{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"\n",
"*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
"\n",
"*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# In Depth: Principal Component Analysis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this section, we explore what is perhaps one of the most broadly used of unsupervised algorithms, principal component analysis (PCA).\n",
"PCA is fundamentally a dimensionality reduction algorithm, but it can also be useful as a tool for visualization, for noise filtering, for feature extraction and engineering, and much more.\n",
"After a brief conceptual discussion of the PCA algorithm, we will see a couple examples of these further applications.\n",
"\n",
"We begin with the standard imports:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns; sns.set()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introducing Principal Component Analysis\n",
"\n",
"Principal component analysis is a fast and flexible unsupervised method for dimensionality reduction in data, which we saw briefly in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb).\n",
"Its behavior is easiest to visualize by looking at a two-dimensional dataset.\n",
"Consider the following 200 points:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
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1AEAyrFxfxeUsVO3osojAEWiZCe9aknpaafyKHCNjtzVhEJ3p4WXbtm06ceKEpk6dGjzmdDo1YcIEbdiwwfA927dv19ixY80uCgDABFat2BpvvMr0uhFadOt5+vyU0HE4182u1diRpVm/ymwuM73b6ODBg5Kk4cOHhxyvqKhQS0tLxPlut1tHjhzRhg0b9Pzzz+vYsWOqq6vTnXfeqTFjxphdPADIemZvXJjqQml9kej+Py5nof7njHGaNfn0iO6lTJcZmWN6eOno6GmSCx/bMmjQIB0/fjzi/B07dkiS8vPz9eijj6q9vV3Lly/Xl770Jf3ud7/TsGHDUirHgAFMpArIz88L+TfSjzq3BvUurd28X880bQ1ZAbfxsyP7/Lkzzq7WWeOGqdXdrkpXcTAEpKPOY21GGC18VLiKIwYPRytz7+scdLeryuC1/i7Xf9ZNDy+FhT0/AF6vN/jfktTV1aWiosjmuqlTp2r9+vUqLS0NHnvyySd14YUX6je/+Y1uvvnmpMuQl+eIuttmLnM6aS7NNOrcGrla70eOdQSDixRYAXebptWfntJ05iPHOnTgyMcaMWywhg0tUllZiWpGn2Z4rpl1vvdou+F4lfaTftUk+Xd7tDK/ua5Zy15+NxjybrvmLF18jv1mt+bqz7rp4SXQXXTo0CGNGjUqePzQoUOqra01fE/v4CJJxcXFqq6uVmtra0pl8Pn88nii77iZa/Lz8+R0Fsnj6VB3t7kLScEYdW6NXK/37R+5DR76fu3YfUT5n0pu9maiLTjpqPOSgXmGi+EVD3Sore1Enz/f7ekMBhep5zpPvvyuaqoG26YFJht/1p3OooRbkkwPL7W1tRo8eLDWrVsXDC8ej0cffPCBrr322ojzX3zxRf34xz/W2rVrgy01H3/8sT766CNdffXVKZfj1Kns+DLN1N3to14yjDq3Rq7W+zBnoeFD/zRnYVL14fZ0GrTgbNV4g1k/AWbWubO4wHC8irO4IO41Ehnvs//wCcOWnQOHT8hZHLmcR3+Wqz/rpoeXgoICXXvttVq8eLFcLpdGjhypRYsWqaqqSrNmzVJ3d7fcbreGDBmiwsJCXXjhhfrRj36ku+++W/Pnz1dnZ6eWLFkil8ulK664wuziAUDWMmtgbayp0ZlqmUhl/59EB/kmu7Mz+p+0LFJ3++2369SpU7r33nvV2dmphoYG/fznP1dBQYH27dunmTNn6pFHHtGVV16p4cOH69lnn9XixYs1d+5c+f1+nX/++XruuedCxswAAOJLdQfi3lJ9uKdjllOszwlcb9DAPB05bjzI12hROitmT8FcDr8/2lZX9tXd7ZPb3fd+0WwxYECeyspK1NZ2IiebF61AnVuDejfPW+8dMFyaP1ygzn/7xx0hY2TSvRR/71aWWO6e+1nVji4zfM3t6exTyLNSNv6su1wl1o15AQDYXzItOEaznNK5FH/4VOpo4rUWsbOzfeXmBHEAQFSBlW0lGS7NH+7AkY8zuhS/0ZiccHQFZTdaXgAAQYkOeu1txLDBpg+AjTV+xmhMToBD0i2XTdTYkaUElyxGeAGAHNd74GsqOzEPG1qkG+aM1y+atpoyADZegAofcBsQuO6U8ZUpXRf2QXgBgBwWb+BrvCnSbk+n9h5t17/VnKbHbj2vzwNgo20NEB6geo/JKRiYJ+9Jny0H3iI1hBcAyFGJDHyN1f2TShdTrLK0tnXon+3ehNeYYcBt7iK8AEAcZq9fYvZ1Uy1ftIGvgfEksbp/Em0hSUR4CArHAnIIR3gBgBjMbF1Ix3X7Ur5oi9F9Z97ZcbthzFqF1ygEBfKLX8wagjHCCwBEYWbrQjqu29fyRVtp9owRpXHfa9YS+0YhyC/pa5dNlLO4gHEsMER4AYAorNrjJ9p1d+0/HtI9ZEb5Ut1OwKwl9qOFIKY6IxbCCwBEYdUGfkbXdUh66tUtId1Dk8a4TClfqgNfp9eN0Fnjhqn9pF/FAx0p7cgcHoIcDumqxhqCC2JihV0Apgisyur2dFpdFNMEHqx5nwzCcEia1XC6JdeVFNE9JCnkvFRbP/5x4LhWrd+jfxw4nlJZ/23ssD6Fjel1I3RVY42knntbuXaX3nrvQMqfh+xHywuAPrNqUGsmBLpV1mzcp1Ub9mjV+r16c8PetN9j7+4cT7tXT/3XlpDXA91Dfd1F+unXPtBf3j8Y/PN5k6p00/+YkNRnHDnWoe0fuTUsxRYct6dTK9fuCv45U2OLYF+EFwB9YtWg1lTEm1Ic6/VVG/Zk/B4D3TluT2fM7qFUu33+ceB4SHCRpL+8f1Az6kcmNGhXktZu3t/n3aStGlvUV1ZNoQfhBUAf9acHT2C115KBeXIWF4Q8XN7f7Y7ZOhSr9cjqezRrcGy4nfuMu4k+3HdcZ4woTSjsmbGbtFVji/oim1sb7YDwAqBPMvHgSeQ33PCHybkTq/TXLQeD5XKoZwquFPmQjdd6ZPXD1e3pVPnQooTWX0nkswJ1Oa7auHVlbHVpQg9ns0JdusJZLH1pNbFTa2O2IrwA6JN0P3gSeYgaPUzCu0PCF5Lt/ZCN9xC24uEaEH7/VzfWBO+lryvZXj+7VudNqooY8zJ08CA99PymuA9nM0NdX8fuJKOvrSZWt8SB8ALABOl68CT6G260Ze5j6f2QTeQhnOw9xvrNPpll/8Pv/+X/7hnYmuxDN1pdPnbreZpRP1If7juusdWlOmNEqbY2tyX0cHY5Cz/ZTXqbfH5/n0NdJvYqMqPVxOqWOBBeAJgkHQ+eRH/DNXqYhHN88j9Ge/ZEa1mRpK3NbcGQkeg9xvrNPpnf+mOFsmQfurHqsnZ0WcgA3WQezo2fHalp9adrx+4jOs0GGyWa0WpiZUscehBeAPRbiT5EjR4mUydW6Z0tB0MeLrFaTnq3rBQMzNOGbYdT6lqI9Zu9pKR+648XypJ56CYTSJJ9OA8bWqT8T7l06pQvbjmsZlarSSa7uRCJ8ALAVGZOH03mIWq02uuV08+IeLjEKpPLWaj3d7u14vVtIccTaeUI3Pc/271Rl/YfXFwQ97f+8Prrff/hknnoJhtIsvXhbGarSSa6uWCM8ALANOmYPprMQ9TlLFRNWYna2k7o1Clf0g+XQKuJkWitHG5Pp1Zv3KtV6/fG/OynXt2iOVNHG75WMLBnsfNo9Re4/90tHv167a6EHrpGITK8LqXQbrFwdng4pxKWszWY5RLCCwBTpHP6aKYeorHGmBi1cvQOG/H4/VLTO82Gr3lP+uLWn8tZqNrRZTpnQmXch26sEBn4rGxYp6Qv92CHYIbo2NsIgCliDYS0i8B4iHAOg1aO8LCRCKNzA6Eo0foLhJhYLS5GISiw55Tb06n1W1u14vXQc559Y1tKextZJd59IrvR8gLAFNkwfdTlLNS5E0PXPZk4pkz/ccn4iLCQyvRsh0OaXjdcb73bIr8iu37MqL9YIaj3KsPh/H7p+89t0lcusUcLDGut5DZaXgCYInwnZDtOH3V7OvXXLaGL2239qE3HPu6K2DE7aiuNehZ6y3NEHvf7pbXvtkgOafaUUXrs1vNCunPMqD+jcuU5esbVJNJSZJfWi2j3aaewjNTR8gLANHYdCBlvptBDz22SX6HjKsJnrTgc0ucbRumiydVyOQuDM50KBubpyPHOkF2h/X5p1fo9umhydci1zKi/aLNpuk76EmopskvrBWut5DbCCwBT2WkgZPhMIaOWFCn6nkixwkbvejhyPLIlwy/pw/3HNSWsrsyoP6NyGe1MbcROrRd2DcvoO8ILkMPMXJPFboxmCoU/2Htv5hgQ3jLRl7ARJStJ6vt3E16uQEvFs69vi7inADu2XtgpLMM8hBcgR2XDVNlUJTJTyCFp/lX/pid+8/ekBtEahY6xI0sjznNIqjE4LqX23UQLO72PB1oq1mzcp1Ub9gS3SriqsUZjhjtpvYBtEF6AHJTONVnsIJGZQn5JhQUDkhpXES10uJyF+sol/2r1cEi6/hLjz0nlu4l23WjHvzBjrC6aXB0ck9N10peR4JLLLX0wF+EFyEF2mmaajgdeohs5etq9mjTGpcduPS/uuIp4oSPR8RnJfjfRrltdXhJ30bveU6fT3fqWyy19MB/hBchBdlmTJdEHXiDgjCwvUVlZSdzPNZopNOFTZfpgd1uwZUSSnvqvLYbXNQpUiYSORMZnJPvdRLvuzn3HY5Ynk61vud7SB/MRXoAcZIdppok+8MIDzm3XnKWGM4eFfI5Ry020GTm79h/XU69uiXrdaIHKrECY7HcT7brjqktjlieTrW92aumDPRBegBxl1TTTRLuBEnngGQWcJ19+T0vmny9ncUHclhujGTnxlukPv96zn3TRDB08SBc3jNKbvQbCphoIk92M0ijsnDGiNGYIymTrm11a+mAfaQkvPp9Py5Yt08svvyyPx6Ozzz5bCxcu1OjRow3Pb2tr0/e//3299dZbkqTZs2frnnvuUXFxcTqKB+ATmZ5mmsy4h0QeeMZBw69Wd7tOnfIl1HITHqZiXdfoeoFl9Xv7/JTTNWvy6cHWnGTG7PQ+v3Z0WdzzpehhJ946NJlqfbNDSx/sJS3hZfny5XrppZf0yCOPqLKyUosWLdJXv/pVvfbaayooKIg4//bbb1dXV5dWrFghj8ejBQsW6P7779ejjz6ajuIBsECy4x4SeeAZBw2HKl3F2n/4RNyWm9ffadbL/70r+Po1n6vRJVNHx7xuIgu9rd6wV7Mmn570INV07JIcK6BmsvWNBeVgJtPDi9fr1TPPPKO77rpLjY2NkqTHH39cF1xwgVavXq1LL7005PzNmzdr/fr1ampqUk1NjSTpgQce0E033aQ77rhDlZWVZhcRQJoZtTZ8uD/2AFIj8R54RgHnf11TJ5ezUKdO+SKChqNXy014cJEU/PMlU0cbXtflLNTFDaO0av2emPfv80u79h9PKqxZNag1k61vLCgHs5geXrZt26YTJ05o6tSpwWNOp1MTJkzQhg0bIsLLxo0bVV5eHgwukjRlyhQ5HA5t2rRJc+bMMbuIANLIqPVAkla8vi3i3ETGPcR74PUOOCPKS1Qz+jS1tZ0wXFHW75fe3+3WpDEurQwLLgEr1+7SORMqo1531uTquOElz9GzTkwyYY1BrUDiTA8vBw/27Mg6fPjwkOMVFRVqaWmJOL+1tTXi3IKCAg0dOtTw/EQNGMCG2QH5+Xkh/0b6ZbLO3Z5OHXS3q8pVbPlDzqj1INZy9F+4cKwqXH0f21bhKlaFqzik3t2eThUXDoi49nNvbNPXLp8UtUx+v3TU0xm1XBWuYt146Xg98/utMe+rdnSZ4diZEeUlhn8/jSwvSer8/oK/X6yR6/Vuenjp6OgZkR8+tmXQoEE6fvy44flG42AGDRqkrq6ulMqQl+dIaK2HXON0MrI/09Jd52+ua9ayl98NmSZ88TnGA+MzYe/R9sgBrTHO/8ynK9Py/9V3th4K1ks4n18aMjh6yMtzOHTmmGEqGxr9u7t8xpmaMLZc3/rxW4avf+bTlaoZfZpuu+YsPfnye/L5/cpzOPS/rqlTzejTDN9TVlaS1Pn9DX+/WCNX69308FJY2POXgtfrDf63JHV1damoKLKSCwsL5fV6I453dXWlPNvI5/PL42lP6b3ZKD8/T05nkTyeDnV3+6wuTk7IRJ27PZ0hD+ieacLvqqZqcEZbYHq3/JQMzIscZyLjAONwSMUDHWprO5HUNWLdW35+nrw+RQ0uUk9rRvP+Y1HLdd6kKuX7fXHLdfjox4bHHfrXfTWcOUxL5p+vVne7Kj8pe6zPTfb8/oC/X6yRjfXudBYl3JJkengJdAEdOnRIo0aNCh4/dOiQamtrI86vqqrSmjVrQo55vV4dO3asT4N1T53Kji/TTN3dPuolw9JZ59Fm0xw4fELO4sjWzHQwGt9iNFNHCu0+cqjnXGdxQdz6Cd/9OTAjKKD34OAKV7EOGLT+BAQ2IfzVnz6M2iL09t9bdPkFY+IGwGHOQsOZR1d/ribkvpzFBcHvI5GfhWTP7y/4+8UauVrvpoeX2tpaDR48WOvWrQuGF4/How8++EDXXnttxPkNDQ1avHixmpubg+vArFu3TpJUX19vdvGArGHmwl+p7B/0jwPHQwbhBmbHPHbreYZ7AU0a49Ku/cflV88uy7HWWul9PHz3594zgsLD0w1zxmta/emGrT9fvvhMDS4aGCxrLLv2H0+oHnovSudwSFc39gQrNiAE0sv08FJQUKBrr71Wixcvlsvl0siRI7Vo0SJVVVVp1qxZ6u7ultvt1pAhQ1RYWKi6ujrV19frm9/8pu677z61t7dr4cKFuvzyy5kmDcQQbR0USdra3JbwgzOVtUXeeu+AnjWYPRSYHVNRVhTRshFt9k6s60fb/Xnl2l369KihEYODf9G0VdPqT9cNc/41oNYh6dxJVfo/q3fEDS0B8U4Lbw3qvSgdGxAC6ZeWRepuv/12nTp1Svfee686OzvV0NCgn//85yooKNC+ffs0c+ZMPfLII7ryyivlcDi0bNky3X///br++us1aNCg4Aq7AGILXwfl/d1u3fW//9Lz4FRPF0bvLpZwqawtEnyPwWt5Dml3i0eLXtqc0MM73vUro7Qi+f3RNx5sOfLJGJHAoBaH9Jf3D0atg3AO9bQMRWPUGhRYlI4NCIHMSEt4yc/P11133aW77ror4rXq6mpt37495Nhpp52mpUuXpqMoQNYLtGhEPDgV2sUiRXbPpLK2SLTWEId6xpOsXLsr4Yd3vOu7nIW65nM1EYvJSdLH7ScNu80GFeTrmaatIWUwYjRgNxC2Ut1zKdm1XQCkho0ZgSwRtYvlv3sWXXt/tzuiO2PSGFfS42aMxto4HNKCeWer66QvqYe30WdJPa03taPL5PZ06lPDnZpZP1J/+H/7Q855fV2zrm6s0a/X7gp2m/3HnPHq9J6K2z0UGLgbeK9D0sW9un5iiTfWKNaqvgDMQXgBskRlWZFha4JfPUvzG3VnPHbreUlvmBdcuTYsCJ0xolRuT2dSYcjlLNTVjZEtK79e2/Pn3q044Xx+acxwZ8jg4ApXsbodxtO1A3URuMfpdSN0zoTKpPfaibfnUrRVfRn3ApiH8AJkCZezUFcbdLHkffLkjtYiksqGeSc6ToYEoZajJ+T2dKa0e/Cnhjsjjvn8MuwqCr+vQHl7f/6woUW6Yc54/aJpa0gZou1VlEp3Tqw6mzTGZbiqL+NeAPMQXoAscs6ESh061qG17x6Q9K8H99iRpTFbRJJ5iBttaLhq/V69uWFvcHBudXmJdu47rnHVpTpjRPTBr1L0bijDcTWfHI8Xiho/O1LjR5fpw/09q3oHpmYnGx5iTXmO9nmtbR0Rx1Id98KUa8AY4QXIErGm70pKukUknNvTqQ/3H4/aIhLoijrRcTLY3ZPIVGGj1prwgb9Sz/HvzDtb3pO+hFqI1n3QGixrKlOWU53ynMj6O4mEEqZcA9ERXoAsEGv6bkAq3UMB4cEoGp+/Z4Bw7/EeiXSZGJWtpGhgRNiK14oT0PTXj0JCVrJTlvsy5Tle11kioYQp10BshBcgC8SavisppPukdnRZUp9tFIyiMRownGiXSXg3TKph68ixDv3qDx9GHE+m6yaVKeS9