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@tobydriscoll
Created September 2, 2016 20:22
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T&B Lecture 3 (matlab)
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lecture 3: Norms"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Vector norms"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The contour lines of the major $p$-norms give some idea of the metric structure created by them."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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TFoyQtEqw40nQiaqrEWnXHWb+BaINtkHJ5nHZPBIAiHFCvkEU44SS1KzrkYcvh0fk8SSn\nkpUJAGyDLulkl+2IJMYJRKJKUs1ho09cpe+Ir2HMvpGftRORBkZIfDHNG64g8QXl7aQ/o6lotm8P\nm2VG0oiPxEC1XXYAEOOEkjQzCXp4+PaXJco26JJGfCSKyjeIYRM/kYVKqmvSxcSDToya3goKjJCU\nBQWJL6ZzfV9MLKh6EycXjTTdmI58s0sBX22XncQf+QZjfpLI//d7qD5Z+h2yOJWkafjOQE7fqVxS\nIpqUlDcdIzgKkrKgIPHFla9vr1310qs/4D5weKt2i0YkGCLpuHyDqBURmgKirJaTXSRyKkkza/d/\nRLyaqmvSNJs4oCApCwoSX1zh+ubA5E0sDFosGhEdsvQ7AICk4zQdT0wKUSY5bNKoMhFNUjl9F3CN\n2Tde0QiOgqQsKEh8MdX1HXCNHV6jrhppcaXROB3S4hf0NSD7Mkg2siTNXJJq1pCbnIeS0sXmkFNm\nI1CQlAUFiS+muL6D9o3TzGtTwtpRP+B1qL5kZPrUHrOTvFxFVl5YxkPTQY6ZbB5JjIsvSc3SyvvA\nhSZdqV6LgqQsKEh8cbnrO9j7AgzaVbTVNdu3g0YsDCQkkiODirm49h4gpM4kjQxrJWAimpSSaC7I\nKVVnBlcy3aEgKQsKEl9Mfn0TI4N6tjqtqJE04qs9Zrd5JK184aqCnMPMN4j8L2nyB9ztPY0DXodq\nTUCmNDigICkLChJfTHJ9q1o60oq9u/aYXa4SYUg0HUjAVHvMDty/aerbwS9vcEBBUhYUJL6YeH0H\n7RujMtarqEaCLlm1hMk0kKWoYm6eVqoj/DAuj8ezLKlrB7/c7pcoSMqCgsQX465vFTsy8K9Gtcfs\npFBUtaCQ87wT/0gjvpqjhziXJZU1qeMpABhXTEJBUhYUJL740vWtXumIczWSoyKUImXhX5bU1CRS\nTMpYH9pAEgVJWVCQ+OKv17d6pSOe1cjmcdUcbQWUIprIssRnFlR1TQpdmYSCpCwoSHwhX99qrTri\nVo04/5YMPyz9DmJ54FD7VdSkcSuTUJCUBbef4JFg7wtwqRk+YzhUI9mmXJJmrpir8nYbkUNJmjnf\nIFpOOmqOtvJmoydLZZvtO9hrUlT6ehi0B3tfUHGJehgzQ+0JIBPw2oM9L0Tl/Iz9yM327bypUe0x\n+92t+wDgjcI1fFY1whgxTqiYm7d7YTEAVB5pJAETJ+Sml2SKi5rtO9gPHZXzs6DUBF6O3o2wAQWJ\nO4I9L8zI28G+mTdZ/cqPGkkjvsojTZZ+x+6FxShFKiLLks3jurt13+W2ZmfPJU3aznpgnTEqY/1Y\nx1Osx40AUJC4hLmRgbdeDCQwyjcY3yhcw1sBIzIR44SqBYtL0sxchUqZxgIAsHbUMx43yrgyKjEv\niJqkNChIPBFwgRqrjqw89WKQRnx3t+6zeVyYo+ONcaGSzeNSe0ag1yXfllPqC7jbey2Mh47KWB/E\nrJ3SoCDxhBp77rX3Wga8Dk7UqPaYvfJIY0maeffClfyU0JFQxDhh98KVJWnmmqOtPIRKRJO6pTbW\nmqQzzpjeNufI9EFBimgGvA6yv5HaE7lYMcLASCtwVVXS65KX5j2igiaptzNZuIKCFLmQvV952G2P\nfK/lG4y7F6KrWzNwVVWSNWnA61B3Jsj1gIIUofgDbk52Iq89Zq852opWOi0iV5XkVbQqotcl52YU\nWzvq/QG3ujNBrhkUpAjlcEd9bkaxumoUmqZDK512EeMEslZJ9fRdprFArcVJiCKgIEUixOSt4s7Q\ngGm68IKESjyk73LTS1ISzeyN4IgioCBFHO29Fn/Ao66tDtN0YYnsdFBZkzKKB7wO9kZw5PpBQYos\nBryO9p5GdW11cv8FTNOFH8TpoG5JCQ0O2gUFKYJQ3chAikYA8EbhGlxmFK7wUFJCg4NGwW7fEYS6\nRgbSgqEiKy9c03RO3ygAOIdH5ce9vtGJT0sXYgHAJMSSHwvFMBRmMU4oSTUDQOWRxt0Li1W5+cg0\nFpC9VDhZ9I1MBxSkSIGk1NUyMtg8rsojjWTZiioTUBanb9Q5PNri8jmHR8ljokBEZkzxFyWHPPjS\nC4dHQxWLvFB+lUmILRIF8kJZsTQKsTkAQOWRRrV2VMo0FgwMOtp7Ler6d5Dpg4IUEZDS0V23Vasy\nOlEjTReNnL7RVsnX6xttlXytko9oRqEomOJjy8wGuL5Ah4hTq+QDgBbJR8YiglQoCkSiNBpIVczN\nE3VCzdFWVbZVJF2Fmu07ZiVmq77eDpkOuGMsX1DagPLA4a1qdWTQrho5faN1Do9zeLTe4ZEVqMgo\nsNEGOfCqc3iIPmlXnKQRH2lRqEq2tttlpXc3hjvGKgsKEl/QuL5V3FrC0u+oOXpIW2pENKC+0wMA\npdkGAGAmQlPPqlXytUg+oo6FolBmNqg+q+mjriaRZUk0zKUoSMqCgsQXil/fA16HtaNelWQd8f6q\nVT+4WogO/cLmMgmxpdkGHkRoUkh+j4RNzuFRDSmTiprkD7ib7TtyM4rJ/kkKgoKkLFhDCmdknzf7\nobWiRuN06Gz536s9oytAaktVeUbIuzj5GrvL2aoBZSJ28MojjQDAWJPIyqRm+46URLNel8xyaOSq\nwAiJL5S94Wq2b09JMrO3GNk8rpqjrZyrUY3dJeflyswGTbvaxqUZq/L4fdtVjJPaey0Dgwpv/YUR\nkrJghBS2dLusoIbPm3MXQ2hIVJVvLDUb1J6RApiE2Ko8Y1Wesd7hqXN4sjs/5VZlVYyTiAu822VV\nPHGHKAV2aghP/AG3taM+NwPV6K84faMVrX3Zr30KAJ33zO+8Z354qFEopWbDO8VZ75RkAcAyS1dF\nax9xk3MF0SRLv4PxJujEBd7e04jtG7gFU3bTorm5uaGhoaurSxCE7Ozs8vJyk8k09UsaGxvfe++9\ncQeTk5O3bNkyxauUygA027cLumTGPeu4VSOnb7TG5mqVfJyns5RFjgVLzQYOy0skd8c+r9vea/GP\neJT6aGDKTlkwZXdltm3bVldXN3PmzPnz558+fXrfvn0HDhzYtWvX7bffPsWrLBbLwYMH9Xp96MHU\n1FTKkwUAGPA62PfzJt8vvKlRqBR1Fs5XezpMIXm8MrOhzuFZ1tjFmyyRVg6k6TvL3kKZxoJm+w5M\n3HFKEJkSq9WanZ29dOnSEydOkCNvvvlmTk5OYWHhyMjIFC9csmTJvffee7XDZWdnX+NEQ9j/QZVr\nsPP6zzN9Tp4ZXt3yWsMJpoNOTe/w2WqbZH71k2qbpPZc1Ie8G7G19vIWZ+/wWbWn81ee77Ktbnnt\n5JlhloO6Bjv3f1ClyKkU+cAiMlhDugKvv/46AGzevDktLY0cWbFixZ133ulyud5///3LverMmTMn\nTpzIyclhNMsQrB31KYlmxk0Zao4eKkkz89OnrsbukmtFkZOjmwISLXXeM98UH7vM0lVjZ1q8mQJ5\nWz+Wg5IPCG7ixyEoSFegra0tOjq6qKgo9OCSJUsAwGq1Xu5VnZ2dwWDwlltuoT6/LzPgdXS7rLkZ\nxSwHJTtKcNLDu1XyZb/2aX2nB6VoIkSW3inJIu8SJ36HklSzGBdfc/QQy0HJJn64YRJvoCBNxblz\n506dOpWWlqbT6UKPz507FwBOnDhxuReSOqfRaHz66afvv//+Bx988D/+4z+++OIL2hNu77HkZhSz\nXPpXe8wujQzzsA05MdFVtPaVZhs675nPoeOZE0xC7DvFWVX5RvJ2OSfbI4MlZE8/m0diuacf2TCp\nvQd3leULFKSpOH369NjYWEJCwrjj5MjQ0NDlXkgEadOmTXV1dR6Px2q1PvfccytXrvzggw/ozbbb\nZfUHPCwXHtk8rtoue9WCQmYjXg5yy2+Kj8XAaJqUmg3vlGRxksEjRnCbx2XpZxeykLQ2Wa6HcAK6\n7Kbi3LlzABATM/5dIkfIbyfls88+i4qKqqioWL9+/cyZMy9cuPDb3/52+/btW7ZsaWxsFISpPEXz\n5s2TT3JVs2W8NzkntjoSGDmHR98pzuLHQqYJZBveMksXkHZE6kHipMojjfkGkY3pTq9Lzs0osXbU\nX4PdTv6QIsqCEdJUREdHw2TCQ46Q307K9u3bDx48+OCDD86cOZM886GHHvrmN785MDDw1ltvTT3o\nZ5e4qqm291r0OgNLL0PN0UMVWXnqqtHFwEiI7bxnPqrRtWESYslCWtWrSsQIztLgkJJo1usMZO/K\nq+LaPqTIFUFBmoq4uDgAGBkZGXecHCG/nZSbb7554pKj5cuXA4DDQSUp0d7TyLIvAw9Ghhq7q6K1\n753irNrCOSpOIwy42Hko31hjd6mbvitJM+cbRJYGh9tySrulNmbDIVODgjQVgiDEx8cfP378woUL\nocd7e3sBQBTFy71wbGwsOKEFBsnUud3Kty0haQdm4ZHN41LdyLCssau+0/NOCabpFKPUbKgtnFPf\n6VnW2KXiNCrm5tk8ErNikl6XjBZwfkBBugI5OTmjo6OffPJJ6EGbzQYA8+dPvvK/t7c3Jyfnxz/+\n8bjjJMDPyspSdob+gJul1Vvu+MJmuIk4faNymg6tdMpC0neFopD92qdque+IwaH2mF0aYZQ/JBZw\nbHDHAyhIV4Dk2Z5++mn5iCRJr7zySnR09B133EGOeDyet95666233iK1JZPJZDAYDh48+Je//EV+\nldfr3bNnT0xMzLJly5SdYXtPY6axgJnVW93SESkalWYbME1HCZK+K802qOi+E+MElqtlSZDU3sN0\ncS4yKeiyuwLf+973Xn311Q8//PBb3/pWSUnJwMCAxWI5c+bMhg0b5CqRw+HYuHEjAHz44YcJCQlR\nUVFPPPHExo0bv/e9761du3bevHmSJL388suff/75I488kpmZqeD0yErYe/9xl4LnnAKyUkSt0hHZ\nwQjddAxQ3X1Xkmq2eVw1Rw9VLVjMYLjcjOJm+44Br4NxixNkHChIV+CGG2546aWXqqurm5ubSeJO\nr9f/5Cc/KS8vn+JVK1asePbZZ5955pnf/e53ABAVFTVnzpz/+q//Ujw86pHYJevIqqM3CtewGW4c\nZCeFznsiq0GqipD0nVqaJLvAbR4Xg3CcrJPtkawoSOqC20/wxVV1s/cH3AcOb2UWHlUeaaqYq06y\njpTZ3ylWuPyGXBGnb3SZpatQFFTJkVr6HbXHGN0D+QPuZvuOgpzSq9Ik3H5CWbCGpGHaexqZhUck\nWYdqFGmQOImsPmY/ekmaWYyLZ9NSSA6SGIyFXA4UJK1y0VzHpFHQpRZBLLL540A1Uh2TEFtbOMcU\nH0saqDOmasFiZnvLpiSaseOquqAgaRVirmMzVu0xe9WCxSx3USMsa+winUAZj4uMwyTElpkNpdkG\n9pok7+PHYCxit8MgSUVQkLQKs7VHZIki+72OSGyE9m5OkO3g7DUp3yCKcfFslsrimiR1QUHSJO29\nFmZrj2qOHmLv88ZMHZ+QOIlxPYk47tgslcU1SeqCgqRJuqW2DJFFvo5sBcvYy4BqxC0kd8fe4yDG\nCfkGkY27gQRJDAZCJoLrkLRHt8vKprE32Z/GuuIB2gOFQr7pNKdGTs/5Fkeg13MeAFodZwGg133e\n6Tk/7mkmQwwApCfHkAem5Oh0Q4zJEFNk1k04JacQj0NFa1+N3cVyfRJpBM5gWZJel6zXGbpdVmY1\nWkQGBUl7MNv3iHgZGAwkU2N3aWX1q9Nz/qU2n9N9gUiRyRCTnhxTaJ4JAGWL9LLwTPpaWataHGdb\nHWd73Rd1q8isKzLP5F+fiCYxXjMruxsYLEu65n2SkOsEBUljkA0uGYRHln6HNDLM0svQKvnqOz08\nqxERIQCoaRwyGWLKCvSm5OiyRfrmjSlXdR4iVwBQtkiQz0xUqsVxtq7NTTSpyDyzyKyTn8wVch+H\ndCG21GxgM2i+QRRPdjEIksg+SdhJiD08XuvIFJwadLAx19UeY7o3udM3uqyxi89MHdEhEsqQMKjr\n52nK6oTJcDGJV7ZI2LMumURdLY6z5XvdRWZd2SK9LF38IGuSSYhl012QZZCUKRa091hS8jbRHggJ\nBQVJY7Bxe1v6HWJcPEsvQ0VrX23hHN66phIpkuOhq42ErhmTIaZskVC2SNhanNDiCNS1+asbh0jM\nxJUymYTYqnxjRWsfs7g232AkFnDasTvx2vkDbmZ99BFAl522IIVWBp+Q2mN2