsco0chKkvndLHlyrILletkA/SiBbI07bs/hr9eBgEPjFkKh96Eht1QPHzisIo4sulRGR4ESM6Ory1nQHjhlen4gp9ujWTjXDI1l0/NLybHbgGkZ//gqoN8WN4KqAVaA4ny8M+EgjlyW7JYFq+ac5PM3qnZJL37vS/L88374mejYujSfEA+DYZoK4e6bZHjYSj4VpORBaUZzCpOO+75UMMUgEdumsfFU3PJtScCsHJ3Aw+tPsz184vISDarEgwDiBL8MyEk+GOXy60tD5bdC7M+I49DZWyb9kdeU/dRpJ65YvTSdhQeXgiromrXb39Wbm99C879OuRMjY9tZ4HBIHjhrsVcOi3vuOft+urbXHsixqiSylazkTf3NGA0CO6/ahppSXJyVzEwnJXgCyEyhBCrhBCH9G16H9cFhBDb9Z9Xz+aeQ4KyFWA0w8RLI2MX/ACufUTW2wEwJEQ8fEctPHo+vPC5QTdVMcSoXAdosj5O5Xqo3gxrH4QpV0HJQrj4h2AceZHWcdnJ3HBOMc/duTg8JoQg124hqMGkXBspiQmkWk0qpDOAnK2H/13gHU3TJgDv6MfHo0fTtNn6z9Vnec/4UzgPvl8XqaAZQgiYcJEU+wmXQpMu+O/9r9x2t8hJXU/X4NqrGDpUfghJ6WCxw47n4O3/hpRcuPr38bZsQDEZDfz8EzMZq0/UhsixybDO7BIZClIe/sBytoJ/DfCkvv8kMDhNNYcCRtPxx1fcB5/7t5ys7ayXoZztf5fnEizyD/wvFw+enYqhRdWHcu6nYK4s0VG7FaZeI78ERiG5+sTtbD32n2Y109GjYvgDxdkKfq6mafX6fgOQ28d1FiHEFiHEBiFEn18KQog79eu2NDc393XZ0CY5S9bcyZ0hj1+6TXr8k66QhbEadsmKmyqeP/roapJlj0sWy6fE5v0y734UZ3KFJm7n6IKfqjz8AeWkwUIhxNvA8WZi7os+0DRNE0L01fB1jKZptUKIccC7QohdmqYdOfYiTdMeBR4FmD9//vBuHjvufJh4GRxcCXM/J9vSHXgd2ivk+aoNMP26OBqoGHQOvSW3pUvl01+IogXxsWcIcP6kHKrauinLltVn06wmOt1+/IEg1e09+ANBJuiN0hVnz0kFX9O0Ppf7CSEahRD5mqbVCyHygabjXadpWq2+LRdCvAfMAXoJ/ojCmACffBw2PgJzbob9r8vxUEej6o1K8EcbO1+A9LEyy6szX47ZCyG1ML52xZFzx2dx7vis8HGaXmHT6faz4pfvAVDx8yviYdqI5GxDOq8CodSTzwGvHHuBECJdCJGo72cB5wKjo4uI2QrLvilXTqYcE+2q2hAfmxTxwVkHRz+AmZ+Wk/v2fLlCe8y58bZsSBFakbu9uj3OloxMzjb/6+fAC0KI24BK4HoAIcR84C5N024HpgB/EkIEkV8wP9c0bXQIfjTRgp89RcbyA76+J38VI4udzwNabNvMz7+uGukcQ6q+QOvZTdVxtmRkclaCr2laK9CrE4imaVuA2/X99cCMs7nPiCC6PkrJIpmj37RPlla+8jfS41OMTIJB2PaU9OYzyyLjacXxs2mIEgrprNrbGB7z+oOYE9Qa0f5A/SsOFtGCXzRfbve+Iid1dz4fH5sUg0PFGlk+Ya5aeHcy0qJq7ozTc/Y7VKmFfkMJ/mCRkChzrU1WyJ4sx0L1Uw68ET+7FANDd5vsk1C9WWbnJFhg6vBfczjQhDx8gFsWjwFQvXD7kZG3hnsok5ILWjASz6/7SG6rN8lOR4k2MBhVXH+4o2nwxBVyvUXeDLBmyS95U1K8LRvy2KMEP5SOqYqp9R9K8AeTMeeCMETCOz3tsiZPwAuH35YpnMUL4fL/i6+ditNH02Sl1ILZ0HpEin1KrpynsaTKUhuKk2I0CH549TQWjM1A01fiHC+k09TpJt1qxmRUQYrTQf1rDSZX/hqu+GUkvANyxaXZJuvn1++AAyvja6Pi1FnzK/jPd+T+kXfh0fPg6BooXy3HFn9Fdkfrbu1dd0nRJ59bUsqUfDvpydLb33S0nR/+ew+bK9rYXt3Bk+srWPrz1Xz/n7tiXrerxsHsH70V7qCl6I3y8ONFSp708FOLZQgn1CLRUQUdVZBWEl/7FCdm54vwzo/k/mU/lzVyACrWQuNu+f837eOw6v/J8WFY8jjehJqmPPVhBf6gxuPrKsLn0qwmXtpWgz3JxJhMK7csLmV7TQcd3T4ONXWFm6soYlGCHy9suTI1014gV1oe/SByrmIdzFaCP6RZ99vIfncr1GyW+0c/gMY9MO1aSC2S8fvuFuXhnwEWkxGLyYDbF2Ryno17LpxAYoKBNKuJMZnJrPjle/xl7VEMAhaMzaC+Q7YUbepUHn5fKMGPFyl6eSJ7oWygArIheleT9PanXasm+YYqwaAsgpZRJretR6BmqzxXtV5up18nV9QWzJGT8vaC+Nk7jEm3mql3uJlVlMblM2LXqjx35yI63X7uemYr//vGfrKS5RNBk9MTD1OHBSqGHy9CE7ephTKOD1B0Dsy6QRZZe+ziSBs8vxde/IKM8SviT2c9+LphvF5m6uBK8HZC2QXyOHc6jD1P7l9wH1z7sBR/xWkTCutMzu9dQG1aQSqLxmVywzklrD3UTGVbNwBNnUrw+0IJfrwIefX2Avmz7Jsw/zYZD77yQWjcJYUEZMbHnn/Cuz+Jn70Kic8NrYflftkKQMiiaABLvwEJSbLdZUjgC+bIblaKMyI0cTs5z97nNVPybQQ12FHdAUCzEvw+USGdeDH2PFlCOWuSFIcLo3qczrkF1vxatsGbfAW0HJLjh96SDbCzJ8XDYoWnE34zU8bmQU7E2gvAWSOrYJYug+9UgElNGPYXoZW3k/P6LpE8IUee8wdlHqeK4feN8vDjRd50uOUVWVHzWIwJsPCLsv9p3XZoOSDz9w0JqgxDPGgrh0dXwJa/Qk8bNOyU6ydSi6TQg/TihVBi389M3UYJzwAAFv5JREFUzbczrcBOerK5z2vGZSfHRMxUSKdvlOAPVebeAuYU2PAHaDkohSW1ONJAJRq/Fz74JXhdg27mqKBinSyD8fYPI2MZ4+Sq6IxSeTz1mriYNtL58orxvPbVpSe8xmIyUpIhHadceyLNatK2T5TgD1UsqbJxyu5/yCyP7EnSo3TU9L62Yg28+2M4snrw7RwNtJXLrRaI1K/P0KteTr4Kplwte9QqBgRxChPeE3JkmekZhWl0evz0eAMDbdawRAn+UGbR3XLbWQ9ZE6SHfzzBDwmSW05a8a+74X1VnuGs6aiCA/+RqZehwnfL7pUraGfdIK+ZdBl8+mkwqD+leDJej+PPKkoF1MRtX6hJ26FM+hiYeQNsf0bm6BsTpfgf2zgllDXSowv+wZWQPxP49qCbPKJY+T1ZyTS1WPadveHvcn5lfJ9dPxVx4pPzijAImK4LflOnm5LM48yPjXKUWzLUWf4tKTZjl8uQjhaMbYANcuEPgNsh4/g9bbI8r6cTOlTnoDOiq1l+cWpB6KiUMXuj8o+GKuNzUvivyyaTp5dUaFD1dI6LEvyhTsZYuH2VrM0SSgf8113wqynwzy/K47aQ4HdEQj497fD+L+CxCwmXHVScOrtelIXPhFEeZ4yLrz2KU6IoXa5Or27riRl/Z18jP3tjXzxMGlIowR9OpOot8SrXyfosO5+Xwt5eKcd7OiIefXerzOjpapTXKE6Pox/INRIli+RxphL84YDNYiIj2UxVWzedbh9PfVjB4+uO8vXntvOnD8px9MhmKr5AkM8+toE1h5rja/Ago55RhxOphZH9BXfChw/JSUVNz0hwO2S1TZBL/zv0/bajYM0YXFuHK9Wb5ZOUsxbSS2V9+8p1ysMfRhRnWKlqc3HdH9ZzqKkr5tzeOieLyzIpb3ax7nAr2SmJLJuQHSdLBx/l4Q8nzMmQlAG2fCn4ALte0s+lxIZ0ILJCt/1o7Pvsfz0S91dINE3OezxxBbz/gJwnsefDgi/C1Q9FFlgphjwlGVa2VXZwqKmL718+mX/cvYTHv3AOAHvqHADsb3AC8GF5K9ooCnkqwR