RSt7oqGkr9cHsh3hBcgC0boqdrd49NgvNwePBRau+9RwZ8LjKFZv3JtQcInV3ZPqVOFUxqkcOPKx8UaQSrwcZmy9YFT2REOJmVs/ANmI8AJkiYsbTteb6/cGpwNfZTAFuffCdYmMo3B7OrVq/d6Y1238ZMpxrO4eM1sL4o0XGTFscNQNE82aDp2qRENJuq4PZAvCC5AhycwcSebc8DEUsxtG6aLJ1YazXnpLZBxFvM+QpNMrB4d0jfRlbE08iYwXCZ8q3XvDxGSk4z6SCSXprEfA7ggvQAZEe+gahZR4D+je75EUMYbizQ17dNHk6qj7AvUWbxxFtBVwe3vhzR36P6t3RJQzgZ6mpCQziDUwVTrZB3/495HqOjCxJBNK0nF9IBsQXoAkpLLuRrSHrtGU4kljXDEf0OHB5uKG06OOoagdXaavXFKrFQa7PwfEG0cR3lIQTe9yGm1DYMYU32jjRXbtP274XST74M/k1GRCCdA3hBcgQak+3KI9dI2m8t787xNjzhqKaGVZv9dwDEXBwDxtbW5TdXlJ1JaTRMdR9G4p2LLbraZ3mg1bVQJBIl1TfKO1Aj316hZ1eLv7FDSYmgzYC+EFSEBfHm6JriAb2CAw2oBOoxDkV88Ylzc37Am+f/zoMn3/uU0915Fx980XZ4zV5NqKpAawupyFqh1dpgvrR+rD/cf11H9tCTknz6G07qoc3FOp175BUuh3UeEqTumzmZoM2Eue1QUA7CDeOiqxBB66gT2G8j4ZQBrOIalmZGnEuYHWkUAI6i3PIV00uVqP3XqeZk8ZJTmkLR+1BV83Ci55DiUVXHoLdJuNHVmqr1wSWc7ANgTh1zNriu/0uhG65bKJEccT/S6iiVa3FWVFcns6tbW5TW5PZ8qfD8BctLzAFqze46Wv626ED9KUQleijXVu700Eo81UcXs6tWrDnqgDawMtMA5JsxpONz7pE+F1HfjzRy2eiDE635l3dsQeRume4htvn6ZURKvbdI3fAdA3hBf0e/1hj5e+rrsRHgi2NrdFBBe//tVNEW1AZ7RgY9QyFBDYE2jjtsNatWFPxCaKvYXX9bkTq/TXLQcju6v80rOvb5M+CRG9v5d0T/FN1xooRgHzrv/9F8bBAP0Q4QX9Wn8aSJnqQzl8X6BrPlejcyZUptx6YBRsog1mdajnwT508KCQlplAPVaXl6jrpC/qtOu/vH8wajn8wf+J/F7SPZsmXQGpd7m3NrcxDgbopwgv6Nf620DKZB/KRvsCBWYZmdl6EN4a4XBIn/9ksbpgS49BPT703Kae7iSHdHHDqIS2AYgm099LugMSS/QD/RfhBf1aJh4g6RxPc9DdbhgIVq7dpUW3nqfHbj3PtNaDWK0R0VpmAn8MLG6XqMDY1t4fl20PdpboB/ovwgv6tXQ/QNI9nqYqytRdf6+F5Mx8GEZrjYhomVHkTCS/v2eforf+dkD+T+p6zHCndh3wBM+Z/OlyzaivVkVZkd7f7c76BztL9AP9E+EF/V66HiCZGE/jchbqms9FbpBoRStF73osGJinh57fFLr2jKS17x0I/vmSc0araV1zyGf8vx2H9cWZ4+RyFubMg53VcIH+h3VeYAuBBdLMfIj0Ze2WZFwydbSu+VxNcB2RvrZSxFt3JNbrgXo8Y0ToejIOR2RLTNM7zXHrJx3fCwDEQ8sLclYmB2ReMnW0zplQ2edWinjdXMl0g/VuOfG0eyNWzA2sC5PN41oA2BMtL8hq8Vohoq1mmw59baWI1s0VuLd4rxt9XusnYSrayrhXf64mY/UDAImi5QVZK5FWCKvHbSQz0ynetPFkppUb1U34VOurGmsMW4ysXu0YAAgvyErJDMa1akBmsjOd4nVzJdoNFq1uHrv1PF3V2DO42O/vmc5dUjRQ0+tGBOunP6x2DAB0GyErpWswrlmb9CXbxSPF7+ZyOQt1dWNNcA2WaN080ermw/3HtXLtv2ZF9bVbCgDShZYXxGXHboJ0DMY1s9Uh1ZWDY3VzvfXegZ6NE9Uz0PaqxpqI8rk9nfpnu9ewbqTIRexS7ZYCgHQivCAmu3YTmL24ndlrwvQlXBl1c0WUT9Kv1+7SORMqDbt8pH/NJArUTbzdmlkuH0B/QXhBVP1pU8RUmDkY1+xWB7PDVbzyGe2xJElfu2yixo4sDV43VplSKbMdW+0A9H+EF0SVDd0EfRmM2/vBm45WBzPDVbzyGX2XfknO4gJJPTsoV5YVxS1TMmW2a6sdgP6P8IKocrmbIN5UYrPWPDFrplO8VpFo3+WWj9xa9Mvm4M7SgYARq0yJlNnurXYA+jfCC6LK1V11Y00lNnMXaLPFahUx+i4/e2a5fv/Xf+1dZGbAyIZWOwD9F+EFMVm9iJsVYj14zd7Hx+wxIbFaRXp/l53eU1r6679HnGNWwMjlVjsA6Wd6eOnq6tIPfvADvfHGG+rs7NQFF1yghQsX6rTTTov6nmXLlumJJ56IOL5lyxYNGEC+slqu7aqbqQevFWNCXM5Cvb/brRWvbzN83WHSfeZqqx2AzDA9Gdx3333atGmTnnjiCRUUFGjhwoX6+te/rhdeeCHqe7Zv367LLrtMd911V2jhCC6wQCYevFaNCQlcN5qrG2tMu34uttoByAxT00Fra6t++9vf6ic/+YkmT54sSVqyZIlmz56td999V2eddZbh+3bs2KG5c+eqvLzczOIAKUv3g9eqMSFG1w245nM9exmF60vXVq612gHIDFPDy6ZNmyRJ55xzTvDYmDFjVFlZqQ0bNhiGl46ODu3Zs0djx441syhAn6XzwWvVmBCj6zokLbjubJ0xojQiqDDdGUB/ZHrLS1lZmQYNGhRyvKKiQi0tLYbv2blzp3w+n9544w098MAD8nq9mjJliu68805VVFSkXJYBA9i2KSA/Py/k30i/eHVe4SrWDXPG6xdNW4NdU/8xZ7wqXMVpLVe06545qkxrN+/XM01bg0Hlf84Yq1/98cOIrq2zxg3rt60p/KxnHnVujVyv96TCy759+zRz5syor3/9619XQUFBxPFBgwapq6vL8D07d+6UJA0ZMkRLly7VkSNHtGTJEl133XV65ZVXVFSU/G+ieXkOlZWVJP0+qx051qEDRz7WiGGDNWyo+b+BO53M9Mg0r086cLTd8Du9fMaZmlZ/ulqOnNDwYSVp+c6NGF33yLGOYHCReoJK7+AS4PNL7Sf9qunn///iZz3zqHNr5Gq9JxVeKisr1dTUFPX1tWvXyuv1Rhzv6uqKGkKuuuoqXXTRRSotLQ0eGzdunBobG/WnP/1Jc+bMSaaIkiSfzy+Ppz3p91kp/LfeG+aMV+NnR5ry2fn5eXI6i+TxdKi722fKZyK2/Pw8vbP1kJa9/G7M7zRfUvVpRZLfp7a2E5krX9h1t3/kjlyB12BsTJ5DKh7oyGhZk8HPeuZR59bIxnp3OosSbklKKrwMHDhQNTU1UV/fvn27jh07Jq/XG9ICc+jQIVVVVUV9X+/gIvWEpKFDh+rgwYPJFC/EqVP2+TLdns6I33p/0bRV401eU6S722ererEzt6czGFyk9H2nZhnmLDQcg3NVY41+vXZXyKwrZ3FBv/854mc986hza+RqvZs65uXss8+Wz+fTpk2bdO6550qS/vGPf6i1tTU4+yjcD3/4Q/3hD3/Q73//ezkcDkk93VNtbW05M4iX1UjtJZHZNwfd7bb6TqNND59eN0LnTKhkujOAfsXU8FJZWalLL71U9957rx5++GEVFRVp4cKFmjJlSnCmkdfr1fHjx1VaWqqCggLNnj1bK1as0IMPPqh58+bpyJEjevjhh1VfX68LLrjAzOL1W6xGah+Jzr6pchXb7juNNj2c6c4A+hvThyk/+OCDOvfcc3Xbbbfpxhtv1BlnnKGlS5cGX9+8ebOmTZumzZs3S5ImTpyop59+Wlu3btWVV16p2267TePHj9dTTz0VbInJdoHfevM+uV0rVyN1ezq1tblNbk9nxq+dTmbcV7SF5Yw+0+Us1G3XnNUvvtNkuJyFpm+BAABmc/j90Zassq/ubp/c7v45oDAWt6czLc3zAwbkqaysRG1tJ2L2jWbrmh5m3dfW5jYt+uXmiON3z/2sakeXhRwL1Pmu5qM6cPgEXS4ZkujPOsxDnVsjG+vd5SpJeMBubk4Q76es/K03mVYFOzHzvgLde73F6wqiJQMAzEd4gaTYg4btLNZ9JduV1J+69wAgl7HzISRl76DhaPe1u8WjRS9tTroric0GAcB6tLxAUv9sVTBjkK3RfV3VWKOVa3el3JVEVxAAWIuWFwT1p1YFMwcPh98X6+oAgL0RXhCiP6zpEW2Q7aQxrpTLFn5f2dhFBgC5gm4j9DvpHjzcH7vIAACJo+UF/U4mBg/3py4yAEByaHlBv5OplhEG3gKAPdHygn6JlhEAQDSEF/Rb/WHwMACg/6HbCAAA2ArhBQAA2ArhBQAA2ArhBbZgxlYBAIDswIBd9HtmbhUAALA/Wl7Qr0XbKoAWGADIXYQX9Gvp3ioAAGA/hBf0a4GtAnpjE0UAyG2EF/RrbKIIAAjHgF30e2wVAADojfACW2CrAABAAN1GScjWtUay9b4AANmJlpcEZetaI9l6XwCA7EXLSwKyda2RbL0vAEB2I7wkIFvXGsnW+wIAZDfCSwKyda2RbL0vAEB2I7wkIFvXGsnW+wIAZDcG7CYoW9caydb7AgBkL8JLErJ1rZFsvS8AQHai2wgAANgK4QUAANgK4QUAANgK4QUAANgK4QUAANhKWsPLggUL9O1vfzvuefv27dMtt9yi+vp6nXfeeVq0aJG6u7vTWTQAAGBTaQkv3d3devTRR7Vy5cq45548eVI33nijHA6HXnrpJT3wwANauXKlnnzyyXQUDQAA2Jzp67zs2rVL99xzj/bu3asRI+LvTrxq1SodOHBAL7/8spxOp84880wdPXpUjz32mL72ta+poKDA7CICAAAbM73lZf369Ro/frxee+01VVdXxz1/48aNmjhxopxOZ/DY1KlT9fHHH2vbtm1mFw8AANic6S0vc+fOTer8gwcPqqqqKuRYRUWFJOnAgQP6zGc+k1I5BgxgLHJAfn5eyL+RftS5Naj3zKPOrZHr9Z5UeNm3b59mzpwZ9fW3335b5eXlSRWgs7MzpNVFkgYNGiRJ6urqSuqzAvLyHCorK0npvdnM6WS36Eyjzq1BvWcedW6NXK33pMJLZWWlmpqaor7ucrmSLkBhYaG8Xm/IsUBoKS4uTvrzJMnn88vjaU/pvdkoPz9PTmeRPJ4OdXf7rC5OTqDOrUG9Zx51bo1srHensyjhlqSkwsvAgQNVU1OTUqGiqaqq0o4dO0KOHTp0SFJPWErVqVPZ8WWaqbvbR71kGHVuDeo986hza+RqvVveWdbQ0KAPPvhAH3/8cfDYX//6V5WUlKi2ttbCkgEAgP4o4+HF6/Xq8OHDwa6iiy66SOXl5frGN76hbdu2ac2aNXr88cd1ww03ME0aAABEyHh42bx5s6ZNm6bNmzdL6hmc+/TTT8vn8+kLX/iC7r//fn3pS1/Sf/7nf2a6aAAAwAYcfr/fb3UhzNbd7ZPbfcLqYvQbAwbkqaysRG1tJ3Kyb9QK1Lk1qPfMo86tkY317nKVJDxg1/IxLwAAAMkgvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFshvAAAAFsZkM4PX7Bggbq7u/WDH/wg5nnLli3TE088EXF8y5YtGjAgrUUEAAA2k5Zk0N3drcWLF2vlypW64oor4p6/fft2XXbZZbrrrrtCC0dwAQAAYUxPB7t27dI999yjvXv3asSIEQm9Z8eOHZo7d67Ky8vNLg4AAMgypo95Wb9+vcaPH6/XXntN1dXVcc/v6OjQnj17NHbsWLOLAgAAspDpLS9z585N6vydO3fK5/PpjTfe0AMPPCCv16spU6bozjvvVEVFRcrlGDCAscgB+fl5If9G+lHn1qDeM486t0au13tS4WXfvn2aOXNm1NfffvvtpLt+du7cKUkaMmSIli5dqiNHjmjJkiW67rrr9Morr6ioqCipz5OkvDyHyspKkn5ftnM6k69L9A11bg3qPfOoc2vkar0nFV4qKyvV1NQU9XWXy5V0Aa666ipddNFFKi0tDR4bN26cGhsb9ac//Ulz5sxJ+jN9Pr88nvak35et8vPz5HQWyePpUHe3z+ri5ATq3BrUe+ZR59bIxnp3OosSbklKKrwMHDhQNTU1KRUqlt7BReoJSUOHDtXBgwdT/sxTp7LjyzRTd7ePeskw6twa1HvmUefWyNV6t7yz7Ic//KHmzJkjv98fPLZv3z61tbUxiBcAAETIeHjxer06fPiwvF6vJGn27Nnau3evHnzwQe3evVsbNmzQ/PnzVV9frwsuuCDTxQMAAP1cxsPL5s2bNW3aNG3evFmSNHHiRD399NPaunWrrrzySt12220aP368nnrqKTkcjkwXDwAA9HMOf+/+mizR3e2T233C6mL0GwMG5KmsrERtbSdysm/UCtS5Naj3zKPOrZGN9e5ylSQ8YNfyMS8AAADJILwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbIbwAAABbcfj9fr/VhTCb3++Xz5d1t9Un+fl56u72WV2MnEKdW4N6zzzq3BrZVu95eQ45HI6Ezs3K8AIAALIX3UYAAMBWCC8AAMBWCC8AAMBWCC8AAMBWCC8AAMBWCC8AAMBWCC8AAMBWCC8AAMBWCC8AAMBWCC8AAMBWCC8AAMBWCC8AAMBWCC85pKWlRXfccYfOP/98NTQ06MYbb9TOnTutLlbOWLBggb797W9bXYys5PP5tHTpUl1wwQWqq6vTDTfcoObmZquLlVOWL1+uefPmWV2MrHfs2DF973vf0/Tp01VfX6+5c+dq48aNVhcr4wgvOcLr9ermm2/W0aNH9ZOf/EQvvviihgwZouuvv15ut9vq4mW17u5uPfroo1q5cqXVRclay5cv10svvaTvf//7+tWvfiWHw6GvfvWr8nq9VhctJ6xYsUJLly61uhg54Y477tB7772nJUuWaOXKlZo4caJuvPFG7dq1y+qiZRThJUds3LhRO3bs0GOPPaZJkyZp3Lhxeuyxx9Te3q4//vGPVhcva+3atUtz587Vb3/7W40YMcLq4mQlr9erZ555RvPnz1djY6Nqa2v1+OOPq7W1VatXr7a6eFmttbVVN910k3784x9rzJgxVhcn6zU3N+vPf/6zFi5cqMmTJ+uMM87QggULVFlZqddee83q4mUU4SVHjBs3Tj/96U9VWVkZctzv9+v48eMWlSr7rV+/XuPHj9drr72m6upqq4uTlbZt26YTJ05o6tSpwWNOp1MTJkzQhg0bLCxZ9tuyZYtKS0v16quvqq6uzuriZL2ysjL99Kc/1aRJk4LHHA5HTv49PsDqAiAzysvL1djYGHLsueeeU1dXl84//3yLSpX95s6da3URst7BgwclScOHDw85XlFRoZaWFiuKlDNmzJihGTNmWF2MnOF0OiP+Hn/99de1Z88eTZs2zaJSWYPwkiX27dunmTNnRn397bffVnl5efDPb775ph5//HHNmzdPtbW1mShi1km2zpEeHR0dkqSCgoKQ44MGDcq530aRWzZt2qTvfOc7mjlzZs6FSMJLlqisrFRTU1PU110uV/C/f/nLX+rBBx/UnDlzdM8992SieFkpmTpH+hQWFkrqGfsS+G9J6urqUlFRkVXFAtJqzZo1uvPOO1VXV6clS5ZYXZyMI7xkiYEDB6qmpibueYsXL9bPfvYzzZs3TwsWLJDD4chA6bJTonWO9Ap0Fx06dEijRo0KHj906BCtishKL7zwgh566CHNmjVLixcvjmh1zAUM2M0hixYt0s9+9jPdfffduvfeewkuyAq1tbUaPHiw1q1bFzzm8Xj0wQcfaPLkyRaWDDDfiy++qAcffFBf/vKX9aMf/Sgng4tEy0vOWLdunZ5++mnNmzdP//7v/67Dhw8HXysuLlZJSYmFpQNSV1BQoGuvvVaLFy+Wy+XSyJEjtWjRIlVVVWnWrFlWFw8wze7du/Xwww9r1qxZuuWWW3T06NHga4WFhRoyZIiFpcsswkuOCKwB8Pzzz+v5558Pee22227T/PnzrSgWYIrbb79dp06d0r333qvOzk41NDTo5z//ec7+VorstGrVKp08eVKrV6+OWMPoiiuu0A9+8AOLSpZ5Dr/f77e6EAAAAIlizAsAALAVwgsAALAVwgsAALAVwgsAALAVwgsAALAVwgsAALAVwgsAALAVwgsAALAVwgsAALAVwgsAALAVwgsAALAVwgsAALCV/w+PViUx8YKHVAAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rng = np.random.RandomState(1)\n",
"X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n",
"plt.plot(X[:, 0], X[:, 1],'.')\n",
"plt.axis('equal');"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(200, 2)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By eye, it is clear that there is a nearly linear relationship between the x and y variables.\n",
"This is reminiscent of the linear regression data we explored in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), but the problem setting here is slightly different: rather than attempting to *predict* the y values from the x values, the unsupervised learning problem attempts to learn about the *relationship* between the x and y values.\n",