llZvYqtjlvmZDtVN\n3qzH+5fsGACAc/9p6vp52taVieynQZSpeWPKu4+kmJKj69r8WY/3Vzd52c/kr0WvYAAAIABJREFU\ncpQyN4JXzM1jYLeTrQ20B0JCQUHSEu09jQzc3ozDI7LpDifJOqfnfHWT94YfOeus/q3FCWrp0ERM\nhpitKxObN6ZsLU5odZzlSpaIEZzZ5klykER7oNyMEtzdnDEoSJqh22X1B9wMqqwsw6NWyfcLm4uT\ndgwkKmp1nO36eVrXz9O4So7JyAGT032BE1kiprtWydcqMdrjlayTpT2KbG2gPRAig4KkGU4NOhi4\nvRmHRxWtfe8UZ6m+E3mLIyBLUfPGFD6NbaGYDDF71iW/+0gKiZZaHAGV5yPElpnZJe7EOIFNkJSS\nhK3tmIKCpBm6XSx2D2MZHi1r7CoUBXWNDE7P+aU7B8r3urcWJ2hCikIxGWJIEq98r7t8r3viOlyW\nlJoNhaLATJPYVJIyjQUYIbEEBUkbsLEzsAyPWiWfc3hU3WQdydERGzefCbrpULZIIJaHJTsG1M3g\nVeUbWyVfvcPDYCw2lSRibUBNYgYKkjbolqyzkugvhj3ZxTI8UlGNSGBEcnSc2BauB2J5kDN4aoVK\npJhUY3M5faMMhmMUJIkF7T0W2qMgBBQkbXCK/qJx0pqBTXi0rLGLZHgYjDURUjEqNM/UXI5uakhh\nqaxAv2THQF0bI3/BOApFoTTbUGNj4bgjlSTae/elJJr9ARYxHwIoSJqAUb6OVXhE7FhqhUfVTd7y\nve7mjSlhEBhNRA6VqhuH1ErflZkNbBx3YpxQkppFO0jCBUksQUHSAKcGHQzydTaPxKZzXY3dpcqq\no9A0HefdS68TkyFG9oWzT9/J7RsYjJVvEKWRYdpBUqZY0I1eOyagIGkABv46su8R1SEIpOLNPlnn\n9JxfsmOA2NIYD60KJkPM1uIEkr5jr0mlZoMpPpbBUlmyT5LlJF3TAWbtmIGCxDts8nU2j1SSykKQ\nKlr7WG6iQyBFo63FCXvWRVBfMpK+U0uTagvn1Hd6GLgbKubm2TwS1SHQa8cMFCTeYZCvY+b2VsXL\n0OIILN050LwxRbvG7uth68rErcUJ7B3hpAU4A3cDG2sDeu3YgILEOwzydZaTXSWp1Is6qngZZDUK\n76LR1JCFSnVWP2NNqso31js8DNwNDKwNmLVjAwoS13S7rHpdMot8Hf0CUo3d9W/5TJN1qEYyxOZQ\nZ/WztINfXJZEv5LEwNqAWTs2oCBxzalBFsuPGKgRCY9YVo9QjcZBNKm6cYhl47tCUWBgAb+YtRuk\nW0lKSTKf8nZSHQJBQeKaAa+D9n4TtcfsDOwMjMMj4vBGNRoHsd6x7HrHLEiqmJtHu43QrMRs3I2C\nNihIXEN7vwmbxyWN+GjbGRiHR07P+fK97j3rklGNJlK2SGDsu2MWJEkjPqpZO0Fn8Afc/oCb3hAI\nChK/EMM31SEsJ1nk6xiHR+V73YWcbfXNFbIXnM1wbIIkMU6oyMqjmrXT65JnJZp9aG2gCQoSvzAw\nfLNZfsQyPCrf6waAsGwLpCD3LxLSk2PIe8WAQlFwDo/SDpLyk0TaWbuUJDOav6mCgsQvA/QbqjLI\n11W09pWaDVSHkGlxBFocgQjpxXA9kDasLY4AG9MdWZNUR3lbCgZZu1mJ2Wj+pgoKEr/4A26qhm82\n/rp6h6eKSb6OGBkiqhfD9SCb7tgUk8hWSVSHIG2EqGbtsIxEGxQkTmFSQOrKT6IrFfUOT6nZwGaH\n8vK97qriBDQyTB+TIYZZMckkxJriY2nv3VcxN4/2aiQsI1EFBYlTGBWQKEdINTZXGZN8HelBgKWj\nq4UUk9h0cKjKM9LuJCTGCbT72qUkmXuw8zc1UJA4hfaacAb5ulbJ5/SNMuhc5/Scr2kcwmTdNUCK\nSXVWP4PEXaEomOJjqSbuLmbtKJeRsF8DPVCQOMUfcFNN2dkGXbTzdXUODxs7A0nWhdPerywhiTs2\njjsG1oZ8g5HqbhSCjpFDJzLBzzCPkBZ2VIeweSTa+8O2Sr53Sqj3bG1xBHrd5zl01kn9Qx8dmWST\nOjEt4daF6uyWeznuXyTUWf0tjgDtClyZ2bDM0kV1iJJUc+WRRnrnl5va0XbARiYoSJzCwPAtxlFM\nptU7PKb4WAZ2hpomXpJ1Uv9Qw4GPpf6hk/1DtiN9YlqCmJqQmpYw7mkf7b6oUrcunCOmJeQvNKmu\nT3JLoa6fp9EdSIglWTt6iVzZ/E11PcMpbycKEg1QkHiEtqOBQQGpRfIxsDOQary6zjqiQw372wFg\n1epcMS2hZPVXp9YYqX8IAD460mc74nxo18tiWsKq1bmr7vqqOEG9mFG2SKhr81c3eWkbQ8rMhhq7\n6x2RYuhMzN/0BCklyTww6MhNp3T6iAYFiUcGvI7cjGJ652dQQGKz/KimcUjFZJ3UP/T87kMN+9s3\n/PD2DZWLV63OneYLifCsSstdtTp3Q+XikyeHLPs/fnD9y7cunHNFMaPHnnXJS3YM0BYkBrv25RuM\nNo8L5tI6P3ZZpQcKEo/QXnlHu4BU7/CYBOr5uro2X9kiQZXwSI6KVq3O/fCTR6/nVGJaAqkqkXNW\nP9Zw68I5GyoXs4+WTIYYYgGnqkkMsna0ewihr4Ee6LLjDqJGVE0NtAtILTS/bmSqG4fKFulpjzKR\n53cfumv5bgA48HblhsrFSp1WTEvYULn4uRfuE9MSHlz/8vO7Dyl15ulTtTKhzuqnPUqhKLS46Jq/\npRGK5yefTTR/0wAFiTsGvA6qhm82K5BoF5Dq2nzpyTGMwyOpf+iu5bsb9rcrK0WhyLL00Yd9dy3f\nPalPjx5FZl16cgztBndFRqG+k6L5m8FqJD0GSXRAQeIO2vk6KUC9nyaD9bDVjUNVK5kmtRr2t9+1\nfPeq1bkH3q6knU8T0xKee/G+DZWLqx9rYBwqVa1MqG4cojqEKT7W6aPb/DvfYKTa1A53j6UEChJ3\n+Ec8VC120oiPqqOhnv56WPbhERGGZ1+8j1JgNCmrVuc+98J9DfvbWWoSCZKobnNOmn9TzdrlJ9Hv\n1zCIKTvlQUHiDtpr7mweKd8g0jt/i+QrohwetTjOsqweVT/W8NGRvgNvV7L3v4lpCew1qWyRvqaJ\nbpBUZjbQ7iEkjQzTOz8A4D4UNEBB4g7qKTvKjgaqBipCXZuPWXgkqxGb4SbCXpOKzLpeN93WdmTL\nPqpDUPU1oNGOEihIPELPYmfpd1ANjwDA6Rulavgmbm82netUVyMCY00i/m+q1gaTQLeMRNvXoNcl\n48ZINEBB4o5ZlFuS0O4YRL+A5C8yz6Q6BOH53Yd4UCMCY00qW6Sva6Pr/2awMICqrwE3RqIBChJ3\nCDRXINkGXbRXINEvIAXKFlH/LpP6h57f9b9bt62iPdD0kTWJgRe8yKwj+8HTG4K6r4FmLzsCRkiK\ng4IUcYg6ugUkeieHS/k6qkMQfv5Yw7Mv3qd629NxkFVK1Y810B7IZKBuYiwyCnSd35SNdilJZhQk\nxUFB4g59HMWUF22LHe0VSC2OswzydaRTKm9qRFi1OldMTWCQuCs0z6TqtTPFx9L3NdA12iGKg4LE\nHbSbBtE7OYGqo4HBnj0AUP1Yw4YfsltvdLU8vm1Vw/520jKcHvcvEqh67YivwemjpUlUU9MAoNcl\n41IkxUFB4g7aW/PR+6DSdjQ4PeednvO0/XUPfv/lVatz+QyPCKQZK+0gibzPtMtI9IIk0tGO3h0Y\n7c9pZIKCxB30ljjYPC6q+bpeane7BAZ2ho+O9NmO9HHlZZiUDZWLPzrSR9vdkJ4c09KlaV+DSE+Q\nBJ0B18YqDgpSBCGNDFPNYziHR6la7BgUkJ7fdYh/NYJL7obnd9ENksoW6VsdZ6kOoekyEpoaFAcF\niTu0mwqgVw8gMCgg2Y70TX+fPXW5deEc6eQQ1SDJZIihWkYqMgpUrxkxTqDXSli7n1OeQUHiCAZ9\nvmlHSFQtdk4P3X42ZMM9qkMoiJiWIKYm2I446Q2Rnky9HQbVCImBr4Hq+SOQcBCkCxcu/PnPf25o\naPjkk0/G/crr9f7v//6vKrO6Bmgv/JZGfFQXIVG92yXVdaqOhud3HypZ/VV651ecDT9cTBzqlKDt\nazDF091TGJjYShEF0fwW5oODgw899JDdbic/fu1rX9u5c2dSUhL58ejRo+Xl5Z999pl6E4ws6Hm+\nnZ7zVB0NHx3pk/qHeDbXTSQ1NUHqH/roSB+9aVMNkmTnN6XLRtQJuE2fttB8hLR9+/bOzs5t27b9\n/ve/f/LJJ48dO7Zhw4Zz586pPa9rgUmf73hKJ2+VfFRXIPVSztfZjjg1lK8jiGkJq1bnUs3aFZpn\nUjXamQSKy2PpXe0IJTQfIb399tsPP/zwd77zHQCYN2/eV7/61XvuuWfXrl2bNm1Se2rQ3Nzc0NDQ\n1dUlCEJ2dnZ5ebnJZFJxPrQXrlPNwDjdF6ha7KT+ofyFav51ro38haaG/R9voNkA1um+QO/kDLJ2\niIbQdoR04cIFr9ebnZ0tHzGbzY8++mhtbW13d7eKEwOAbdu2/fCHPzx48KAgCKdPn963b983v/lN\n1Qta9Mq8tC12tKGa+KKHmJYgnaTYsiHdEEPbS0IVqjdhVPsgRybaFqTo6OiMjIz3338/9OB3v/vd\nhQsX/vSnPx0dVe0rsq2tra6ubs6cOU1NTa+++mpjY+OOHTvOnTv32GOPBQIUEyDqQjVlR7tHg9Q/\nJKYl0Ds/JVJT6c6Zwb5T2u0ehCiOtgUJAO69997f/e53TzzxxAcffDAyMkIObtu27eTJkxUVFWrZ\nGV5//XUA2Lx5c1paGjmyYsWKO++80+VyjZPPUHCd3RT0us/TK7Az2NCBEkREqc6fdkc7eidHNIfm\nBWndunU/+tGPDhw4sH79eofjYq/D1NTUF198cWho6Fe/+pUqs2pra4uOji4qKgo9uGTJEgCwWq2q\nTAkoW2Bp9w2iaveS+oc052iQEVMT6MVJDJYiUb1yqF7zVBvzRyaaNzUAwMMPP/zAAw/09/enpqbK\nB81m8xtvvHH48OE///nPjOdz7ty5U6dOzZ49W6f7UluBuXPnAsCJEycYzycUqkkMqgVqql0+NU1q\nWsJHR/pWpdESVKo1JKrXDKbsNAfvEdIV60ANDQ0AcOONN5rNZr1eH/qrGTNm/MM//ENlJestqE+f\nPj02NpaQMP6mlRwZGqK7awCCIIhG4V2QysvLOzo6Jv2V3+//6U9/+pOf/ITxlK4IWQUVEzM++iRH\nNLpGCkEQhDa8p+ycTueaNWt+9rOfrV27NvT4n//8582bN/f19cXGclcUjY6OhsmEhxwhv52CefPm\nkQfYYAJB+ET+kCLKwnuE9NBDD0VFRT3xxBObNm3y+XwAMDY29uyzz65du7avr2/BggVvvPGG2nMc\nT1xcHADIlj8ZcoT8dgo+uwSl6SEIcp2QT+j/vPVrtScSbvAuSGvXrn399dfnzZvX1NR09913//GP\nf7z//vu3b98+Y8aMTZs27du3LysrS+05jkcQhPj4+OPHj1+48KUl7r29vQAgihS3yFMXqp2bqS6I\nEdMSTlLeEZwqWlxBRaC9HxJV/CO4QZ/C8C5IAGA2m//nf/7n/vvvP378+D//8z9/+OGH8+fPf/31\n1x966KErpr/UIicnZ3R0dFz3cZvNBgDz589XaVIANF2w6fQXlNBbEJOaSrffAVU+OtJHz/bd66a+\nZzy9KwdbfWsODQgSAMTGxi5YsEB2Uefk5MyePVvdKU3N8uXLAeDpp5+Wj0iS9Morr0RHR99xxx2X\nexXt7VVou2Cpdg+ivSBG0myERLXHhNNDcT0yA9D5rS00IEiDg4MbN278l3/5l7Nnz37/+9/Pysp6\n/fXXV61adfjwYbWndlm+973vZWVlffjhh9/61rf27Nnz5JNPfuc73zlz5swDDzwQuliKPfTuGRks\nuae3IEZMS8hfOEeL/Ro+OtJHO19HNUKit/cEYISkQXi/9zl48GBVVdUXX3wxa9asZ555ZtGiRYFA\n4Je//OUrr7yyfv36tWvX/uu//usVbQLsueGGG1566aXq6urm5maSuNPr9T/5yU/Ky8tVnJWmu/Gb\nDDG0d6CQ+odgIdURlEdzeziNg3YNSdPXfATCuyA98cQTX3zxRVFR0S9/+Uuy7Z5Op3v88ccLCwt/\n9rOfvfLKK4cOHWpublZ7mpNw00037dy586peoukdkU3xFDe2AQBTMt164arVX9Xilki2I06qEVKL\n4yztd55eswba+634sPmk0vCesrvhhhu2bNnym9/8Rt4ElvCP//iPf/jDHxYvXnz8+HG15qZFaH9E\n6VGUpWt1nKV3/ls1m7JbdRfdbdfTKafs6J0cKNeQ/AF02SkM74K0Z8+e9evXR0VFTfzVTTfd9Pzz\nzz/22GPsZ0UJgfKOyGKcIAUo1pDIdtSUzp+eHEO17bSYliCmJmhLkxr2t4upCZQjpECRWXfl510H\n2PAbkeFdkNLT06f4bVRUVFlZGau5aB7ajqNCUaCataO9U9yq1V99ftchqkMoi+2Ic9VquuER1W2o\naG97LwV86LLTFrwLEqIs2vUdmQwxRWYd1Z7fty6co63VSA3726k6GlocAdoWu0KRomBIIz5RRzVl\nhzUkhUFB4gjapob8JJGqIJmE2BYXXcGjGiSRrF3D/nZ6QyhIw/72VatzqebrnJ7ztPN1CBIKChJ3\nUL3tompqoLq3DQAUmmfWtfmpDrHhh4uf362NrF31Yw0llPN1LY6zReaZFM8v+YpoRkg2j0TP9u0P\nuDVti+UTFCTu8FGz7tDOpxcZhVaJYoR0/yKBqq8BAG5dOOfWhXOqH2ugOsr1U/1Yw6rVubRXINF2\nNFC9WoCk7Khd876AR0/ZhRSBoCBxB70ISYwTpBEfxWYNtJciGWKA/taxGyoXf3Skj2e73UdH+hr2\nt2+oXEx7IKqOBgLVGhLQvAnzB9wCRkhKg4LEHVRTdvkGimUk2s5vAEhPjmnpoitIYlrChsrFPNvt\nnt91aOu2VbQ7BtW1+coWUW9+SM9lZ/O4KC9CQkeD8qAgIUpC2/ldtTKB6vJYAkmF8eluILNi0FGC\ndgGp3uGhbLEbzjdQ3OrFP+LRx2HKTmFQkLhjYNBB7+T5BqNtUKJ3/kJRoGq0o708liCmJRB3A28t\nwKX+oerHGjb8kHqyDgDq2nyaXhJLbw24DJoaFAcFiTto9yOxeVz0Tk7b12AyxKQnx9AuIwHArQvn\nbKhc/OD6l/nRJKl/6OePNWzdtopBN1WSr6NaQKJtsZNGfPlJRnrnH/A6UJAUBwUpsshPEmk7v2n3\nby5bpK9pYiESq1bnrlqdy4kmETVKTUtg0/61rs1PNV8HAK2Sj2rKzuaR6KbsAm7avb4iEBQk7vAH\n3FSNdpTOTCBJGKpBUpFZ1+s+zyBIAoANlYt50CRZjbZuW8VmxBZHgKqjoVXyUXU0AJOmJBghKQ4K\nEnfMSjTTXopENWtniqfbr+Fi1o6y105GdU1ir0Zs/HWlZorhBVEjerdfmK+jBAoSj1B1lNLesqxQ\npFtGAoCqlQl1VrotG0JRUZPYqxEAVDcOlS3SUx2CQY+GkjQzvfP7A+6URIrnj1hQkLgjJclMeSkS\nXaNdmdlAu4xUZNaxsTbIyJrEsrHQ87sP3bV8961fm8NSjerafABA219HvYA0SHcR0qlBB3q+aYCC\nxB2zErPpOr+TRLopOyHWFB9LO0hiZm2Q2VC5+LkX7mvY337X8t20+zhI/UMPfv/lhv3tz754H4OO\nDKHUtfm3FtNdclvv8NAuINk8EtU+34AFJDqgIHGHoDNQdX6LcQLtfWNpr0YCttYGGTEt4bkX7lu1\nOrf6sQZKoZLUP/T87kMPrn/51q/NOfB2JQOHdygtjgBtOwMAtEg+qgUkIJ5vmha7Aa8DU3Y0QEHi\nEco1JEGMi6e9Gqm+k+5qKpMhZmtxAuMgCS41FnruhfsA4K7luxWUJSJFdy3fLfUPHXi7knFgRKhp\nGtqzjvqNf6vkK6MpSOTapt03CCMkGqAgcYdelzwr0TzgpZi1AwCqZSRTfKzTN0o7a0f262McJBFk\nWZL6h+5avrv6sYbr6TMkSxHJ0bGsGIXCJjwCFvvyDVN1NKDFjh50W/ki18wpbye9nEBJapblZBfM\npXR6MAmxJGtH9XvHZIjZsy65pmlIrU3kxLSErdtWSf1DDQc+btj/8fO7D926cE7+QpOYljB1qo24\n9RoOfAwAz+/6XzEtYdXq3A8/eZTRvC9DTdNQFeXqEQDUOzy083W2QRfVHg1osaMHChKPpCSZBwYd\nuem0zp9vEGuP2WmdHQAAqvKMFa19VXkUvxcAoMisq2vzM1g3MwUkWtpQCVL/0EdH+mxHnCf3Dz10\npI/sP5v65Z7cJ/uHbEf6yKtuXThHTEs48HYl7b7d06GuzdfrPt+8MYX2QDU2V20h3cKYzSNVzM2j\nd/5Tg45ZSShIVEBB4pFZidndUhu988tlpHwDLcGQs3a0g6SqlQnle90qCpKMmJawKi2XtPYhMdBE\nM17+Qtjww8WMrQrTobqRUfWIdr7O0u+gui8fAAx4HbkZxfTOH8mgIPGIoDMw2G3FNihRFCQh9t/y\njXWUtxiAS2uSyve6GXyfTh8S9KxKY9F37vqpbvIWmXUMMp919PN1AEC1gAToaKAJmhp4hIGvoWJu\nHlWjHQCUmQ20fQ2EPeuS1XI3hAFOz/maxiHaa48ItP11QL+A1O2yzsICEjVQkDglJcl8yttJ7/wM\nViOxWSELlyzg5XtxB89roXyvu6o4gfZW5QBQ7/CY4mNpR8yWfgfVFUgAgDuX0wMFiVNo92tgsBoJ\nAMrMhho73SEIJHFX3eRlMFY4Qd6xrSsTGYxV5/DQDo8s/Y6SNDPtpkHoaKAHChKn0O7XAAD5BiNt\nrx1ptMomSNqzLrnO6sfE3fRpcQRqmHgZAIBcBlo3fANAt8uKnm96oCBxil6XrNcZqJaRSlLNDLJ2\nxNpAdZSLY11K3Dk91Pc4DwOcnvPle