9uzPs8nPcdGdNPSocj70CiXeaHR4d0AHz6Qqxowdc0eOlWWPebQTV70KjdJpuRnCpuB7x6D/xvAfzjdgh4oHk/uJrBVgDJmTD3ZlX8bBhRkpFEj08+9S4dn828MemsmJRDrj2RPXVS6A80dALQ6PRwtCV2waLXH+T5zVUEgiPvi0AJ/nDjov+G+V+QApQ3Q45Nv07W13c7wFENhmN64jbulQ21NU3G8/1uGeYZibx0Kzz9cTi0qu9rdv9Tlknwe+H5m2H73yA5W355gvzSAOnhK4YdoVW3SSYjE3NTwuPTC1LZUN7KT17by7aqduwWGdH+sLw15vUfHGzmO//YxcZjxkcCSvCHM3kz5XbWjWBJkyGdjmrImRx73Z5/witfgpotchIXIou1RhomPff6H7fJEE00W5+AHc/DK1+Bt/8Htj4OR9+Hq38PX/iPLGucP1t6+SA9fMWwozhd/g7MLEolIarn7bTCVOodbh5be5QN5W0sn5hNrj2RD4/ECnuoFk95y8grVaImbYcz82+F5CwoXiDLK/jdcrJx/IXQoPf7TM6W4QkAVxN49UksZy34eoZXk5WuZpkqeULPW5MTrG1HZdjqYr0Nod8L//5a5DIfsOERWSJh9o1y7O518NEz8MqX5bHy8IclxbqHP6ckPWb85kVjsFsSWH+klXf3NzE5z0aCQbD2sIzjh0o4tHZJwa/QBb/L48dsNGBOGP7+8fD/BKOZzDJZg10ISErTBzW5SCtE8cLIfmdDxMOH4xdiG8r8+QL49WTZcaovPF3yM8+8Hjb+KVJQrkNPXU1IgoV3yf32ozDuvNjXp42J7NuU4A9HitKT+K/LJvHZhbFtQrNtidy+bBzf/dhk7JYEFo3LZHFZJi1dHo40d+H2BWhyumkJCX6rC03TuOr3a/n1qoPx+Cj9jhL8kYIlLbJfMAdMyXJ/+bdlyAIhBb+zIXLdcAvrhFJOD58gPu9xQqINJl8pn3ha9D/UUPmJz78mm8yEWkxGfzmCTMUESLDISXHFsEMIwZfO///tnXt01dWVxz/7JuQmJDcJJCEkIUJ4qbxRilDRghYf2BGfI47T2lVXH0ukTqd1tOO46nTGNTPW6RrrsnWYqq3VJeMM9e3oqDBVfCCovCPyFkJIAgGSEEICOfPH/v1ybx5XArnhJvfuz1pZv989v1/uPTvn5vs7Z5999hnd1tPvyNjCEGt/dhnTRgxm5sh8AD7YdoBHl2/lioffZX9DMwA79h9hz8Gj7Nh/pC2qp79jgp8o+II/YKCGEPpx94XjNdVyZgE0eD38gOfJ62+Cn1Wox5WPdb625U2dv2hu0BDVAm8eo2ojrPotVK7T14NH6ojIX1A1ooPgZxfrpHeoyCJzEhjffVM6OIOS3Aw+2H6Aj3bUUnukmXJP3HfXHuXjXbposfJQ+1QNTS0neHzFDppa+ldWTvPhJwq+S2fIOM3cmDFIF1/5SdZChVBfBWkNGtJ59CDsXgnNt3W9CUtfwzmNQgLNT9/aGs5Q2XoClvwFTP1L9fEHQ16++gHwwa+heqM+CAfmhR+Es34EI2Zp2GUkgRT9+/hbUBoJjYgwY2QeyzdX03xcXYXba9QN2HyilVfWad6qvYc7pmqo5h9e2cSWqnr++fpJZ7bSPcB6+IlCumYJpHC8HjMLwj1i0B5rfaX28LOGQukMKH8ZnvuWXj/WoJOYJ46f2Xp3l5ZGddHkDtcomvq9GoXz1DUaRnmiORxqGgxporP8MSr2/u/njQ6/X/EUmP7drj/r0vv0gWAkBTNGDqb2SDMNx8LffT+//rLPdM6rvuk49U0tvF1exZ1LPqW+SVM0LFm1m8bm49z+zMcsfqfvL2Y0wU8Usoao37l0ur6+9D6Y91DE9UIV+/p92ttf8IxusLLzXe0hr34cXr8Hdq3Q+3tj9eFnr6lAf9mkazQavdC5YbpiktrtsOt92L4c1j6rZf7EbNDb/7Tj3r/+piUnY/y1MGbuqdfR6JfMHJXXqWzOOUM4u1A3Ry/J1Ui2ysNNPPneTl5cs5