"\n",
"In principal component analysis, this relationship is quantified by finding a list of the *principal axes* in the data, and using those axes to describe the dataset.\n",
"Using Scikit-Learn's ``PCA`` estimator, we can compute this as follows:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"PCA() In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org. "
],
"text/plain": [
"PCA()"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import sklearn.decomposition\n",
"PCA = sklearn.decomposition.PCA\n",
"pca = PCA()\n",
"pca.fit(X)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The fit learns some quantities from the data, most importantly the \"components\" and \"explained variance\":"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 0.94446029 0.32862557]\n",
" [-0.32862557 0.94446029]]\n"
]
}
],
"source": [
"print(pca.components_)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.7625315 0.0184779]\n"
]
}
],
"source": [
"print(pca.explained_variance_)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To see what these numbers mean, let's visualize them as vectors over the input data, using the \"components\" to define the direction of the vector, and the \"explained variance\" to define the squared-length of the vector:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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xpN+XXrP0edXxeam3hOuFZFI6hp6c1VOpBVimxuE9uaYKMAvV73Ec89hjj7Bz5w6+//2dDAz01z2mvb2dt799G9u3X8mpp56Oqi5OlZX29gyaNrfnlpEXIYQQK1ocx/QP13C9kLa8NXG7aWiYRlLyvn+4xqYefVVMIcVxzFNPPcnOnTu49dbv8fLLu+sek8lkufTSt7F9+5WcffZ5GMbyCnYSXoQQQqxojhdSrPpkUjNf8jIpnWLVx/FCUtbKvSy++OIL7Ny5g507d/Dss8/U3W9ZFhdeeBHbt1/JhRdeRCqVakAr52blfkpCCCEEEEYxYRRhzHKmjq6phFFAGK24VRQHrMWiaRpnn30u27ZdyaWXvo18vqUBrZw/CS9CCCFWNE1V0NRkjYtpaHX3B2GyeFdTV8aU0fBwYaIWy0MP/XTGWiynnno627ZdydvffgWdnZ0NaOWhkfAihBBiRbNNjXzaYLjkzhheKrWAtpyFbdbf1yzK5TJ3333nRC0W3/frHnP88SewbduVbNv2TjZsOKwBrVw4El6EEEKsaIqi0NWWouoGDBddMikdXVMJwtd2G3W1pZpusa7rutx55x3s2PHv3HPPD6lWq3WPed3rjpyoxXL00a9vQCsXh4QXIYQQK17aNji8JzepzkuApqq05aymqvMyXovl1lu/xw9+cBsjIyN1j1m7dh1XXLGdy962nWOPOwFdU5t6VGkmEl6EEEKsCmnbYFOP3nQVdqMo4ucPP8z3b/0eP7jj1gPWYnnTiSczOOpSrPr89yujK7IYn4QXIYQQTeNQy/sritLw7dBzfQ9PPfUk//7df+PWW2/h1Vderrs/m01qsWzb9lotlvpifDp+EDFccqm6QdMV45uNhBchhBBNYSWU9z/Qe3jppRcnarE888zTdT9vmhZbTjuHiy69gj9837swVH2iwu5qKsYn4UUIIcSytxJGFGZ7D//94h7+6Vt38uD9P+DXv5q5FsvJp57JRZdczrnnX0w2l2e04lGsRbSnX9sGvZqK8TV364UQQiyp6VMeWW3xA8PkEYXWnIXnh9TcEE1VaM1ZjJSW/4jC9FGRYnGEO++9k3vu+j6PP/qzGWuxHHfCybz1kndw0cXvoL1jzZT7simD0ZJHWlcxxs4DWk3F+CS8CCGEmJOZpjzachZmyjrwDx+E8aBUcXwGRx0MXWHfUIWKExBFMaqqkLF1sk0wouB4IX1Dozz28x/x43tu5+cP/QdBUF+L5Y1vPJ7t23+biy65nCo5WrPmjIFsfKt3GMWMl65ZTcX4luenLIQQYlmZbcqjUHJ4fu8IHVkDS1+47biTg1LF8djTXwZiUoZBS9ZE1xWCIKZU8am6AVnbWJYjCq7rcv/9P+Lfd/w7995zF65Tq3vMYRsPZ+vFl3P6OZdywZknk00Z1NyAXXtH9xtEDNOYEkRWQzG+cRJehBBC7Nf+FoKmbIOqGxD6ARvWZBZk2qY+KFm88GqRSs1Hyavk4hhQ0TSwLJXhURfPC1FYHuElDEMeeuin7Ny5gzvuuI3R0ZG6x3R19XDhxe/grZdczrFvPAE/iHC8aCKMHCiIlGs+h3dksE2NMEze90otxjcTCS9CCCH260ALQfNpk4GhMk7ePuRpm5mCkuMGaJpC2kxGe4oVj1zGoFjxcdyA0YqLrmo8t3eEjV152vPWkl+g4zjm8ccfZefOHXz/+zvp7++re0y+pZUzz72Ed1y+nTdvPhVVVSfumz4qcqAgkk7p9HRk8R0PJoW2lVKM70AkvAghhNivMIoJwpAoVqi5AaqqYOrqREAwNJUwjBdk2mamoBTFkLEMHDXAcUIKJYeyExAGEUEYAgpeFPHM7hFeGahy1Po8G7tzpKzFL0j39NNPsXPnDm65ZQcvv/xS3f3pdIZLL30b27dfyZZTz+KVIQfXCwnCGJ14v6Mi+wsiazszZFMGw45X/5pNWoxvPiS8CCGE2C/XCxkcdQkLVVRVRVUhYxu05ywyaRM/jNA0ZUEWgs60Y0ZTFWxLxzY1yqrHnoEKphGSsw3CAHRdxTZ11nakKdd8dveWqDgBaUvHD+MFrwnz0ksvcuut32Pnzh08/fRTdfebpskFF7yV7duvZOvWi0mn0xP3GYYxr1GR2YKIMcNU0mTLoRjfYlq570wIIcQhqzo+fcNVoigiiiCf0QnCmGLVw/FCNmgqbgT5jLkgC0Fn2jFjGhoZW6dU8cmmTLK2R3d7CscLUVQFhWTXkWlo5BSFcs1j974i6ZTBEWvzmMah14Tp6+vl+9+/hZ07d/D444/V3a+qKmeddQ7bt/82l176NlpaWmd8noMZFVnpQeRgLEpvRFHEjTfeyHe/+12KxSInnXQS1157LZs2bZrx8Tt37uRP//RP626/5557Zv0ZIYQQi2vy+pPDe3K8OlSlXA1IWRq5VLKY9KV9RY47qpM1uZm39M7XTAtVFQXacxaOF9I7VMHQk4MGR8seUZQs2s1nTABUFYoVH8tQ0cbqnyiKclBVZkdGhrnjjtvYuXMHDz30U6IoqnvMli2nsn37lbz97dvo6uqa03uUMHLoFqX3brrpJv71X/+Vz3/+83R3d/OlL32JP/iDP+COO+7ANM26xz/77LOccsopXH/99VNub29vX4zmCSGEmIPJ609MQ2NdR5pCyU3qrHgxmqaiayrru3LocTRRpv5QjC9UrTg+fUNVbCsJHaoCaUunI5+iWPMZrXi4QUR7zqIlY04EHdeL8IKQjhabKKpfh3OgKrOVSoW7776TnTt38OMf34fv19diOe64N7Ft25VcccV2Nm6UL9iNsODhxfM8vvnNb/Lxj3+cc845B4Avf/nLnHXWWdx7771cdtlldT/z3HPPccwxx9DZ2bnQzRFCiFXlUA8unGz6+hPb0llr6nh+8vwK4IcRtqkRuIceXCZTFYVi1ePVQgAka2w2dmU4/og29g5U6R2uYJsGGVvH0Cft2nF9TF3D1BX8kLp1ODNVmfU8j/vv/xG33PLv3H33XVSr1br2HHHE69i27Uq2bbuSN7zhmAV9r2L+Fjy8PPPMM1QqFU477bSJ2/L5PG984xt59NFHZwwvzz77LBdddNFCN0UIIVaVhT64cKb1J4oC1tjaFs8PiUgqtgYL+B7Ga7xs7M4lYcwPcdyQKE7WlmzszhLFMS/3lShXfVpyJmEYU/MCbEPHUBUqtWSr9fQaKeNVZuMo5L4f/5Tv3/o9fnjX7TPWYunpWcvll29n+/YrefObN6+o3TrNbsHDS29vLwBr166dcntXVxf79u2re3yhUGBwcJBHH32Ub3/724yMjHDiiSfysY99jCOOOGKhmyeEECvSQh9cGMcxcRxjaArDRZeu9vriZpVawJq2FClLx63Vb9mdr9mK4dmWDlkmrVfJcXhPDgV4/tVR+oZqpG2NfMYkm9LpHarh+CHtOYvJTY7jmMcfe4yf3n8H//GjHzA40F/Xhra2Nt72tivYvv1KTjvtLWha81ejXYkWPLzUaknp4+lrWyzLYnR0tO7xzz33HJCcmvmFL3yBarXKTTfdxLve9S5uv/121qxZU/czc6FPGkZc7cYXrY3/Uyw+6fPGWK39HscxQ0UXP4xY05aauF3Xkwq4haLDUMkll5nbotqK49NfqFGselQcn6GSw2jVY31nhmzKJAgjyjWfdEpn7VhV3YXo85obUHED8llzxufLZ00qbkAQxeSzFscfabKuK0PvUI2q46MqCrqucsT6FmpugBtEGEbM7hd3cdcdt3DPD29j3ysv1z1vKpXmLWdv5a2XXM6VV1xGWz5zyO9lsa3W3/VxCx5ebNsGkjnE8X+H5HyHVCpV9/jTTjuNRx55hJaWlonb/v7v/57zzjuPW265hfe///3zboOqKrS1Lf9fvqWWz9f3v1hc0ueNsdr6ver4xGqFtV15rBnqf1i2ieMG2GnrgKMv5ZrP0GAVN4bOjizrdJXuNR4v9xUZGHVRVI1s2uTwjgw9HVmyqeT5FqLP9apHKlWlLW+jzhCyoihmuOSQy6fIpZMvyO3tWY7cGFNzA4Iwwg8iDF3luV3Pc/N3bua2nd/j+V3P1D2XYZqce95W3vaOd3LehReRSqUZGK0RaQatremmmSJabb/r4xY8vIxPF/X397Nx48aJ2/v7+znmmJkXOU0OLgDpdJoNGzbQ11dfXnkuoiimWKxfcLVaaZpKPp+iWKwRhgu7qE7MTPq8MVZrv5drPiOjNVpyJq4z80V/tOwxVKjgpmYPL3Ec89K+EoWSQ3vexnU8XEAFNnVm6CtU0RToabVIWTq+41H0gwXr85obUKt5xGE443k+nh/ieCGlYo3AnboLqOL4PPXcbm6/fSc/uvs2nv6vJ+p+XlVVfuvkt3DRpZfz1oveRi6fXHv8APxSDSUM2buvSFpXl/1W5pX4u57Pp+Y8krTgn84xxxxDNpvl4YcfnggvxWKRp556ine/+911j7/55pv527/9Wx544IGJkZpyucxLL73ElVdeedDtWIgteytNGC7MVkYxd9LnjbHa+j0e2znjusGsF/3xx+2vX2puwHDJJWVqM14QWzJmspMpjMcOA3xtx04QhJSr/iHtctJVhYylM1xyp6x5GVcse7TlLHRVwR8LMkOFAt+/7Va+f+st/OaJX8xYi2XzSVu48p2/zQVb38aIZ9GaTabPpr9HhaSvXC/EaJLpmNX2uz5uwcOLaZq8+93v5rrrrqO9vZ3169fzpS99iZ6eHrZu3UoYhhQKBXK5HLZtc9555/GVr3yFP/mTP+GDH/wgjuNw/fXX097ezrZt2xa6eUIIseIc6ATi6Yf+zWam0vyTzbTNGJKRn5f2lRguuYe0y2mupyIPDY9yy623c/vtt/DYww8QBvV7nY56/bFcdMnlnHLmJRz7+iPZ1JNLRm32jk7ZPTXZ+E6khTjmQCyuRRkX+9CHPkQQBHzyk5/EcRy2bNnCN77xDUzTZO/evVxwwQV8/vOfZ/v27axdu5Z/+qd/4rrrruOqq64ijmPOOOMM/vmf/3nKmhkhhBAzm+tF/0AjITNtjZ5spot7xUnWyBRKDilTO+RdTrMdRpi1FZ7+9UNc/7lbuOeeu3Bq9UsD1nRv4LSzL+HcC9/OKZtPwLaSmjTjRekWKuSJxlPiOD70Y0CXmTCMKBQqjW7GsqHrKm1tGYaHK6tyeLERpM8bY7X3+6HWeUnWvBTpH66Rz5p1p0cPF13achabenIoikIcx+wdqODGYKnUTcNMf/x8xHFMpebx858/xO23JbVYRkZG6h7X1t7JCadeyBnnXErXYceQTRmYukY+a7K2I0Mcx4xWPI7e0Eo2ZdRtKZ8e8g7m3KNGWIm/6+3tmcateRFCCNEYB3Po32Q1N8DxQgZGa+wdqJC2NXJpk3zGIAypG8FJjg/w6OzI4jr1dV4OVIp/JnEc88tfPs6OHf/O7bfvpL+/fuNGLt/CyW/Zytnnv41j33QSAyPuWJVdhZoXkrZ1Kk6A54coClNGi2Yb2dnfyc5i+ZHwIoQQK8h8D/0bP06gVPN5ZaBMHMVs7M5SqvoUqz69hSojZZ2j1ufZ2D11VCKMkoW7hq7izvDcs62RmckzzzzNzp3f5ZZbvsfu3S/W3Z9OZ7hw6yWcdMZFvOWMs+kd9smmxo8tCKk4PhnbwPVjFJSx9TtxUvBu2lTQoYY80XgSXoQQYpUan2YarXj0DlWougHd7WnabYt1ayzWjJ1hVKx4WKZeF4pUBcIoYrTsEnghmsqUAHCgBbC7d7/Erbd+j1tu2cHTTz9Zd79hmJz2lnM58/zLOPvcrRyxvoO9A1UUJUZVfYKx4JTPmHhBSKnsoWgKYRwRxVCseOQz5ozrfeRk5+Ymn5wQQqxCk9d+6LqCoirk0yalSjLNs64jnZTlB3RNoTRt+qfq+PQVqgwXXfaNONhaMnrRnrMmfm6mBbB9fX3cdtst3HLLDh5//NG6dqmqysmnnMFbL7mccy+4mHy+FUjWz4yWPXKpZCt1xjYoVj0M3cQyNNa0pOj1q6gqlCo++YxJd3uabpkKWpEkvAghmkYcx0s+tL+QpzQvxuseTPumnyFUcwPiGGw7+dlSxadQcllr6ihK/fTP5ODT1ZGi6kUMDleoOj41J6CzzZ6yRqZYHOUHP7id733vuzz00E9mrMVyzHFv5sRT38pbzrmYTYetnxKCIFk/U6oFrF+ToeaFeH6EqiiMlj1MXcULItrzFilbJ2MbHLE2R1vOlqmgFUrCixCiaSz1hWihT2le6Nc92PYlC219MmNrRlRVQVUZm4ZRSFnaxIJXy9SmTP9MDz6aptLRZhAHEcWqx3DZJYphQ7vBbx65n7++Yyc//vG9eF79gt5jjnkjZ51/GWeeexlrNxxG71CVlKVRrHozjP4kAWp8R1D/cA11RGW4WKPiBFiGRnuLRWdLShbergISXoQQTeHTn/5zvv/97/Hnf/5Ztm1756K/3kKf0rzQr3so7ZtejM7U1SnTMJqmEHnxxEjL5Omf6cEHIG3prF2TJlOC55/8Gf9+9+088rMfUa3Wl6zYtOlwtm+/kiuuuJJU64aJarquF6JpKgrJ9FWx6o2N/iSjQZMDVMrS2dSj092eJggjgjBC11R0TZWFt6uEhBchxLLneR433XQDcRzzv//379PW1sa5556/aK83fXRhnGlomIbGcNGlf7jGph59QS+U+3tdQ1fpL9TY3VtiU3eWvkNo3/RidIqi0J6zJrY+G6oKY4txh4vulC3S04NPGIb84mc/5ZYd/8aP7v0BxdGRutfr7u7hiiu2s23blfzWb52EoijU3IBde0cnQpBpaGRsnVLFJ6erpEydiuPjBRGWodWtn5EFt6ubfPJCiGVv796XGa+nGccx73737/Ctb/1/XHjhRYvyejONLkx2MPVLDuV1HTegUHIZLbu8WqgyXHYo10J62meuQn6g9s1Uada2dNZ1pCmUXPoKNdKWThxRV/9EUxVUReHXv/olP773du67+3YGB+prsbS0tPKOd1zBtm1XcvrpZ6BpU6vWznQUQdbWGS17FEYdMmmdIIhx3IDqPKoEi9VBwosQ4pAt9qLW3bt3T/n/nufxnve8i69//Z+55JLLFux1xs10YY3jGC+IiMamUoIwnFP9kkN9XccNeHWoihckQURRQjRVpVipoqtg6tqUha1w4Poqk48TGBqpgQJxDIoCpqZwxNoc6zszZFPmlM/y2Wef4ZZbvst3d/w7e/fsrnte205x2pkX8va3b+d3tr8Ny6o/XHHc5NGfKIoplFwqTkAQRlQdn5FKshDXD1KsabFlHYuYQsKLEOKQLMWi1pdfrr9Q+r7Pe997NV/96jd4xzsW9hDX6dMq4yMfFccniiCKIjRNY1N3SDa1cBfU6a8bx8lF3QtC8mmTIIjQNJWUpdOStaiOtWvttLA4lwMG07ZBLmWwa88IfcM1gjBE1zS621Jsfn0nna1pIOn78VosTz31X3XPo+sGZ55zAWeedyknbD6brjWtHN6Tw7L23y/joz+9hSpVN8D3I1KWRsa2yGdM9g1WyKeTargdLbJrSEwl4UUIcdCWalHrTOEFIAgC3v/+/x9hGLJt25X7fY4DjQ5Nvl9VIJfSGSl7RFH82siHqaNrCiMlD0WJ6BtOdscsVEibPp3jBREVxydlJn+qa25ILmOQTRmUaz6eF05ZFzJuLgcMDo7U+K8XC3hBxMbuDIam4ocRpWrAQ798jt5dP+OeH36fxx57pO5nVVXl9NPP5IxzL+P1J56NnWvBqfn4sc5cD2RWFIXOVpsXXi1SKDp0tqVQNQU/iKl5AV3tadKmTrnm09Gy/A7pbdQWepGQ8CKEOChLuah1pvBy7LFv5OmnnyKKIv6f/+cjXHLJ29AME73qUXMDNAVcP5ooEV+suJRqwYyjQzONHpm6QhRH7O6t4ocRbTmLMIwpVwNSdrI+pOaGC7pwd/rp0KoKQRBjajGlio9hqLTnLFQ1WWBbdQNGSx5Oa4Axj1OkoyjiuT0jVGo+6zszAJTLRR756T389Mc/4De//AVxXF+L5aSTtrB9+5W84x3bybW08+K+IlU3oLMji+f5xGFE1Ql5qbc0p+CqqirZtImmgReERB6oKuTT5sT7XIy1RYeqUVvoxWuWz2+DEKKpLNWi1jiOeemll4Dk4q6qKmEYMjo6ynvf+36+8Y2vsXHj4ewruFS9KqlUleHRKq4bYhgqYRgzOOqgawrr1qRpzZpTRoe6WlP0j9TqRo8qtQA/SLbhappKuRagqgq5jDFRQG0xLq6TDw4cHHWoeQF+GJFNGXTkbSxz/Dwfna5WmziK8YPk5OQDHTA4PlowVHTYN1QlZUQ8eP+d/OTHd/DLR35C4Pt1P3PEkW/gvK3v4O1v38ZvvekNpG2DOI7Z3VvC8yN6OjLkczbFUkwYRlimPufgGkZJXZk1LVn8MCaK4iknWUdRPOezkebjUEZNGrWFXkwl4UUIcVBmWlw62XwO5ZvN+Dfc3WMjL2u61nL00W/gZw/ez6uvvsLll7+T973/A1TCNCNlj3zWxLaSi+dIySWXNjANFYhRUBkcdScWuJqGRmHU4bm9I9iGRvukqYnx0aN9g8mJw5u6s8QoaKoytrV44d7jTMYPDsyldUpVl8ERF1NX6R+uMlxyyWdNMlayG+eoDa10t6WIYvZ7IR7vy6HRCv/xHz/mrh/s5Nlf/xTXqdU9tqNrPW/cfD7/43d+hy0nvXkizI2PqCiKsiDBdXyNTxDGU6a9xs1l7c58HcqoSaO20It6El6EEAdl+uLS6Q71wjP5G+6GwzYxMjzEKaedyRvfdAo/e/B+AHbu/C7/58OfIhwrdKaqCoURhyiOWdeZoTDqMlKu0dORwdDVurL3hqGyd6DCEetyM7YhmzYYGHEIophcuv7CNtt73N83+7l+66+5AX3DDinToCUX47g+jhdRrnkoQDpl0dli1530PJNSxeG2H/6Ie+/6Pg8+8MMZa7G0tXdyxrmXcMIpW2ntPhpFUzjm9Z0oilJ3ce5osRckuM60ZXuyuazdmY9DHTVp1BZ6UU96VwhxUBbzwjP9G+7f3vRtfvn4Lzj5lDMA+NsvXoPnudx22638z9//f8ikTQA8P6LkeBMXIMtQGSiGEzVippe9V1Dww2jGgBXH8djtMUNFh2zKZHrGmOk97u+bPTCnb/2T33/PmjR2SWXXK8lWYlPX8MIIQ4tJmRr9IzXStl530Y3jmF/96pfccssObrllBwMz1GJJZfK8+ZTzecu5l/KWt5xJFCv0FqqMlF3WtqTJ2lMvEeMX55asORFcdf3gg+v0NT6ZlI4+j7U787EQoyZLMdoo5kbCixDioCzmhWf6N9xcvoVzznutIN1bzrqA//jRnQwNDfLYow9y4QUXAhDGMVEYo2vJegndSF7b85PRoell72NiDE2dcrGJ4zgpTT/qUKr61LyQqOThuMOsW5MmmzJnfY/7+2ZfKDljL5CM+Ji6ShTHFIpO3bf+ye8/jqHqhuRsk87W1NhW7ZgojmhvtanWgikX3WeffYadO7/Lzp3f48UXX6jrW9tOcfZ5b+WMcy8l03MCNT8mbel4QYzrBwyM1GjPWmzszqKq6pSfHb8465o6EVxTM4xUzCe4Tl7jk4S64IBrdw7GQoyaLPZoo5g7CS9CiIM2/cIThEkdlLSt092WPuih8wN9w73o0iv4jx/dCcAD993BOeecn4QTRUHVFAI/QlVAJTlk0PVDshiEYbIgdPzi4vsRa1ptfD/ZWeO4AfsKVfb2l/GCiDiO6WyxWduRZrjk8nJfmTUtyQV18sU1jmNqbrImpFjx6GpL4QcRVSf5Fm4aKi+8WiSOYzpabIZK4cTi1Iyt4wUR/cM1NnZruH5ywGHN9cmmUnh+SMUJSNs6up6EiSiOqdSSBa6ZlM5zz7/I975zL7ffdsustVhOP+McLrp0G2eds5VUOqnhMlJyeGlfid7hGv3DNUxdo7PF5oh1eVpz9duTxy/OuqZOBNdC0cGyTaIoTtp6EMF1fI3PYm49XohRk6We5hKzk/AihDgk4xee4ZJDXyE54dfxAl4ZrFCqegf17flA33BPOf0c0pkc1UqJh35yD8MjFbo785iGSs42ebVUJJsycLyI7rY0cQTFqkcYxLTkkimm4aKLbels7M7RP1Kjd7DKaNVlcNQlDCNSZlKzRFVVyk7Axu4sxYpPPmOyqSc3EcwKxRp9hRrDJZfe4Sq6ptA/XCWMkzDkBUmQKlU9wigmCGPWtNjoukIQJFugFQWCIML1Q1w/oub69BVqOF5IPmMko0j6axfyMIwpjQ6y8yff40d3385//vqxuj5SFIXTTj+Ty962jWM3n0t3Z8eUvoxjSFkGG3uytOYsjlibJ5c2GCm5jFbqdx3B1Iuzoigc3pNjqOjiuAGj5eTU6IMdMTmYs4rms2toIUZNlnKaS+yfhBchxCGruQG9hWQ9QT5jYOjqIW0fPdA33CDSOe+Ci/nBbd+lUi7xxGM/4dQztpLPmrS32PQOlnh1oEI+Y9LdmiKIIvYNVomJ0VUV14+mXGRTlsavS0MUKx5eEGIaGtmUTj5jYhoapYrPcNmjI2/j+tHEwYK7e0s8/+oorheha1CuehBDzQsJoohsSidlGtRcn2LZI2bsYhvH6KjoukJOVxkcqdFbqKKqsKY1RTZl43gBA2NrNMIoSs75cUo8/NN7uf++23nq1w8TRfW1WN78Wydx/ta3c+pZl9DavgZNUSjXfAqjLj1rkhGX1yoGB4yWXVoyFlEUY5s6PR06jl+a08U5bRvkMiZ22mKoUCGO4iUr1jbfXUMLNWqyVNNcYv8kvAghDslibB+dyzfc//E7/4Mf3PZdAH7xwJ1cfPHbqLgBihbQlrdIWzqGoeIGyYXt9Ye10pI1MQ297lu6qqpkU8lF6dXBCmnbQNPUsTN/4omFvm3ZZOqhVPMZHKnxcl8JBYWejhQ1N2R3X5k4jsmkDGpehELyOjExXhhhmzpBGFKqeJiTSt47XkjVCciOhSWA7rY0YQT7+od58omf8suf3cNvfvnTGWuxHHnUG/id3/4dLrn0CiKrY9KamyREVt2A4ZJLHMcYhkLfiIPvRWgatGUt8lmTfYUaIxWP129omdfFWVEU0raBmzIIgvowtRgOZtfQQo6aLMU0l9g/CS9CiEOyWNtHD/QN9/UbzmfNmk4GBwf40Y/u5oZMzPquVnL5FKViekqF3QNdXMIoJoxjDEOl5oeUnQBVUVCVpBhcLp1M3bhBiKooFEYdihUPTVNJW0lBNV1TsE2dYtmlFHnJtJUfEkxaZ+MHEaqiUKr55LMG5thFt1TzyaZ19LEpi8D3eezhn3DXHTv56QP34NSqdW1eu/4wzjn/bbz10is4/4yTSVk6u3tLDI9tGx9nGho9HWlcP6R/pMpw2aVS9bFtnZSV9ElYiolj6Cv41NyAE4/sYFNPbllenA8lLC/kqMnBTHOJhSM9L4Q4JIu5ffRA33Df8Y4r+OY3/xHXdbnrrh/wu7/7bnJpk8D1CYKIlKUe4BUSSbCIGSnVkp08UUw2rRNGMeWaR6nikUkZFCsaXa3JIlrb0hiteBNrUaI4mZoIbI3Bokva1ogjBS8IqboBqqriuMlaIENTMDSFtpxN1Q1QFMinDX7zxMPcf+/t/OjeH8xYi6W9o5Ozz7+Mcy98G8e9aTMtGXPioltzg1lDpOMGE+tpUqaOZejU3IBXB6v0KQ5r16Tpbk+hqyZ9hRq7rFFef1jrspwCOdSwLKMmK4OEFyHEIVns7aP7+4a7bdtv881v/iMAO3fu4Hd/993zfv44jomjiHLVo1B0WdueZrDoUnFDNEXBC2IGCjUsS0PXVLK2gRdEtGZNVDVZdKvryciKZWqoikWpGlDzYlQ1xvVDPC8EIhQF4iimEoTsHawkhyuO7uY/7r2dJ35xL8ND/XXty+bynHXuxbz7XVdx3jnn4IfMeNGdLUSOn0w9vtNqtOxhWzoKMVnbIIxjRsouqqrQ0WKTtpNgs1wrxS5EWJZRk+Ynn54Q4pA0cvvoli2nsGHDYezdu4cHHrifwcEB2toyc/rZOI4ndkgNl1wGRipUnZCX+8q0ZA3iSKFvuIrjhpiGSkfOZF1HGj+IGBytkbI0MrZOqeKT01UMXSVlanheQFvOJIhiOltThGHMaOhh6TqWDoqq4A/t4dGf/ohf/eIehvr31rXNtlOcfe5beesll/OGN51Gd0eeTWNl+We5Zs8aIsdPpjY0BcePiOJk1KcSMfG4IIySHUMll2zaIJs2lm2lWKm1IkDCixCr1qEcTjdZI7ePqqrKFVe8kxtv/AphGHLbbbfy0Y9++IA/V3X8KTuFIiKGSx6GrjBSTha36pqCoamsXZchnzaIYkiN7UwaKbvsG6qyqTtZF1Kq+KQsjWzKYHDUIYohmzJQgMFiDd8PCWpDPPnoj/j1w/eyb8+uujbpusHJp57NRZdeztnnbgXNolz1sSydzlb7gP03W4hMpsHA80IMFdJ5k3ItII5idEMljmP8AAxDY6Tq0d5ik7b0sTUhy69SrNRaESDhRYhV6VAOp5tJI7ePbtt2JTfe+BUAvve97x4wvIzvVBnfKdSeN3lloEK5GpBOaazvzDBccilVA1qyyUnOmqqM7VpSUBSFtWvSvNxXYbTisabFolj1KVV9ylWfbNogn85g6Bq79+zlwbvvYNev72fPC/9Z1xZFUXj9cSfzrv/5P7j8HVfgxTb9Iw6vFmq4vodlaOi6ysCIM7GrZybjQTSdMhguuxRGHbJpA01VqDo+oyUH09BIjS0+dv2IkXKIqiqoqkIUJwXmdEWlJW2OBdrlOXohtVYESHgRYtU51MPpZtOohZDHH/8mjj769eza9Rw///nP2LNnD9ls+4yPHd+pMr5TKGWpjJZdVFWlq91Oap/UArK2Ts0NiaOkuJypa+Szr21jzqZM1rSE5DMmQZiU11disAyNwKnyy4d+wP333c6vf/nzGWuxHH3MCZx1/mWccuZFKFYrZ52wljUtKSo1j+GySy5jsS6tk7ENgnD/n830IOoHMcHYIuFKzR/7PKDqBmhqstajpz2NH4SMlD2CMMa2VCxDJZcySaeMRRm9WKiRPpBaK0LCixCrymLUZJlsoRdCzuWCpygK27ZdyRe/+FcA/Nu//Rvvfe//mfH5xneqjO8UiuOYmhcmtVhilZoXMlrx6cgnRwn4YUD/cMSGrgztOWviYMYgjCYuoIqiMDg8ys777+LH99zGo794AN/36l574+FHc9b5l3HmeZexdv1GgKS0vqGTtnTiOGZgxIEY1o0VkwMw1dk/m9mC6NBISKHokM+YrOvMoKkKe/rL7OkrU3GSENTRYjNc8gijCFM3qDghph5QGHFoGQsBCxU8F3qkD2TX0Gon4UWIVWSxarIshrle8OI45tK3bZsIL9/5zndmDS/jO1VSpoaqKnhBlJTeNxVAoSNn0TdcY6joUnY9XD8gnTKnPEccQ6HokrYU7v/xvfzgjlu4884fUK1W6l5v7brD+K3TtnLsSRdwwgknkLZ0NC2p91LzAqIo5rCuDClLn/dnM1sQNXSVWHntMMrx07A3decwDY1de0bZ9coIpqbRmjXRNQXXj0CBIEyqAx/dunCjF4s10geya2g1k09diFVkMWuyLKS5XvDGA05grOHoNxzPrmf/i1/+8pf855NPc+wb3lA3cqMqoKlJUbmMrTM06iTbncdOog6jGJSkHw7vygMxjh9RcwP2DlbI2To///lD/OyBu3j85/dSKo7Utb29o5OtF72dt15yOcefsJlS1eO/Xxkl9EOqcQwoQIyqKGzoyrKxOxm9me9nM1vYGd9d1JazqDgBnh9imRq2pXN4T46MbfDsy8NomkJ7zkZVFSxdJZcxydgGlZpPuebT0XLgRcIHstgjfWL1kvAixCrS6G2mc5kGmusFr7M1ZndfeSLgXHLZFex6NjlR+Z/+5WY+9tE/pVzzp4zc5FI6hqZQdQLac1ayU6jm4/sB2UwSZoIwZu2aFJ2tacoVnzCO6N3zLP96z+388uf3MjpcX4sllc5y9nkX89ZLtnHSltNJ2ebEFFM2ZbKuI0s+bVB1Q/wwxNA0OvIW3e3piVGH+X42s4Wd8d1FKVul4oRTgqiiKORSBpmUwWGdGbLppFaNqasTn4OisGCjb8000ieai/y2CLGKNHKb6VyngeZywRuteDheOCXgbL34Hfzdlz9HHMfcc9f32Xr5+2jLWWTTxsTIzcjY4YgANTekI2/hByEv95UYGK0SRzHrOjO0ZW1efH4Xjzz4Qx756V3s3fNSXTsM0+LY3zqL406+kLYNJ9DRmqelO8srQzUytk97zsIyNSqOj6oq9HSksU2dKGbG4GabGrmUTt9wjXzGRFMVTEObCEHTP5vZwk6ygwhcL5o4lmAyNwiTEJMxsc36Pl7I0bdmGekTzUfCixCrSKO2mc5n3cNcLniO5+L6Ia3Z19ajdPesY/PJp/H4oz9n78sv8F//9RsuPv8tExf2ySM3KUsjiiJe6itTLLtoqkrK1Bkc2Md/PHILj//sHna/8Ezda6uazvG/9RaOP/lCjj/pbLKZLCMlh/5Rh4GRKi0Zg9RY4bpixcMyVEbKPmlLZ6+RnHLd1ZaacZShNlbCf3DUYe9AmUzKIJc2yKcNwpC6z2a2IGrqKhnb4NWBCus6M3Uh1XFDsnZSg2YmCzn61uiRPrFyLUp4iaKIG2+8ke9+97sUi0VOOukkrr32WjZt2jTj44eHh/nLv/xLfvKTnwBw8cUX84lPfIJ0Oj3j44UQB2+xt5lOnxqyDJW+QpVi2SVl61TdADvWsAyNtrxVt+5hLhc8RVGSE5L1qWcXXXTpFTz+6M8B+OXP72bruacTx+D5r7UnbesMDNcoOx4jJY/BoX5+8/D9/PqRe9i96zd1r6coCm8+6TROOGUrb3jz2Vh2Hk1Xydo6I2UXFIXuNpveYYfeQpVMSqc1Z7F7X4U4hsO6shzWlUHT1FkXqU4Odxu7M5SqSfjpG6oxUnI5an0LG7un/sz+gqiKQiZloCoKfhBOCaj5jElr1qTqhFgzjLws5OibFJQTi0WJ43jBx+tuvPFGbr75Zj7/+c/T3d3Nl770Jfbs2cMdd9yBaZp1j7/66qtxXZdrr72WYrHINddcw5YtW/jCF75wUK8fhhGFQv3K/9VK11Xa2jIMD1eW7Mj61a4Z+nwh626Mm2lqKI4jXtw3SsUJ8YIIiEmbOl1tKdZ2ZFBVBceLOHpDy8QumplORx43XHRJ2zqulxyOOPmiWCqNcNE5byYIAjo6e7h554PUvJCKk+zsUVUFRYl59vlenv7VA/zm4Xt57slHiaKw7nWOPe5ELr50Gxde9DbybZ38etcgrhugagopKwkR+woVXC/ED0IcL0JVY3Jpi3zGJApjcmmTYza10TJphGi46NKWsybK/c/0fuM4ntgJVSx7dLWlOHxtfsbPZ7bpuGzKqFvzMz5NB0wZCZs++jafHUAH+l2fPup2KK8lXtMMf2Pmq709CflzseAjL57n8c1vfpOPf/zjnHPOOQB8+ctf5qyzzuLee+/lsssum/L4J554gkceeYQ777yTI488EoDPfOYzvO997+MjH/kI3d3dC91EIVaMQwkgC73NdKapoVLV46mXCrzcV6azNZVcxOOkYNru/jKeH3FYd5YwiibWPcxlamtDZ4aBEafuG31razunn3kuP/2P+xga6OWBnz7Ikcf81liYcHn4ofu5+85beeY3PyMM/Lr30L3+CI4/+ULeeNIFnH7y8RyxNp+cLF31yacN+r0ARVXRNIWRssfgiEMcJ6PNhqFiaBpRHBEEERs6M6iqWjc6NH2R6kxrfBRFwTJeW9tSqgUHdUpyR4s96+/HUhV5k4JyYjEseHh55plnqFQqnHbaaRO35fN53vjGN/Loo4/WhZfHHnuMzs7OieACcMopp6AoCo8//jiXXnrpQjdRiBVhMQp/HayZdgjFcUyp6uOHMZqSXMCNsW9VLbpJ2QkYKjnYpkZrzp6y7mEuFzxFUeoCThiFnHHeZfz0P+4D4L4f3kphpMivfnE3v3rkfpxata7t7Z3r+K3Tt3LSWy5mw8ajkhGPMGK47JEbdUhZBu15m662NI8928/gSI0ojBgcqeL6IaauJiNAuo4XBCgoBFGyvTqXserWc0xfpLqYpyTvL6AuZZE3KSgnFtqCh5fe3l4A1q5dO+X2rq4u9u3bV/f4vr6+useapklra+uMj58rXZ/b0NNqMD4MN9fhOHHoFrvPK47PnoEyjheSTRnoukoQRIxWPdwg5PC1eTJLEGDGR34qjk+h7JLPGBPv2fVCyrUAXVNpy5tU3YAwZmIkIm3r1NyAgVGH9V05smljysUsn7XIZUxqbkDVDSBOfiZlJWtj8lmLIzeo9BdqFKsejhcQxhEnnX4+hmnhey6PPPB9Hnng1rp2Z/LtvO74sznu5AtoX/cGQMHRVfYOVjF1lcO6snS3pzlqQyv5jDmxJqPi+PzS9ekr1Kg6YdLHSkw2bRIEEbZlYBkqKgojZZeu9gwpe2oNkzAKMQ0Ny0zOLbLMZOoripPFttNNf/xCM2ZYizIf8/ldP9TXEq9Z7X/XFzy81Go1gLq1LZZlMTo6OuPjZ1oHY1kWruseVBtUVaGtLXNQP7uS5fOpRjdh1VmMPo/jmKG9I2imweGd+Sn3rQEGRms4Ycz61vSifrMt13x6B8uMlj1KVY/BoothaGSyBmlLp+L4GIZG2jZoyVq8OljBj2JShp4UjAsjyk5AS9rkiMPaaG+v/2+2XPMpVHxGq0mAUVBoy5tsWttCLm3SGse0tWao1DxioL9QIZe1ef0b3siT//kE8NpohZ3OcvLpF/KmU9/Kmg3H8sqQi66p+EFMTEwQxXhBTBxFtLbaHNuWYeP61imjWG9OWQSKwoO/fpUIhXzWoOYE1NwATdNoz1vksyb9hRqoCuu787RM+x0YGK2xYW2Gtd3JGpbWOKbqRwyMOuRz9b8v0x+/XMnfl8ZYrf2+4OHFtm0gWfsy/u8AruuSStV3sm3beF79OSCu6x70bqMoiikW64eHVytNU8nnUxSLNcJwZSzsWu4Ws89rbsDe3iK2qVEs1eruV8KQvfuKpHV1TmtaDmbdTLnm8dyekWRqJJ2UmI+jiD19RQojNdauySQ7XfyQmusThCoZW0dXFUplhyiKiaMYTYHWjE614rDH9ae8fsXxeWlfkdGyh+eHOH6I70c8G4Q8/cIgrz+sjTCMKVY9wjAmiCJGyy6vO6ydq65+P5/8k/8DisKpb7mQs7dezrEnnM5IJcSPIgpFB9cNqEYxhqGhqwp+GKOS1Fbp7a/Q11miVsnj1qb+fVrbatPVYvNyzaNYTL5gGWOHPBqqSuAFmKpCytDYN1AiCgIMXSMII8o1H9vUsLUUIyOv/Y2ydYXQ83npFScZSRtb4zPb45cT+fvSGCux3/P5VOMW7I5PAfX397Nx48aJ2/v7+znmmGPqHt/T08N999035TbP8xgZGTmkxborZfX1QgrDSPpliS1Gn7teiOeHpC2t7o9WHMd4fkix4jJadtFVZb9B5GDWzVRqHr/+7yH6hmukbZ1ixSNt6Zi6iuvH1JyAVwfLdLakMA2FKILRkkdnq01Hi00QxoRRTKXmE8cxRPDCK0WiOJ54/c5WO1mQO+pS9QK8ICRl6qRMjSDUeXWgwqv9VY5YlxwwmB47aHGk5NI3VOHs8y7m/7vjCYaLDm0tOaqOz3A1oG+4im3qDAw7xMTomooyNuoShkl468jbqAqMjLqUq359P8QxGUunNWNSdgMyKYOsrZNPm0QojJZc/CCgLW9Sqfq8WPPJpc1kBCqd1HmxdG3K74WlaxzWma37LGZ7/HIkf18aY7X2+4KHl2OOOYZsNsvDDz88EV6KxSJPPfUU7373u+sev2XLFq677jp27949UQfm4YcfBmDz5s0L3Twhmt5sdVAcN6BQchkpu1RqAWEYs6YlxWFdGTKp+qnZgzkwr+r4PLd3lL7hKvm0iW1pBGFMqeajjNVTGa14+IWIYjk5tdlxfbwgIowi/LE/sjUn2T1jGiqqopKyNAxdnXj94bKL70e4QRJc8umk/X4QJXVMNBgacfCCDIaeVKFNmTotWYvhkkvfUNKesqOwd2gI29BIWTqqouB6AYoCpq5j2xrhWJiyTYU4AsNIApQbJFNV0+ux7BuqEscx+axJKmXgeRE1N8TzHcIwZrTisabV5piNrWiqykjJQ9dVNnSmacvNfl6QLGoVYu4WPLyYpsm73/1urrvuOtrb21m/fj1f+tKX6OnpYevWrYRhSKFQIJfLYds2J554Ips3b+aP//iP+dSnPkW1WuXaa6/liiuukG3SQsxgpsJfjhvw6lCVctVjtOJhaCojZZeBkRqvDlY44ciOKdtmVQX6CtV5HZg3vqOo5oakbYOUrQEKhq5g6CaDIzUqTgAkU7dxDKap09magrFRjuFyMgWTsXXW2DYpU6dnTXpKIbm0rTM46jBccjD0pPJtMprkURsbdRoueyjEFIouPe3piUWvuqqyb7iC7wWsX5Mhl4lwvJAgChkYddBVsEydjhabQtHF0jXSWSMZAYohiGIMTUtGZJSpw9fj79/zIzb15Cb6W1cVPD/k1aEaURizcW2W129oIW0ngau7Q2e46FKs+LTlbPZHTkkWYm4W5b+SD33oQwRBwCc/+Ukcx2HLli184xvfwDRN9u7dywUXXMDnP/95tm/fjqIo3HjjjXz605/mPe95D5ZlTVTYFULUm14HJW1rDI46jJYdilUfBehotcnYOkGQXHAfe7aPTd05/JCkpkoYUyi59LTPfDGd6cC88XokuXSyGDcIYnR9fFQgJggjan7Axs4sXhCzbk2alKmPhSGHtK1PnFSsKrCnv0LK0iZGjKYUkgOKVQ9TS3bhjJRc4jgJbpoCIyQBabjkUHV9rPEKrQroqoJLjOsH+GHEmhYLJ4hwvRDLUHH9ANswKJZ9XD8il05GslxvbCouiomimJasSXpSkJhcj8U0NNZ1pCmYGuWaT8UJyKZ8LEPj9Ye10JKxcb2pVX3lAEIhFs6i/FekaRof//jH+fjHP15334YNG3j22Wen3NbR0cENN9ywGE0RYkWaXAdlcNShf6RGzQkwdY21HemJERldV2jJmry4r0gQxBx9WAumYTJa8ShWXHQVTF3DnnZBnam2yHg9kpaMScbyKBRdMumkBH1MjBeEGKpK1QlZ02rTkrFeO1k5beB4EdmUScrSKdd8ojgmDCP2FWr4fkTK0tB1hSBIQsngSI0oSkaDgjCiNWsSx+pYVdpk2zRAseLTmrXx/JAgjFjbmaVvoEwQJtNTmZRBa8Yk1Z4cTVAoJjuKsimdQtmlXPMwNA1VhSCKkhOZLZ2NXdkpQWN6PRbb0llranhBRLmaLDY2tGTqad9QZUoYS1nJqJAcQCjEwpCvAEI0qfE1Etm0QdXxKRka2ZSOoU+tpVF1fBQUUAElWcA7vj6kOjbqsXba2oqZDswbX2tTqnqUawH9IzWCwQqWqaLrWhIC1KQeSXvuteAC9WFIUxU0RaF/xMH3I3KZ19aVRHFE1QshVtDUmHItqW5bdQJqXohtqKTsZLFyR97E9cOJKacwijGAw7qzpEwNXUvWjaTt5DTnMIpZ25GmUHLpABw/JAhjiCNsSyOOFda0WLz+sDY2duem9MlMa40mKuGmkvo1vh/SP+JAzJQwNlpKTrP2/ABSUlFWiEMl4UWIJqYoChnbwLZ0ilWPOE6mNzRVmVgAW3YC0rYGsUI0Fh5MQyNj63hjBea8IJooRw8zH5hnm8lJzL/67wGCIMYPQ8pOQFBKzuBxvJDDurJ0tpgoqkLNDVBVBVNX68KQPbZGpVB06MhPnboqVjyqtYANXRn8MKSv4OAFIbqm4bshpqbQljXx/BhNU/CDZCFwTEzV8clkLNpzJrqqkEubjJbdsUCXPL6rNY2pa/QP19h8dBpDVyjWAmpuUvDv2I2tbOrJk7KSInqTD5ic7ZBB09AghvLY6Fd+0llGuq6g6QpKrDBa9va7aHeyxTh7SoiVQsKLEE3ONjVsQ53YZquQFGpMmckoiOOFtGUNTENBHQsPigLtuWTkZbTk4bQGGNPOD+pqS01ZrDs06vDfr4zQX6ihKgpBGBHGMQpgGRqmruH7Ic+/WiRjG2hjUzEZ20BFoacjPRGGFEWhvSU5EqDiBqTR0TQFxw0ZLDpkbJ2WnEXNDVjfpRIEMZ6fhKQY6GxJzkkarXiMln0qjp8s/m3PkMmYxHHMy/1lRkouhaLD4KiDoSms78omIzGWQVc75NJmsj26JVlE3N2eoi1nU3MDdveWZjzscLYzl9pyFjUvIBjbVaVpCmEYU/OSQLOmxaJUSwraKYqy31CynI5+EGI5kvAiRJOruQF+GKNrCqWqR2eLTRwnIxjeaIQ6Nl2UTZlTys/blk5Xq00cxfhBssV3pgPzqo5PX6HKb/57iF17R1EVBScIiaMIy9SJomSXTkeLSbUWsm+wSk9HmrUdJp4f8epAhUzK4KgNLVMu0rmUQU9Hlprr4QUhkQf+WD2X7o4UqqJi6hrZlEHNDUhZOlEYU3VD1rSmyKQMogh62jOsW5NJdgip8Py+Mg8/1YfvRxi6iqoqVKoBjgqFokM2ZdHTkaaz1UYdW4cyOUQcaAt5V2tq0mnNr525lB6bDgqjiKobEHmgqpBPm7TnLEwjGe15qbc0Vutm5lByMFvYhVhtJLwI0cTGt++qisIJR3aw65VRRqoehqqi6yr6WNG6ZCoJXD/CMtSJEBGGcNSGVrrbUkQxdSMB4xfSgZEqrwyVcP1kFKFa89E1lbSl0prXcf2IUiXAMlQ68ikcL2K04mGZOus6k2q75Zo/sdsIkhGjrlabQhEyaYMoivGDiN5CFU1RqXoB+bRJW9ZkX6GG4yULgg1DJYpjhosutqVzWFd24mLu+AEjRWfsnCEVBYUYlbYWi1zKIJu2aMkYbOzOoqr1lTxnOmASpm4hL9d8NnZncf1oSvBxvGQLuWUooCgTi3VNPenvYsVlcNQBoD1vzRhKUpZ+wNefvoVdiNVIwosQTWz69t3jD9foG6lRrvl4XojjBpRrQRImygPk0yZrWmxac8noTD5j0j3LVEQcx+zuLfFyX4mhUYc9fRXcIMTQQpIVJjFl10PXk/U1wzWflkx2Yhv3ujUZMraBaWj4QVi3VXjylu9qLUjeg21gjY1QtLfYtOcsbEtnXYdCoeTSV6iRtnTiiLoRojiO2dNfoewEHH1YK1EUE8UxqpLUoilWfVQlWUfi+hEpqz68TO7PmYxvIU9+fupjJtffmRw8xtu2b7CKril0t6cnFjNPDyVdbak5vb5suRarnfz2C9HEwigmCEOieGyBrKaysStLqZqMmEQRpGyN9WuylKoevYUae/rL5DMmm7rztGbrK++OGy45PP/qKJ4fMjRaI4gidC2phxIBoZrsINJVFdvS8f2ItK2haSqWqZOxjYn6KzNtvYapW77Hp2HStk57i03a1FHV10YwbEPj8J4sna02tpUc/piaXoel7GIZyS6feNprpUwd1w+T06dn2bI8fTv0dLO9D6ivvzN5Tcxw0cUPIzZ2Z5lpwGQ8lGTTxkG/vhCriYQXIZbAfHaOzOexrhcyOOoSFqqoqoqqQtoycP1kNMPUVbJjheI0TaWjxSYMkvL6mZRO1Ql4qbdUt44ijmP6CjUcNwRi3CBC11XCIMayNBw3JI4jPB9KVY+q45OyDFoyJo4bkssYU3bkzLT1etxMZfGjKGJgxJmyriRt68QxFEo+4ahbt14kHKvqa5kqYRCiTuszTVPwayGKoszYDpj96IW5vI/x9zI9jGmqSj5jEpMsEJ7JeChJ2nDwry/EaiHhRYhFNtvOkZkWjNbcYL+7TCYHG9cL6S1UiMYKq+UzOkEYT+yuUZVk15FtahQrLjU3IJsyUGKo+SFVN2DtmgzVWlC3jsLxQipOgGmoFIoOxDG2ruISgaJgGDFVJ4A4xg8jLF2luz3FaMWjuy1N1k62GWtqckrzTFuvJ5upLH7aNqa8177h6n4XsWqqgm1paFHMQMUlO20qLAxjPD+mJWPO2I44jonjZOFzoehOmd4Zd6D3Md7u6WEsjmP++5XiAUNJ2tJn3Y4919cXYjWQ8CLEHB1M3Y3KLDtHegtVXni1SDZtYujJt31TV6i6AQrKAXe5BGEy4hJFET3tSdG1cjUgZWmkx+qTeGFEZ96i5oYTYWa8RD4oBEGy9XimdRRhFKOqkE0ZvDJQHnucieYFVN0Q4iQYmZqKAti2TsY28cba60465VYButpSU7Zez8V4oInjmMGRqYtY4zjZMm1bGsWyR1+hyqaeHC0Zi6IbYOkapYpPytImtiwPjK2j2dCZ2e/W5KrjMzjqMFJ2WbcmTTZlzrqF/EBtn/y7M5dQkrL0Waee5vP6Qqx0El6EmIODqbsRxzH9hfqdI1EUj5Wpd9A0WNOSxQ8iXtpXwvFD3nBY68QFbnxBZ+9Qld5CldaMSTZtEMUKYaFKFEGh5E7UbKk4AY7ro45Vc625yWnNqpKU04+i5EIZxtCas1BVZcZ1FJqqoGsa+YyBaWr4ZVDjZFeQH0S4PqRNg3zWQIljutpSHH9EO3v6y8liVjtZKBvH8SFfaKcvon3tLCSfKIIoihit+uQzFl3tKbSyT7mc7Oqp+SFBLcLzQ9rzNie8rqPuhO3pW5Nz6RRpW2PfYJWX+8qsaUk+4+kLhOdjf+thpoeS2aaeDuX1hVhpJLwIcQAHW3ej5gYUq96UnSPJmg0X34/obLOpOAGlqo+iKigq6Ko6Vq5fn5iyiGNw/ZDRssf6zgymoY1Vr1XJZ3TK1YCqG9DdlqJQdBkMQixTpTqcBJLu1jQoEEWgawqapuJ5AQpgaMqM6yjGd84UiiGHdWYZLbv4QUTViUFRyNkGmZSBqirkUho9HWlqfoht6eSzGj3t6YkaK6auMlLyDnqL7+RFtOOnZ3tj9WD0sQq7g6MOu3uLHHdkB0duaCX0AoaLDjUvKQjXkjHZ0JmpCy6zbY3OZyxyaZP+Qi1Z3Dy2jflQgth8QslMU09SYVeI10h4EWI/5lL3Y7aLchjFhGFM2nptmsDzk7UkqpaclFwouwRhjKYmBwyuyVtUnADPDyd26nh+iOOHmMZr5f1VVUkOEgxjUpbGcMmlXPXoG04OOQxjUBXQGDuRGcaKtmmEcUxH3k4WsIYx1RnWUUweKcilTHo6MhSKNYIgxnVdTFND0yCXMWnLmeQyFp4fkU0ZuH6yK2nytMmhbPEdX0Tr+SGFkosXhOQnLXxVFYWWrIUXRPQP11jf08Lha3OsabEPeOHf39ZoRVFozVmUqn4ynacceoCYTyiZaR2QECIh/2WIZa+RZ7zMte7HTBdlTVUmzt4ZnwYKoxjHDXC8AMcLMXWNXFonDKHm1RgoJpVnp5/mHARJ8Bgv72/qKhnboFj1MHWVwdFa8pqKQkeLxVDRIZMySdvJYYOlqofjRaSsmM62FJ0tNkEYURh1aMlaE1MW0/t6Y1eGV1SF4bLHwHCNcs1DGaubkkkZ5GydrG2SGtuBNH40wfTdMIeyxXd8FKivUJ04BmCy2tjupracRbHiTZTfn8uFf39box03YLDoMDDi4IchGdtckBL9EkqEOHTyX5BY1hp9xsuh1P1IWTr5tMnAcJVMajyEhFRqPn6YnH2TtQ1MXUMxYE3eZl+hiqYmoybjNFXB80OyKX2ivL+iKLSPnf3zykCFmheOPZdKxQ1JWwamoRNHMemURk97iqGii6knYeqVgSq6pnJYV25i2mt6X/tB0t4wSs7nac/bdLTYeF5I1fVx3IgwcCcq3pYqHjVdo7sjXbco9VC2+I6PAg0VHYplnzUtKnGcjGrV3BDDUGnPWRi6ilubX0CabWv0+PRUzQmwjWRqR1UUKdEvxDIh4UUsW8vhjJdDqfuhKArZtMGuPR4v9RaTgmtxzGCxhopCZ3uKXMacGEXKZ0yGRmvJtFEQYRrx2IJOn5aMhaVPnZqyLZ01LTYv95WwdRXPC9E1haytk8uYlCoexYqXjIioyaGMazuyY9ufXXQtmYaqOD6OF7BvqIrnR2RSOmEEAyMVRsseQRSSsQw2dueougE1xyMmWStjju2UMjSFUtUHAo5Ylz+oLcb7k7YNjlibo1B0qHohqh8l620yxkQVXs8P0bRk1CeY4/NOroo7/vlOXpek6Qr5tIllJKN9UqJfiOVBwotYlg5lrclCmuniNtn+Lsrlmk//cDWp80HMSNmn5vqMlD1sXSUMbLSxqZowjHG9iO6ODEEQTZq6UWnP22zsztE/UqvbqVJ1AjryNt3tGQZHa1hGUswNFJSMieMF9BZqpEyNXCY5Qdn1ItK2jmWovNRbpq9QQ9WSirSbenIYusrgkEM0tovohVeLWHqMoau06AbDJQddU1jTkqLihgyXPUxD58gNLRRGHXoLVVKWjqEv7BbftpzNUetb6BtOFtGO15AZf8pKLWBNW4qUpePWvDk950y7gMIwOaQyDCPSdhKOJrdbSvQL0XjyX55Ylg5lrcl8HGg9zXy2uE5/3t7BMqNljzCOSdsGLRmbIAxJ2zXKFZ+y41OqeeiaNjGKkE3pECsc1p3F0LUpbUrbet1Olfa8ja6r5NMmYRRRqvgklVWSoJdLm/QPO0RxMqIQxjGmmYzSuEFEPm3g+CGeF6Eq8OpQlY4Wa2JtSRhFKEoyOlN1AnQtCVu6rtKSs8hnoFT1WbcmTUvGoiNv0VtwKFX9sVGQhdviqyjJuUA1L5wYjYvj5DDHQwlI03cBVWrJ71V3m017zsae9vslJfqFaDwJL2JZOpS1JnM11/U0B1N3w/FCRkounh/iBSEtmfHiahquH6Gh4IXJVNT6NdmJUYSRkktbzqQ1a9VdhGfaqWIZKi/3lRkeq/XieOGU4mxVN7moH9aZoas9TdrSGSq6uH6yYyeOYyquD7FCW96iUHTxvCBZk6MmazxK1YAgTIrOpSyNIIgxDCXZeq0qpGyd1NjW7mzKZE1LzMbuHLapL/gC6wN9FpmDDEiT+7bi+Bi6Si6tY5n1v39Sol+IxpPwIpalQz1j5kDmu55mvnU3wrFCdI4fTtkdoygK+YyJ64dUSyFVJ6m3oijJluYDjR7MtFNlfGSo5oasabEoVn1KYyMIuqayriPDus4M+YyVvK772o6dMIzRNQ3fD+kr1Kh5yfOEUYQSJ+cY2aZK1YmwDI2aE1KseuTSJqr62k6f8c8oCCN0TSNjG4s2pbJYNVDG+9Y2NcpVn+GSO2N4kRL9QjSehBexLB3KWpMDOdj1NPPZ4qqpCgoKvh+RmtZGy9Boy1qEUYznh4yUPTKpuVVwnWmaa8poRMVDV1VyKYO1HWk2rMlQqibrbCCp7jterA6S8JEyVSqOR7Hsj50yHVGpxoxUfNo1DU1VyaRMgjA5SmCw6FCt+dRqAZalj60JSdq3VBf2xdxufLBThUKIpSPhRSxLi3kBWYr1NLap0ZY3eTYICUIdQ5/aziiCte1psrbB4evyZGzjgKMHB5rm6myNcccK2hmKioJCuRaQS5vUvJDhoouuKygKOG5IEMZj7VKwdR2yyTRTFINuamQjxurAmGzsyVJzQkYrLllbJ4higihmfYuFaWhJ8b0VdGGXEv1CLG8SXsSydagXkNkW4y7FehpFUdi0toWnXxhkYLhGV1tq4oDA8doktqmzpjVFR94+4MX+QNNcXa0p+scOL2zNmhi6OuOhjqMVjziKGXU8OlpSpEyVwaJHPmuQiw1eHapABIEXk0vr2KaanKMUxuTSBh0tNpm0QbUasKbFIohgtOKtyAu7lOgXYvmS8CKWtYO9gOxvlGKx19OMy6VNTjyqkyeeHWCo6GAaGrquYlsalqGRz5jk0iYVJ9jv+zrQNFdh1OG5vSPYhkZ7i113/3DRpVzz2didxfUjWnMWz7w0TGG0RozCSMWlJWNiaCrdrWksU6N/uEbK1shYSRXfdWsyZGwDQ1eTAxGt5Dwj29SJYlbshV2q4QqxPMl/lWLZm+8F5ECjFJu6s4u2nma6ztYUp76xiz39FYpVjziOSZk6ppFUyn1lsHLAysEHmuYyDJW9AxWOWJeb8f7xaTDXj5LdRTWfloyJbalUaj5xCYZLLhnbwDI1QjeZfhqpuLRmLGwrWYAbxzG9hSp9hSppW2dPv0ZLxqRrrLaKEEIsFfmLI1aUuSzGHRhx6Gy1D6p2y8FMIWRSJm/YaEz8rOdPrWZ7oJ1OB5rmUlDww6ROi+uHRFE8cZqzoigT02BBGDE06uB6IT1r0sRxjOtH2JbBSMlltOpSKMK6jjQ9HSn6hmq8Oliho9WmXPMYGnUpVjzyWZPDujJoqirl8oUQDSHhRexXIw9FPBhzXYzb3Z6e13qaQz1jaXz0KI5jBkdqeH40551OB5rmiomJYtg3VCUmWQysqpAZqw6rTvx8yOCog64ruF6IaWjYpsba9jRDow6+H2HqMRExqqKSTul06yniMOa5PaNYhsa6zsxEOf7xdku5fCHEUpPwImbV6EMRD8Z8FuNmU3NbT7OQZywdzE6nA20bL1d9iCOGiy5d7Wl0TSEIY4pVD8cLSZs6rTmT3qEqewbKpEwNTVPJ2PpEuEnbBqoSU6z5lKoBKUtjTUuKtqxJ1Q148dUSm3qytM+wuFjK5Qshlpr8pREzWg6HIh6M+S7GPdB6moU+Y+lgdjrtb9t4uepTc0O62tKEUYzjhqQsDV1TSJvJcQJeWscwFIIgxjZUUpaGgkKpkgSOtpyJrinJ7iPbYP2aDLalT0w7hREoatJPM73H2XZnNduonRCieUh4EXWWy6GIB2OhituNX3grjs/gqEMuPXNQm++ow8HudJpt23gmZRBE0Jo1iKKYQsml4gREXrLupbMtRaXmEQQxXe0pwjgZkcmnTXK6SrGcrGXxg5Cq49PVliI/6aRrSKalDE2ddev4TG1uxlE7IUTzkPAi6izVoYiLYSGK202+8FYcj95Cja5Wm478oR/SdyjhaqZt40EYUXVHMcZGSdaaOp7/2v1hGFEoudhWMuoxfv5RseqhKTBScRktu4RRjK6qtGZNXC+c8j59P2JNq43vRzO+p+ltbtZROyFE81heVx6xLCxFEbfFdCjF7aZfeE3DYqTkMlLycP2IdR3pKRf2+daEOdRwNX2aq+YGU0ZyFAWsScFnpBwAr91mWzrrOtLs7i2y65UilVpATExH3sY0VPoKNfwwZkNnBl1TqdQCbEtnY3eO/pHaAdvczKN2QojmIeFF1FmqIm6L6WCK28104Y3jmJasRbHq4fvJKMbasROU4eBqwoyHq75ClaGiix+GGJpGR96iuz09r1GJA43kOG5I1jaY/K6jOKJQ8ohj6Gq3URWVno40jhvieCHDpaQeTU97ZkrgS9v6AQNhM4/aCSGah/z1EHUW81DEpTTf4nYzXXgnT7VUHZ/RSkxb1kLTlIU7yyc++J890EhOPmPSmjWpOiGWqVNzfJ56aYRXBsukLYPRckBr1kBXVTpaDIplD11XyaUNNnZnac1aE+9tLoGw2UfthBDNQcKLqLNaT9Wd7cI7PtUyOOowMOrM6xTomUyemspnjIlziEbKHjUvnPeakANNkwG81Fuid7DKUMlhaNTB0FQUwDZUQGGw6NDZYpO2dWp+CICh149UHSgQroRROyHE8rfg4cV1Xf76r/+aH/7whziOw1lnncW1115LR0fHrD9z44038nd/93d1tz/55JPos3yDE4trNZ6qu78Lr23pdLba2KbO4WtzczoFeiaLtSbkQKMim7qz/Lo0RLnqoSigqiq2qZLPWGPnFQUUKx7teZsgiFAUBU1V5r3deaWM2gkhlrcFTwaf+tSnePzxx/m7v/s7TNPk2muv5Y/+6I/4l3/5l1l/5tlnn+Xyyy/n4x//+NTGSXBpqNV2qu6BLrxVJ2RNiz2nU6Bns5hrQvY3KqKqKtmUwVEbWnh1sELVTaZuDD05Y8kyNGpuQKnqTxziGIYhu3ur89ruvFpH7YQQS2tB00FfXx+33nor//AP/8DJJ58MwPXXX8/FF1/Mr371K9785jfP+HPPPfccV111FZ2dnQvZHLEAVtOpuktx4W3UmpAwignjmLaclRzQOFrD9UPKjo9taMm5R0WXvuEarVmTkbLLI8/USJsG7S3WvLY7r8ZROyHE0lrQq9Ljjz8OwKmnnjpx2xFHHEF3dzePPvrojOGlVqvx8ssvc9RRRy1kU5qOVCNdHhbywhvHMTU3wPXCic+0UWtCxl83COOJBcjgoSoKFSdgcKRGzQvZ2J3ljYe3U6r6FEZdaFFojZKidfOZ2lpto3ZCiKW14CMvbW1tWJY15fauri727ds348/s2rWLKIr44Q9/yGc+8xk8z+OUU07hYx/7GF1dXQfdFn1sOLwZVByf/kKNYtUjDGM0TSGfNulqT5FZgG+pmqZO+afYv3zWIpcxD+nC6/ghz+8d4dX+Er4fTXymnW02bTmLQskhNcNnWxtbd5JNGwt6oc9qxsTrtudtNmgqhZJDueLhuCG6rnDs2jaOPbwNXdMYKXv0rElTdQJGqz7p1GvtyWdNKm5AEMWkrP2vXTFmCGiLSX7Xl570eWOs9n6fV3jZu3cvF1xwwaz3/9Ef/RGmadbdblkWruvO+DO7du0CIJfLccMNNzA4OMj111/P7/3e77Fz505SqdR8mgiAqiq0tWXm/XONUK75DA1WcWPo7MhO7DwpVj2Gyj6trRmyqYUZZs/n59+XYv7KNZ+XB0eougEdbZkpn2mhErB+bQuaqVN1A/JpE0NT8cPk/s6OLEduaF2wz3wyM2Xx/N6kXa0tada0ZSgUHap+zPqePG84rI10yqDi+FiWQy5jkklHOH6IZZvYZvLnIopihksOuXyKXLr+v/flQH7Xl570eWOs1n6fV3jp7u7mzjvvnPX+Bx54AM/z6m53XXfWEPLOd76TCy+8kJaWlonbjj76aM455xzuv/9+Lr300vk0EUj+uBaL1Xn/3FKL45iX9pUmvg27jsd4xLNUGBgqE/rJ+oJD+RauaSr5fIpisUYYzlziXczNgab3xj/TkYrHxrUtVCourpP0+eTPtLPVJvSC5P+Pj7ZlTDqyBr7jMezU/3e0EDqyxpTX9YOQlK6yts0mCAKKpWSay3V94ihE01TKVZ+RYo302Nonz0+K2ZWKNQLXX5R2Hiz5XV960ueNsRL7PZ9PzXkkaV7hxTAMjjzyyFnvf/bZZxkZGcHzvCkjMP39/fT09Mz6c5ODCyQhqbW1ld7e3vk0b4ogWP4fZs0NGC65pExtxl++lJmsL1iTtxdk0WwYRk3RL8vVXA4bHP9Mx3cThVE05bOd/Jlu6MzgeHZdEFrMz8jStSmv6wchulZGgYl2jrelVPGxLQ2IIY4n7i+WPdpyFrq6uG09FPK7vvSkzxtjtfb7gk6WnXTSSURRNLFwF+CFF16gr69vYvfRdH/zN3/DpZdeShy/trti7969DA8Pr/hFvK/tPJn5Y0h2nkRLVo10fIFpueZTc4Mpn0kzW4j3NV5YbrjkYpvJAYa2qTJccnmpt0TVSUYgxj/T2dZcTf5Mx3dyZVMGKWvpzvqZ/LqtWYuWjEmlFky6H9pzFoahMjBcw9RVdFXB80OGi65sdxZCNNyChpfu7m4uu+wyPvnJT/Lwww/zm9/8ho9+9KOccsopEzuNPM9jYGBgYnrp4osvZs+ePXz2s5/lxRdf5NFHH+WDH/wgmzdv5qyzzlrI5i07k3eezGQpq5FWHZ/dvSV27R1l194Rdu0dZfeki3KzWoj3Nb2wXHIAYrL7pi1v4Xoh/cM14jh+bVfPMvhM52J8e7g1NiLk+SFRFKOqCmlLpz1vk7LMsdozEW05S06FFkI03IIvU/7sZz/L6aefzgc+8AHe+9738rrXvY4bbrhh4v4nnniCM888kyeeeAKA4447jq9//es8/fTTbN++nQ984AMce+yxfPWrX13x3+zGi6JN/tY7WaUWkE8bi16NdK6jCs1mod7XfArLjX+m5drMz71Un+l8jG8Pb8tZOF7EaMXD8SJ62tOc+sYu3vS6do7e0MrRG1rYJMFFCLEMKPFKmRuYJAwjCoVKo5sxJ5PPuZmpKNpCfMvVdZW2tgzDw5W6EYE4jtk9doGfXK5+3HDRpS1nsekQFw0vtQO9r8KoQyZlsG5NBl1T97sVulzz2bV3hNasOeNjoihmtOJx9Nguoarjs2egjGYaKGGIAgv+mS6GlVBraH+/62JxSJ83xkrs9/b2zOIs2BULr9HVSBezXH0j7e99OW5Aqeazd6DCSNklZRn7LXs/38Jyadvg8LV5nCBmb28Rzw+bosLsaqqmLIRobvKXahloZDXSRpWrP5BDHQWY7X05bsCrQ9Wk6q0GubSBrqn7LXt/MIcNZmyD9a1p0oY6pcJus41kCCHEciThZZlo1LfeRpWr35+5bEk+kJneVxxDoeTi+xFpW8cLkjomByp7f7BnHo1/psYqrYAphBCLRf6qrnLLZdHwuIVaZDvT+/L8kIoTkLI0al5AxjYwJ21pnjxFNt1si1pl940QQiw9GXlZ5ZbiJOW5mr4ledx8DgQcN9P78oMIzw8JwgjL0GjPWVOe50BTZHLYoBBCLA8SXkTDFw2PW+jFw9PfV831CcOYbEqnuy2NPe055jJFJotahRCi8eSvsACWx6jCYiwenvy+gjCiNVuhUvPrggvMvPBWCCHE8iPhRUxo9KjCYi0envy+DutSkjU1DZ4iE0IIcfBkwa5YNpZi8bAsvBVCiOYnIy9i2ViqxcPLYYpMCCHEwZPwIpaVpVo83OgpMiGEEAdP/nqLZUdGRoQQQuyPhBexLE0eGVkJBwYKIYRYOBJexLK2EEcFCCGEWFkkvIhla/yoANcLyaR0DD2pkru/QxSFEEKsfLJVWixL048KMI1kqsg0NNryFq4X0j9cI46X9rRrIYQQjSfhRSxL8zkqQAghxOoi4UUsS68dFTDzr2hyVEA0r6MChBBCrAwSXsSyNPmogJkc7FEBQgghmp+EF7EsLcVRAUIIIZqT7Daao5Vaa2S5vq+lOipACCFE85HwMgcrtdbIcn9fS3VUgBBCiOYi4eUAVmqtkWZ5X3JUgBBCiOlkzct+rNRaI832vsaPCsimDFKWLsFFCCFWOQkv+7FSa42s1PclhBBidZDwsh8rtdbISn1fQgghVgcJL/uxUmuNrNT3JYQQYnWQ8LIfK7XWyEp9X0IIIVYHCS/7MV5rxDI1hosunh8SRTGeHzJcdJu21shKfV9CCCFWB9kqfQArtdbISn1fQgghVj4JL3OwUmuNrNT3JYQQYmWT8DJH47VGVpqV+r6EEEKsXLLmRQghhBBNRcKLEEIIIZqKhBchhBBCNJVFDS/XXHMNf/qnf3rAx+3du5c//MM/ZPPmzbzlLW/hS1/6EmEopemFEEIIUW9RwksYhnzhC19gx44dB3ys7/u8973vRVEU/vVf/5XPfOYz7Nixg7//+79fjKYJIYQQoskt+DaT559/nk984hPs2bOHdevWHfDxd999N6+++irf/e53yefzvP71r2doaIgvfvGL/O///b8xTXOhmyiEEEKIJrbgIy+PPPIIxx57LHfccQcbNmw44OMfe+wxjjvuOPL5/MRtp512GuVymWeeeWahmyeEEEKIJrfgIy9XXXXVvB7f29tLT0/PlNu6uroAePXVVznhhBMOqh36LCcmr0aapk75p1h80ueNIf2+9KTPG2O19/u8wsvevXu54IILZr3/wQcfpLOzc14NcBxnyqgLgGVZALiuO6/nGqeqCm1tmYP62ZUsn081ugmrjvR5Y0i/Lz3p88ZYrf0+r/DS3d3NnXfeOev97e3t826Abdt4njfltvHQkk6n5/18AFEUUyxWD+pnVyJNU8nnUxSLNcIwanRzVgXp88aQfl960ueNsRL7PZ9PzXkkaV7hxTAMjjzyyINq1Gx6enp47rnnptzW398PJGHpYAXByvgwF1IYRtIvS0z6vDGk35ee9HljrNZ+b/hk2ZYtW3jqqacol8sTt/385z8nk8lwzDHHNLBlQgghhFiOljy8eJ7HwMDAxFTRhRdeSGdnJx/+8Id55plnuO+++/jyl7/M7//+78s2aSGEEELUWfLw8sQTT3DmmWfyxBNPAMni3K9//etEUcTv/M7v8OlPf5p3vetd/N//+3+XumlCCCGEaAJKHMdxoxux0MIwolCoNLoZy4auq7S1ZRgerqzKudFGkD5vDOn3pSd93hgrsd/b2zNzXrDb8DUvQgghhBDzIeFFCCGEEE1FwosQQgghmoqEFyGEEEI0FQkvQgghhGgqEl6EEEII0VQkvAghhBCiqUh4EUIIIURTkfAihBBCiKYi4UUIIYQQTUXCixBCCCGaioQXIYQQQjQVCS9CCCGEaCoSXoQQQgjRVCS8CCGEEKKpSHgRQgghRFOR8CKEEEKIpiLhRQghhBBNRcKLEEIIIZqKhBchhBBCNBUJL0IIIYRoKhJehBBCCNFUJLwIIYQQoqlIeBFCCCFEU5HwIoQQQoimIuFFCCGEEE1FwosQQgghmoqEFyGEEEI0FQkvQgghhGgqEl6EEEII0VQkvAghhBCiqUh4EUIIIURTkfAihBBCiKYi4UUIIYQQTUXCixBCCCGair6YT37NNdcQhiF//dd/vd/H3Xjjjfzd3/1d3e1PPvkkur6oTRRCCCFEk1mUZBCGIddddx07duxg27ZtB3z8s88+y+WXX87HP/7xqY2T4CKEEEKIaRY8HTz//PN84hOfYM+ePaxbt25OP/Pcc89x1VVX0dnZudDNEUIIIcQKs+BrXh555BGOPfZY7rjjDjZs2HDAx9dqNV5++WWOOuqohW6KEEIIIVagBR95ueqqq+b1+F27dhFFET/84Q/5zGc+g+d5nHLKKXzsYx+jq6vroNuh67IWeZymqVP+KRaf9HljSL8vPenzxljt/T6v8LJ3714uuOCCWe9/8MEH5z31s2vXLgByuRw33HADg4ODXH/99fze7/0eO3fuJJVKzev5AFRVoa0tM++fW+ny+fn3pTg00ueNIf2+9KTPG2O19vu8wkt3dzd33nnnrPe3t7fPuwHvfOc7ufDCC2lpaZm47eijj+acc87h/vvv59JLL533c0ZRTLFYnffPrVSappLPpygWa4Rh1OjmrArS540h/b70pM8bYyX2ez6fmvNI0rzCi2EYHHnkkQfVqP2ZHFwgCUmtra309vYe9HMGwcr4MBdSGEbSL0tM+rwxpN+XnvR5Y6zWfm/4ZNnf/M3fcOmllxLH8cRte/fuZXh4WBbxCiGEEKLOkocXz/MYGBjA8zwALr74Yvbs2cNnP/tZXnzxRR599FE++MEPsnnzZs4666ylbp4QQgghlrklDy9PPPEEZ555Jk888QQAxx13HF//+td5+umn2b59Ox/4wAc49thj+epXv4qiKEvdPCGEEEIsc0o8eb5mhQjDiEKh0uhmLBu6rtLWlmF4uLIq50YbQfq8MaTfl570eWOsxH5vb8/MecFuw9e8CCGEEELMh4QXIYQQQjQVCS9CCCGEaCoSXoQQQgjRVCS8CCGEEKKpSHgRQgghRFOR8CKEEEKIpiLhRQghhBBNRcKLEEIIIZqKhBchhBBCNBUJL0IIIYRoKhJehBBCCNFUJLwIIYQQoqlIeBFCCCFEU5HwIoQQQoimIuFFCCGEEE1FwosQQgghmoqEFyGEEEI0FQkvQgghhGgqEl6EEEII0VQkvAghhBCiqUh4EUIIIURTkfAihBBCiKYi4UUIIYQQTUXCixBCCCGaioQXIYQQQjQVCS9CCCGEaCoSXoQQQgjRVCS8CCGEEKKpSHgRQgghRFOR8CKEEEKIpiLhRQghhBBNRcKLEEIIIZqKEsdx3OhGLLQ4jomiFfe2DommqYRh1OhmrCrS540h/b70pM8bY6X1u6oqKIoyp8euyPAihBBCiJVLpo2EEEII0VQkvAghhBCiqUh4EUIIIURTkfAihBBCiKYi4UUIIYQQTUXCixBCCCGaioQXIYQQQjQVCS9CCCGEaCoSXoQQQgjRVCS8CCGEEKKpSHgRQgghRFOR8CKEEEKIpiLhZRXZt28fH/nIRzjjjDPYsmUL733ve9m1a1ejm7VqXHPNNfzpn/5po5uxIkVRxA033MBZZ53FiSeeyO///u+ze/fuRjdrVbnpppu4+uqrG92MFW9kZIS/+Iu/4Oyzz2bz5s1cddVVPPbYY41u1pKT8LJKeJ7H+9//foaGhviHf/gHbr75ZnK5HO95z3soFAqNbt6KFoYhX/jCF9ixY0ejm7Ji3XTTTfzrv/4rf/mXf8m//du/oSgKf/AHf4DneY1u2qrwrW99ixtuuKHRzVgVPvKRj/DrX/+a66+/nh07dnDcccfx3ve+l+eff77RTVtSEl5Wiccee4znnnuOL37xixx//PEcffTRfPGLX6RarfLjH/+40c1bsZ5//nmuuuoqbr31VtatW9fo5qxInufxzW9+kw9+8IOcc845HHPMMXz5y1+mr6+Pe++9t9HNW9H6+vp43/vex9/+7d9yxBFHNLo5K97u3bt56KGHuPbaazn55JN53etexzXXXEN3dzd33HFHo5u3pCS8rBJHH300X/va1+ju7p5yexzHjI6ONqhVK98jjzzCscceyx133MGGDRsa3ZwV6ZlnnqFSqXDaaadN3JbP53njG9/Io48+2sCWrXxPPvkkLS0t3HbbbZx44omNbs6K19bWxte+9jWOP/74idsURVmVf8f1RjdALI3Ozk7OOeecKbf98z//M67rcsYZZzSoVSvfVVdd1egmrHi9vb0ArF27dsrtXV1d7Nu3rxFNWjXOP/98zj///EY3Y9XI5/N1f8fvuusuXn75Zc4888wGtaoxJLysEHv37uWCCy6Y9f4HH3yQzs7Oif9/zz338OUvf5mrr76aY445ZimauOLMt8/F4qjVagCYpjnldsuyVt23UbG6PP744/zZn/0ZF1xwwaoLkRJeVoju7m7uvPPOWe9vb2+f+PfvfOc7fPazn+XSSy/lE5/4xFI0b0WaT5+LxWPbNpCsfRn/dwDXdUmlUo1qlhCL6r777uNjH/sYJ554Itdff32jm7PkJLysEIZhcOSRRx7wcddddx3/+I//yNVXX80111yDoihL0LqVaa59LhbX+HRRf38/GzdunLi9v79fRhXFivQv//IvfO5zn2Pr1q1cd911daOOq4Es2F1FvvSlL/GP//iP/Mmf/Amf/OQnJbiIFeGYY44hm83y8MMPT9xWLBZ56qmnOPnkkxvYMiEW3s0338xnP/tZfvd3f5evfOUrqzK4gIy8rBoPP/wwX//617n66qt5xzvewcDAwMR96XSaTCbTwNYJcfBM0+Td73431113He3t7axfv54vfelL9PT0sHXr1kY3T4gF8+KLL/JXf/VXbN26lT/8wz9kaGho4j7btsnlcg1s3dKS8LJKjNcA+Pa3v823v/3tKfd94AMf4IMf/GAjmiXEgvjQhz5EEAR88pOfxHEctmzZwje+8Y1V+61UrEx33303vu9z77331tUw2rZtG3/913/doJYtPSWO47jRjRBCCCGEmCtZ8yKEEEKIpiLhRQghhBBNRcKLEEIIIZqKhBchhBBCNBUJL0IIIYRoKhJehBBCCNFUJLwIIYQQoqlIeBFCCCFEU5HwIoQQQoimIuFFCCGEEE1FwosQQgghmoqEFyGEEEI0lf8/um6zkOqLbDsAAAAASUVORK5CYII=",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def draw_vector(v0, v1, ax=None):\n",
" ax = ax or plt.gca()\n",
" arrowprops=dict(arrowstyle='->',\n",
" linewidth=2,\n",
" color='black',\n",
" shrinkA=0, shrinkB=0)\n",
" ax.annotate('', v1, v0, arrowprops=arrowprops)\n",
"\n",
"# plot data\n",
"plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
"for length, vector in zip(pca.explained_variance_, pca.components_):\n",
" v = vector * 3 * np.sqrt(length)\n",
" draw_vector(pca.mean_, pca.mean_ + v)\n",
"plt.axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These vectors represent the *principal axes* of the data, and the length of the vector is an indication of how \"important\" that axis is in describing the distribution of the data—more precisely, it is a measure of the variance of the data when projected onto that axis.\n",
"The projection of each data point onto the principal axes are the \"principal components\" of the data.\n",
"\n",
"If we plot these principal components beside the original data, we see the plots shown here:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n",
"fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n",
"\n",
"# plot data\n",
"ax[0].scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
"for length, vector in zip(pca.explained_variance_, pca.components_):\n",
" v = vector * 3 * np.sqrt(length)\n",
" draw_vector(pca.mean_, pca.mean_ + v, ax=ax[0])\n",
"ax[0].axis('equal');\n",
"ax[0].set(xlabel='x', ylabel='y', title='input')\n",
"\n",
"# plot principal components\n",
"X_pca = pca.transform(X)\n",
"ax[1].scatter(X_pca[:, 0], X_pca[:, 1], alpha=0.2)\n",
"draw_vector([0, 0], [0, 3], ax=ax[1])\n",
"draw_vector([0, 0], [3, 0], ax=ax[1])\n",
"ax[1].axis('equal')\n",
"ax[1].set(xlabel='component 1', ylabel='component 2',\n",
" title='principal components',\n",
" xlim=(-5, 5), ylim=(-3, 3.1));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This transformation from data axes to principal axes is an *affine transformation*, which basically means it is composed of a translation, rotation, and uniform scaling.\n",
"\n",
"While this algorithm to find principal components may seem like just a mathematical curiosity, it turns out to have very far-reaching applications in the world of machine learning and data exploration."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### PCA as dimensionality reduction\n",
"\n",
"Using PCA for dimensionality reduction involves zeroing out one or more of the smallest principal components, resulting in a lower-dimensional projection of the data that preserves the maximal data variance.\n",
"\n",
"Here is an example of using PCA as a dimensionality reduction transform:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"original shape: (200, 2)\n",
"transformed shape: (200, 1)\n"
]
}
],
"source": [
"pca = PCA(n_components=1)\n",
"pca.fit(X)\n",
"X_pca = pca.transform(X)\n",
"print(\"original shape: \", X.shape)\n",
"print(\"transformed shape:\", X_pca.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The transformed data has been reduced to a single dimension.\n",
"To understand the effect of this dimensionality reduction, we can perform the inverse transform of this reduced data and plot it along with the original data:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X_new = pca.inverse_transform(X_pca)\n",
"plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
"plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n",
"plt.axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The light points are the original data, while the dark points are the projected version.\n",
"This makes clear what a PCA dimensionality reduction means: the information along the least important principal axis or axes is removed, leaving only the component(s) of the data with the highest variance.\n",
"The fraction of variance that is cut out (proportional to the spread of points about the line formed in this figure) is roughly a measure of how much \"information\" is discarded in this reduction of dimensionality.\n",
"\n",
"This reduced-dimension dataset is in some senses \"good enough\" to encode the most important relationships between the points: despite reducing the dimension of the data by 50%, the overall relationship between the data points are mostly preserved."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### PCA for visualization: Hand-written digits\n",
"\n",
"The usefulness of the dimensionality reduction may not be entirely apparent in only two dimensions, but becomes much more clear when looking at high-dimensional data.\n",
"To see this, let's take a quick look at the application of PCA to the digits data we saw in [In-Depth: Decision Trees and Random Forests](https://jakevdp.github.io/PythonDataScienceHandbook/05.08-random-forests.html#Example:-Random-Forest-for-Classifying-Digits).\n",
"\n",
"We start by loading the data:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1797, 64)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.datasets import load_digits\n",
"digits = load_digits()\n",
"digits.data.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Recall that the data consists of 8×8 pixel images, meaning that they are 64-dimensional.\n",
"To gain some intuition into the relationships between these points, we can use PCA to project them to a more manageable number of dimensions, say two:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(1797, 64)\n",
"(1797, 2)\n"
]
}
],
"source": [
"pca = PCA(2) # project from 64 to 2 dimensions\n",
"projected = pca.fit_transform(digits.data)\n",
"print(digits.data.shape)\n",
"print(projected.shape)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.unique(digits.target)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1797,)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"digits.target.shape"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0., 0., 5., 13., 9.],\n",
" [ 0., 0., 0., 12., 13.],\n",
" [ 0., 0., 0., 4., 15.],\n",
" [ 0., 0., 7., 15., 13.],\n",
" [ 0., 0., 0., 1., 11.],\n",
" [ 0., 0., 12., 10., 0.],\n",
" [ 0., 0., 0., 12., 13.],\n",
" [ 0., 0., 7., 8., 13.],\n",
" [ 0., 0., 9., 14., 8.],\n",
" [ 0., 0., 11., 12., 0.]])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"digits.data[:10,:5]"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"digits.target[:10]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now plot the first two principal components of each point to learn about the data:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"digits_df = pd.DataFrame({'pca1': projected[:, 0], 'pca2':projected[:, 1], 'digit': digits.target})\n",
"center = {}\n",
"for (digit, gdf) in digits_df.groupby('digit'):\n",
" center[digit] = (gdf['pca1'].mean(), gdf['pca2'].mean())"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cmap = matplotlib.colormaps.get_cmap('nipy_spectral').resampled(10)\n",
"plt.scatter(projected[:, 0], projected[:, 1],\n",
" c=digits.target, edgecolor='none', alpha=0.5,\n",
" cmap=cmap, clim=(0,10))\n",
"plt.xlabel('component 1')\n",
"plt.ylabel('component 2')\n",
"plt.colorbar(ticks=list(range(11)))\n",
"for digit in center:\n",
" xy = center[digit]\n",
" plt.plot([xy[0]], [xy[1]], 'wo', markersize=12)\n",
" plt.text(xy[0], xy[1], digit, horizontalalignment='center', verticalalignment='center')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Recall what these components mean: the full data is a 64-dimensional point cloud, and these points are the projection of each data point along the directions with the largest variance.\n",