ddtY1t9765qYo/ba7hj59UnLE6ny4m+IlCeg78cI3G5INO3I64MHw9VKThmXV79TyQog+H400qlGu9vXKrNqrYPzYLnpwXTswWC3auUIE+tLN797e2auqIo4fCgu8/0Gq3wwEvdcSu9/TorzJuE3zPjz/xz/WYP6ZH1TcSk2GDBlI6OIO01AD5WUFAQztfXjSLR26eyv1X66h5S1UDK3fo93BDxeG2KZ5dBxo50nyCzVX1HGpsjosN3cUEP5HILoq+81KoUHO7Hz8a9k8XnKvH9UvDro+qTVC9Cao2qJC+FsNNVPysnVUbT36vc/Dqj3QB1eon4Ign+EMn6UYwtdvDuYJqPtNjqw6zSfNWVxZP1eNXF+nmJed/OyZmGInHgq+cxfzJxZTl63xWfmYaaakB/mxyMeOKswH4z9W7aTmhI98NFYcpy8skmBpgc5WmaXAOPtpR2/UH9BFM8JOFrIhJyHOv1mPBWD2+/yud4Bw6SYV/61taXnaxLuBa/9/w9A3R3TzL/hGevv7kdTjq/TPs23Dye/d+qitjQfP9+z38zAINnTywLRxy2RG/hz/mMvjhp7r71zlXWcZQIyoL54zmFzdObgvlzA8F264VhoIERFMupAS0W3+wsYX8UJD8rGBbXh7QNA3V9U1sqNAAg7qmFub+8k+8uKaCHz+3ludWx3dDIhP8ZMFPrTz+Ot1UBdQNlF2isetjLoMRF0F1uYY4DhkPI+fo5OjqJzT2veNOWz4bX9CHRP2+L/f9+6kOqroh+H7Ct4H5UPN5hODneStpI3r4HfEFX8TSGhunhJ+WIS8zra0sNSWAn0dt4ezwPFBBVpD8ULAt+VphdpAn39vJ9Afe5huPrKD5eCtrvtCsnXcuWcPST/bwyLIo39kI/vq5NXz/D6tjaFUYE/xkoWgK3LIUrlvcvtz3c0++SSN8jjfpRO7oS2CI5/LxfeR+LDvA/q2aruDIgbAv/b++DQ8UQVOURSptPfz1UP3Zl9e3bq8eR81Rl03jft19KpijIl69SXMHRUYi+fiCbxinyCXnDOHisQWUDGqfcmRKaS4DUoRFl44hJ0NDnQtCQQqy0tqyaj5+61e4PeKBUF3fxHqvp186WN8vKziAA97K3mh8XlVPU8tpBDZ0gx4JvojcKCIbRaRVRKZ9yX1XiMhmEdkqIvf05DON00QExny9/ebnoJOgWUNh7BUaqgg6qTtzUecol32e4DfVwW++Cku/A7s/9D8AvvhA5wgOfaE9/Q8f0weDj+/DP7QLfn0BlL/S/v0bqsP+/bpKjZ0vvUBHIPs2qEsmEGgfQeNvKJ4SHoKb4Buny+TSXJ76znSCqSntyp/97gzW/exyBqQE2vbNzc9Ka5vkBRiRn8nfXHEOv/Ny71fVNbFuzyHK8jN556453HLBWVTVNfHg65tZsPjDqHn4Kw4e7fTAiRU97eFvAK4D3ol2g4ikAI8CVwLjgJtFZFwPP9eIFRf9BBathtSg9vB/sALuXKuTvLnDNdQTdHVu5Vo937deY+HLX4bXf6r+/3O/EX7Pxv3qGnr9bg33BI24OXpQXUrjr1VX0gePhn/ncAU8NEYfJM5pcrfs4vAIZNf7unAKtNd/zWMaVz/+Wi0r9L5SEghnzDSMGJGRlkJGmj4ECnN8wQ+2CX4wNUCmd32od33f4WNsqKhjQkkOIkJRTjq1R5pZX3GYmvpjbVk5fY4c01j/g40tbaGgsaZHgu+cK3fObT7JbdOBrc657c65ZmAJML8nn2vEkJTU9j3ioRNV/EFDN/PHqtiPnhvu4fvCP+F67a2XnA+X3BdOSnZkv6ZkhnAEzbHDGiU0bBrc+DuYcTt88T7sXaPXX/1xuA51FTpfECoKC35zffvcNlNuhkUf6wggmAMjZ2t5WshSIhi9ytBs/f8oCAXJz1Jff15mWlu6Bn8EsHHvYSoOHWVSiS6KHJqjIu6nbthUGXZ9nmh1zH7o/7j/pU0AfVPwu0kJEDk1vccr64SIfE9EVovI6pqa5NpcuM8y6hIYdam6fg59oT3xyrUqxjc8Ad9/F677d3X/fO1u/Z2Gat1kBKDG6w/4E7a+aE9eoMed72qPfs9Humk46FxBXaWOArIKtA4Q7uFHkp4Nd20Jh1wGszrfYxgxJOzSCZLn9fDzIlw7ORkDCKYGeKtcV+lO8AS/yOv5+56cTXvrKK+swznH9poGauqP8ep6nbvqLZfOSXPpiMhbQFeJRe51zr0Yy8o45xYDiwGmTZuWePuL9Ufm/r0ea3fA8gfgvYdV8Isma3lRRB6R9FydWN2zSkMpc4frCODFheEFXBleaGRmvor/gW3am288ADPvgLd/DpVrNDrIz0d/y1LdjSpaxE1qMPy+5r83epmygkxSAkJxbgaNzZo8LS8rHNUjIgzNSefzKp2YnVCicfyF3oPC55FlW/jFG5tZOGcUowq0o+JP1vZWD/+kgu+c+3oPP6MCKI14PcwrM/oTg8tg8s0aG9/aAuOu7nxPIKBCvnulvh43X2P8P306fE9kLPzgUfpg8DdrOWum+uW3LdMkaP6OUx0narsiGFLXkwm+0ctcPbmEiSW5FISCHD6qK2sHR4Rxgo4Cdh1oZGR+JqF0DZTwffugUTu7a4+SO3AAjy7fxugh4ZFpSkA6PRxixZlw6awCxohImYikAQuAl87A5xqxZs69mq4hPUfdPF2RWaA+eICzr+x8PdIPnzcKDmwPzw0UjtcRw55V+jr7FLYYFNFefpq5dIzeJSUgbQLtT9pGRutAWNwnDstpK8sKphLy9tG9amIxIvD0bRdQmB1ka3VDeNI3O71tgVes6WlY5rUisgeYCbwqIm945cUi8hqAc+44cAfwBlAOPOec68baeqPPkV0E33we7t4JZ13Q9T2ZuqEEqekwbLqGS0ZGzWR06OHX7dG9dgeNUH/8yNntP+9UGDQivMDMMM4AORkDuGZKMbPPLmhX7vv5J5bktCsvykmnKCedhXNG8cLtFzKhJIebpqkDZN7EIlIC0mv+e+hhPnzn3PPA812U7wXmRbx+DXitJ59l9BMyvS/+oBEaAXTxXXr+wg/UTZMRsTNXnrdIZdsyGHu5nk/9pm5DuOUNze1/Kty8pPM6A8PoRUSEf1swtVN5YRTBP3/4II61tBJKH8DkUv1fuGn6Wfx2xQ5mnz2EmoZjTCjO6fR+scI2QDFiy0Cvh+9vFfg1L/na+w9rlE8gYkGLPwl7olmFHtQ1M+lG/TlVOm5mYhhx4tJzh/DZvjqmnJXbrvyfruu8WUpJbgYf/91c0gcEuGpS7+6jbIJvxJbMDoLvc/a8sG/ex+/hF0/VXD6GkSAMz8vkwRsmd/t+f1FXb2OCb8SWNpdOWfvyOX/b+d70HJj7c03SZoulDKPXMcE3YkukD787XHhnr1XFMIz2WLZMI7aUXaQLqMouindNDMPogPXwjdgSDMHlD8S7FoZhdIH18A3DMJIEE3zDMIwkwQTfMAwjSTDBNwzDSBJM8A3DMJIEE3zDMIwkwQTfMAwjSTDBNwzDSBLEub65k6CI1AC7evAW+cD+GFWnL2L29X8S3UazLz4Md84VdHWhzwp+TxGR1c65afGuR29h9vV/Et1Gs6/vYS4dwzCMJMEE3zAMI0lIZMFfHO8K9DJmX/8n0W00+/oYCevDNwzDMNqTyD18wzAMIwITfMMwjCQh4QRfRK4Qkc0islVE7ol3fWKFiOwUkfUiskZEVntlg0XkTRHZ4h0Hxbue3UVEnhCRahHZEFHWpT2i/Mpr03Uicl78at49oth3v4hUeG24RkTmRVz7qWffZhG5PD617j4iUioiy0Vkk4hsFJE7vfJEasNoNvbfdnTOJcwPkAJsA0YCacBaYFy86xUj23YC+R3KHgTu8c7vAf4l3vU8BXsuBs4DNpzMHmAe8D+AADOAlfGu/2nadz/wky7uHed9V4NAmfcdTom3DSexrwg4zzsPAZ97diRSG0azsd+2Y6L18KcDW51z251zzcASYH6c69SbzAd+753/HrgmjnU5JZxz7wC1HYqj2TMfeMopHwK5IlJ0Zmp6ekSxLxrzgSXOuWPOuR3AVvS73GdxzlU65z7xzuuBcqCExGrDaDZGo8+3Y6IJfgmwO+L1Hr68gfoTDvhfEflYRL7nlRU65yq9831AYXyqFjOi2ZNI7XqH59J4IsIF16/tE5ERwFRgJQnahh1shH7ajokm+InMLOfcecCVwEIRuTjyotMxZcLE2CaaPR6/AUYBU4BK4F/jW52eIyJZwFLgr5xzdZHXEqUNu7Cx37Zjogl+BVAa8XqYV9bvcc5VeMdq4Hl0qFjlD4u9Y3X8ahgTotmTEO3qnKtyzp1wzrUC/0F4uN8v7RORAagQPuOc+6NXnFBt2JWN/bkdE03wVwFjRKRMRNKABcBLca5TjxGRTBEJ+efAZcAG1LZbvdtuBV6MTw1jRjR7XgK+5UV6zAAOR7gN+g0dfNbXom0Iat8CEQmKSBkwBvjoTNfvVBARAR4Hyp1zv4y4lDBtGM3Gft2O8Z41jvUPGg3wOTpDfm+86xMjm0ais/9rgY2+XUAe8DawBXgLGBzvup6CTc+iw+EW1Nd5WzR70MiOR702XQ9Mi3f9T9O+P3j1X4eKQ1HE/fd69m0Grox3/bth3yzUXbMOWOP9zEuwNoxmY79tR0utYBiGkSQkmkvHMAzDiIIJvmEYRpJggm8YhpEkmOAbhmEkCSb4hmEYSYIJvmEYRpJggm8YhpEk/D94bkikfk5FygAAAABJRU5ErkJggg==\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"# 271次元のベクトルを4つの列に持つ行列A\n",
"A = np.stack([sin, sin_n, sin_minus, sin_minus_n], axis=0).T\n",
"A.shape\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "nSTaWBUUhZEn",
"outputId": "ed0191a1-8fe1-4dd7-8908-700ea7cb5b18"
},
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(271, 4)"
]
},
"metadata": {},
"execution_count": 5
}
]
},
{
"cell_type": "code",
"source": [
"# 各列の最初の10件\n",
"A[:10]\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "jyuaedwWin8l",
"outputId": "00d4acbd-3f9f-4236-d1ab-ab465e1a9a2b"
},
"execution_count": 6,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[ 0. , 0.0510517 , -0. , -0.00068583],\n",
" [ 0.01745241, 0.05510397, -0.01745241, -0.031021 ],\n",
" [ 0.0348995 , 0.01600259, -0.0348995 , -0.07075095],\n",
" [ 0.05233596, 0.09683902, -0.05233596, -0.04444908],\n",
" [ 0.06975647, 0.14818608, -0.06975647, -0.21303364],\n",
" [ 0.08715574, 0.07358723, -0.08715574, -0.05284413],\n",
" [ 0.10452846, 0.13764128, -0.10452846, -0.13130122],\n",
" [ 0.12186934, 0.20762304, -0.12186934, -0.10019091],\n",
" [ 0.1391731 , 0.13645403, -0.1391731 , -0.21795342],\n",
" [ 0.15643447, 0.08793064, -0.15643447, -0.15536475]])"
]
},
"metadata": {},
"execution_count": 6
}
]
},
{
"cell_type": "code",
"source": [
"# (a) 列ごとの平均ベクトルμを行列Aで表す\n",
"AVG_A_SIZE = A.shape[0]\n",
"AVG_A = np.full((1, AVG_A_SIZE), 1/AVG_A_SIZE)\n",
"print(AVG_A.shape, A.shape, AVG_A[:, 0])\n",
"μ = AVG_A @ A\n",
"print(μ,μ.shape) "
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "PZxsPTlQi6Wc",
"outputId": "4458e712-6de8-478c-fe40-5ac3b8a6d423"
},
"execution_count": 7,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"(1, 271) (271, 4) [0.00369004]\n",
"[[ 0.20957316 0.21103106 -0.20957316 -0.20428987]] (1, 4)\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"# numpy の関数でもチェックする\n",
"np.mean(A.T, axis=1)\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "EVg3a8CcmXZ_",
"outputId": "52ab1cd4-f7d9-4075-99d0-794f89e191bc"
},
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([ 0.20957316, 0.21103106, -0.20957316, -0.20428987])"
]
},
"metadata": {},
"execution_count": 8
}
]
},
{
"cell_type": "code",
"source": [
"# (b) 平均値除去行列Ãを表す\n",
"\n",
"# ランクを合わせる\n",
"# (271,1) @ (1,4) = (271, 4) \n",
"# サイズを合わせた1の行列積を引く\n",
"Ã = A - (np.ones((AVG_A_SIZE,1)) @ μ)\n",
"print('Ã', Ã.shape, Ã[0:3, :])\n",
"\n",
"# A - μ で numpy のブロードキャストで計算できてしまうが…\n",
"print('numpy broadcast', (A - μ)[0:3, :])\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "f45b7FF7mtKu",
"outputId": "c6fda184-2dd9-4fb1-f278-91e818ea2afc"
},
"execution_count": 9,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Ã (271, 4) [[-0.20957316 -0.15997936 0.20957316 0.20360404]\n",
" [-0.19212075 -0.15592709 0.19212075 0.17326888]\n",
" [-0.17467366 -0.19502848 0.17467366 0.13353892]]\n",
"numpy broadcast [[-0.20957316 -0.15997936 0.20957316 0.20360404]\n",
" [-0.19212075 -0.15592709 0.19212075 0.17326888]\n",
" [-0.17467366 -0.19502848 0.17467366 0.13353892]]\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"# 平均値を引いたあとなので、合計の平均値は(丸め込み誤差を抜くと)0である\n",
"np.round(np.mean(Ã.T, 1), 10)\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "hAhwPk8qsafM",
"outputId": "62a76833-93a1-428e-f18a-b08a8e809148"
},
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([-0., 0., 0., -0.])"