"Essentially, we have found the optimal stretch and rotation in 64-dimensional space that allows us to see the layout of the digits in two dimensions, and have done this in an unsupervised manner—that is, without reference to the labels."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### What do the components mean?\n",
"\n",
"We can go a bit further here, and begin to ask what the reduced dimensions *mean*.\n",
"This meaning can be understood in terms of combinations of basis vectors.\n",
"For example, each image in the training set is defined by a collection of 64 pixel values, which we will call the vector $x$:\n",
"\n",
"$$\n",
"x = [x_1, x_2, x_3 \\cdots x_{64}]\n",
"$$\n",
"\n",
"One way we can think about this is in terms of a pixel basis.\n",
"That is, to construct the image, we multiply each element of the vector by the pixel it describes, and then add the results together to build the image:\n",
"\n",
"$$\n",
"{\\rm image}(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots x_{64} \\cdot{\\rm (pixel~64)}\n",
"$$\n",
"\n",
"One way we might imagine reducing the dimension of this data is to zero out all but a few of these basis vectors.\n",
"For example, if we use only the first eight pixels, we get an eight-dimensional projection of the data, but it is not very reflective of the whole image: we've thrown out nearly 90% of the pixels!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![](figures/05.09-digits-pixel-components.png)\n",
"[figure source in Appendix](06.00-Figure-Code.ipynb#Digits-Pixel-Components)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The upper row of panels shows the individual pixels, and the lower row shows the cumulative contribution of these pixels to the construction of the image.\n",
"Using only eight of the pixel-basis components, we can only construct a small portion of the 64-pixel image.\n",
"Were we to continue this sequence and use all 64 pixels, we would recover the original image."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But the pixel-wise representation is not the only choice of basis. We can also use other basis functions, which each contain some pre-defined contribution from each pixel, and write something like\n",
"\n",
"$$\n",
"image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n",
"$$\n",
"\n",
"PCA can be thought of as a process of choosing optimal basis functions, such that adding together just the first few of them is enough to suitably reconstruct the bulk of the elements in the dataset.\n",
"The principal components, which act as the low-dimensional representation of our data, are simply the coefficients that multiply each of the elements in this series.\n",
"This figure shows a similar depiction of reconstructing this digit using the mean plus the first eight PCA basis functions:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![](figures/05.09-digits-pca-components.png)\n",
"[figure source in Appendix](06.00-Figure-Code.ipynb#Digits-PCA-Components)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Unlike the pixel basis, the PCA basis allows us to recover the salient features of the input image with just a mean plus eight components!\n",
"The amount of each pixel in each component is the corollary of the orientation of the vector in our two-dimensional example.\n",
"This is the sense in which PCA provides a low-dimensional representation of the data: it discovers a set of basis functions that are more efficient than the native pixel-basis of the input data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Choosing the number of components\n",
"\n",
"A vital part of using PCA in practice is the ability to estimate how many components are needed to describe the data.\n",
"This can be determined by looking at the cumulative *explained variance ratio* as a function of the number of components:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pca = PCA().fit(digits.data)\n",
"plt.plot(np.cumsum(pca.explained_variance_ratio_),'.-')\n",
"plt.xlabel('number of components')\n",
"plt.ylabel('cumulative explained variance');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This curve quantifies how much of the total, 64-dimensional variance is contained within the first $N$ components.\n",
"For example, we see that with the digits the first 10 components contain approximately 75% of the variance, while you need around 50 components to describe close to 100% of the variance.\n",
"\n",
"Here we see that our two-dimensional projection loses a lot of information (as measured by the explained variance) and that we'd need about 20 components to retain 90% of the variance. Looking at this plot for a high-dimensional dataset can help you understand the level of redundancy present in multiple observations."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## PCA as Noise Filtering\n",
"\n",
"PCA can also be used as a filtering approach for noisy data.\n",
"The idea is this: any components with variance much larger than the effect of the noise should be relatively unaffected by the noise.\n",
"So if you reconstruct the data using just the largest subset of principal components, you should be preferentially keeping the signal and throwing out the noise.\n",
"\n",
"Let's see how this looks with the digits data.\n",
"First we will plot several of the input noise-free data:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_digits(data):\n",
" fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n",
" subplot_kw={'xticks':[], 'yticks':[]},\n",
" gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
" for i, ax in enumerate(axes.flat):\n",
" ax.imshow(data[i].reshape(8, 8),\n",
" cmap='binary', interpolation='nearest',\n",
" clim=(0, 16))\n",
"plot_digits(digits.data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now lets add some random noise to create a noisy dataset, and re-plot it:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(42)\n",
"noisy = np.random.normal(digits.data, 4)\n",
"plot_digits(noisy)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's clear by eye that the images are noisy, and contain spurious pixels.\n",
"Let's train a PCA on the noisy data, requesting that the projection preserve 50% of the variance:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"12"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pca = PCA(0.50).fit(noisy)\n",
"pca.n_components_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here 50% of the variance amounts to 12 principal components.\n",
"Now we compute these components, and then use the inverse of the transform to reconstruct the filtered digits:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"components = pca.transform(noisy)\n",
"filtered = pca.inverse_transform(components)\n",
"plot_digits(filtered)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This signal preserving/noise filtering property makes PCA a very useful feature selection routine—for example, rather than training a classifier on very high-dimensional data, you might instead train the classifier on the lower-dimensional representation, which will automatically serve to filter out random noise in the inputs."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Principal Component Analysis Summary\n",
"\n",
"In this section we have discussed the use of principal component analysis for dimensionality reduction, for visualization of high-dimensional data, for noise filtering, and for feature selection within high-dimensional data.\n",
"Because of the versatility and interpretability of PCA, it has been shown to be effective in a wide variety of contexts and disciplines.\n",
"Given any high-dimensional dataset, I tend to start with PCA in order to visualize the relationship between points (as we did with the digits), to understand the main variance in the data (as we did with the eigenfaces), and to understand the intrinsic dimensionality (by plotting the explained variance ratio).\n",
"Certainly PCA is not useful for every high-dimensional dataset, but it offers a straightforward and efficient path to gaining insight into high-dimensional data.\n",
"\n",
"PCA's main weakness is that it tends to be highly affected by outliers in the data.\n",
"For this reason, many robust variants of PCA have been developed, many of which act to iteratively discard data points that are poorly described by the initial components.\n",
"Scikit-Learn contains a couple interesting variants on PCA, including ``RandomizedPCA`` and ``SparsePCA``, both also in the ``sklearn.decomposition`` submodule.\n",
"``RandomizedPCA``, which we saw earlier, uses a non-deterministic method to quickly approximate the first few principal components in very high-dimensional data, while ``SparsePCA`` introduces a regularization term (see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)) that serves to enforce sparsity of the components."
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.11.10"
}
},
"nbformat": 4,
"nbformat_minor": 4
}