]
},
"metadata": {},
"execution_count": 10
}
]
},
{
"cell_type": "code",
"source": [
"plt.plot(a, Ã)\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 265
},
"id": "GwfKqLiquNek",
"outputId": "a6fa7d69-bb87-48cc-dbe1-1877028be867"
},
"execution_count": 11,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"# (c) 共分散行列を求める\n",
"\n",
"\n",
"conv_matrix = ((1/AVG_A_SIZE)*Ã).T @ Ã\n",
"conv_matrix\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "HdswmyK0qtku",
"outputId": "7aec775a-98e6-4713-c475-ee08af7f1f26"
},
"execution_count": 12,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[ 0.45607909, 0.45632313, -0.45607909, -0.4583532 ],\n",
" [ 0.45632313, 0.45941872, -0.45632313, -0.45874436],\n",
" [-0.45607909, -0.45632313, 0.45607909, 0.4583532 ],\n",
" [-0.4583532 , -0.45874436, 0.4583532 , 0.46310324]])"
]
},
"metadata": {},
"execution_count": 12
}
]
},
{
"cell_type": "code",
"source": [
"# np.cov で共分散行列を求める\n",
"np.cov(Ã.T, ddof=0)\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "LGVGlZpsuhil",
"outputId": "1e736dac-b513-4492-b6dd-59f675aaee28"
},
"execution_count": 13,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[ 0.45607909, 0.45632313, -0.45607909, -0.4583532 ],\n",
" [ 0.45632313, 0.45941872, -0.45632313, -0.45874436],\n",
" [-0.45607909, -0.45632313, 0.45607909, 0.4583532 ],\n",
" [-0.4583532 , -0.45874436, 0.4583532 , 0.46310324]])"
]
},
"metadata": {},
"execution_count": 13
}
]
},
{
"cell_type": "code",
"source": [
"# (d) 標準化したベクトルを並べた行列Zを求める\n",
"\n",
"# 試しにベタ計算でz0を求める\n",
"a0 = A[:, 0]\n",
"z0 = 1/np.std(a0, ddof=0)*(a0-np.mean(a0))\n",
"print('z0', z0[0:5])\n",
"# 関数を使う\n",
"from scipy.stats import zscore\n",
"print('z0', zscore(a0, ddof=0)[0:5])\n",
"print('z1', zscore(A[:, 1], ddof=0)[0:5])\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "ljJA35QPvZXX",
"outputId": "63ffe677-1b2b-4cc3-c160-7e7b8033c3e0"
},
"execution_count": 14,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"z0 [-0.31032415 -0.2844816 -0.25864693 -0.232828 -0.20703268]\n",
"z0 [-0.31032415 -0.2844816 -0.25864693 -0.232828 -0.20703268]\n",
"z1 [-0.23602588 -0.23004735 -0.28773566 -0.16847346 -0.09271846]\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"# 列の標準偏差ベクトルを算出\n",
"A_STD = np.std(A.T, axis=1, ddof=0)# .reshape(1,-1)\n",
"print(A_STD, A_STD.shape)\n",
"# 対角行列を作る\n",
"A_STD_diag = np.diag(1/A_STD).T\n",
"print(A_STD_diag, A_STD_diag.shape)\n",
"# 対角行列との行列積で算出\n",
"Z = Ã @ A_STD_diag\n",
"print('z0', Z.shape, Z[:5, 0])\n",
"print('z1', Z.shape, Z[:5, 1])\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "8o897d78yEsL",
"outputId": "2f095555-7088-4872-c391-2417e4bf7d6c"
},
"execution_count": 15,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[0.67533628 0.67780434 0.67533628 0.68051689] (4,)\n",
"[[1.48074378 0. 0. 0. ]\n",
" [0. 1.47535202 0. 0. ]\n",
" [0. 0. 1.48074378 0. ]\n",
" [0. 0. 0. 1.46947124]] (4, 4)\n",
"z0 (271, 4) [-0.31032415 -0.2844816 -0.25864693 -0.232828 -0.20703268]\n",
"z1 (271, 4) [-0.23602588 -0.23004735 -0.28773566 -0.16847346 -0.09271846]\n"
]
}
]
}
]
}
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