93NG1MYJOuAlZ2B9qZ83S4rYBc7mqAgcQ3tMhKbrB0bawMA\nlC0Sygr0WEyaDuV73WUFemZriusdnqp8urELA8M3AGQaC6ieP8JBQeKX3IwSqmUkAMg3GC0n6Q5B\nrA0VrXTbY8vcv0iAS6UR5HIQzWZTOgKAGrur1Gyg2t4bAGyDLtqGbywg0QYFiV8YlJFKUs02D8Wm\ndoTawjnMgiS5mISadDnq2nwtjgCDpgwyv7C5aNsZgH6DBsACEn1QkPiFQRmJTdaOcZBkMsS8+0gK\natKktDgCbJoyyJDwiIHbW4yLp5qvIyuQsIBEFRQkrqG9GgkASlKzaHvtgG2QBCGahKa7UFocgaU7\nB/asS2bZjpZReDToKknNojrEqUEHrkCiDQoS19BuagcA+QaRttcOmAdJEGK6Q00iEDVq3pjCUo3Y\nhEfAZD3sgNeRIaKjgS4oSFxDmtoxyNpZ+ulaG4B5kAQAZYsE1CSCKmoErMIjButhAXedYAIKEteQ\npna0s3YVc/MsJ7uoDgGXNkliGSQBQNkiYc+65PK97kiuJ6mlRhWtfYzCo5NdDNbDouGbAShIvMPA\n/E362tG2NgBAVb6RTeOGUIrMukj2ONS1+cgCWMZq1Cr5GKw9AgCbx2XzSLQN392SFQ3fDEBB4h0G\n5m8xTihJM9NekAQAJiG2Kt/Iprvdl8aNVN9d+V438dSx31S3xu6qLZxDe+0RAFhOOmirEQCc8jow\nQmIAChLvEPM36VlCDzYLkgCAJHDqmTQTCkXWpKzH+yOht5DTc37pzgGn53zXz9PYqxH5+zLoFQQA\nln4Hg+VHqEZsQEHSAJliQbdEV5CYWRtMQmxVnrHGxjpIgkuaVFagX7JjILxtDi2OQNbj/YXmmSxX\nv4ZSY3PR3r2ewMbOgA0amIGCpAFSEs20s3YAUDE3j8GCJAAoFAX27gaCyRCzdWUi6XcXrum76iYv\nsTAw6ww0jorWPvInZjBW7TF7SSp1qcAGDcxAQdIAbLJ2+QYjg64NBFXcDTJbVya++0hKq+NsmKXv\nSJqu1XFWlTQdgXgZagvnMBiLdGfIN7Dw12GDBjagIGmD3IwS2lk7AChJzao52kp7FLjkblAlSLo4\nAUPMnnXJJH0XHqFSdZNXTtOx2VFiUipa+94pptsxQcZysot2dwZAfx1bUJC0gaAznPI6qK6QBYB8\ng8gsSCIrVNTVJBIqAUDW4/3alaUWR+CGHzlJYKRWmo6wrLGLWbLO0u+QRobRXxdmoCBpA70uOdNY\nQHuFrBgnsGltRyCJO/aOu1BkWSIGPG2ZHUiOjiwzUjcwAoBWyeccHmWTrAMAy8ku2uY6QH8dc1CQ\nNEOGWEC7rx1cam3HJkgyCbG1hXNqbC6nb5TBcFPN5JIBj3y/8y9LZL/XJTsGCs0zVawY/XU+vtFl\njV3M1IjNYlgAaO9pxP51LEFB0gwpiWbau1EAgBgnMLPbAUChKJRmG5ZZqDcuuiIkVOr6eZopObp8\nrzvr8f66NnU8F1ND+gAt2TFgSo5WPUcnU9Ha92/5RjbJOgCoPWavWrCY9ijdLiv2r2MMCpKWyBQL\n2nsstEdhGSQBQFWeUd1iUihyBm9rcUJdm5/Ulnhw4jk954ltoXyvm0RFnEgRACxr7AIANguPAMDm\ncTGqHg06CnJKaY+ChIKCpCXYLEgiQRIbux2BFJPYtxS6HCZDTNkioXljytbiBKf7wpIdA0t3DqgS\nMBEdWrpzIOvxfgDYWpzAlRQBQI3d5RweZeasA4DaY3YG1SPA5UdqoGYVFLlayIKk9l5LbnoJ1YHy\nDaJ4ssvmcdFe5EEwCbHvlGQts3QVGRl5tKZJ2SKhbJHg9JxvcQTq2vzVjUNFZl2ReabJEEO1bOP0\nnH+pzdfqONviCJgMMWUFerV6LkxNq+T7hc3FUo2Ymetw+ZEqoCBpjNyMEmtHPW1BkoOkNwrXUB1I\nRl6Z9E5JFoOOnFcFCZhkZWpxnK1rcxNNUkqcSFbwpTYfANQ0DhERUrEYfosZAAAgAElEQVT3z3Qg\nRoZ3irNY3kPUHrNXLShkMFB7TyPm69gTFQwG1Z4D8lfmzZv32WefTf2cbpe1W7IuzdtEezLSiK/y\nSOPuhcW0e4WFUmN31Xd6Ou+Zz2zE64fISYsj0Os573RfIEd63ecnFp+IMzs9OYY8MCVHpxtiaMdb\nNFjW2EVMkiwHLXjrd7sXFjOI2pvt2zPFgukYvqfzgUWmD0ZI2iMl0dze0zjgddBOcItxQr5BZONo\nkiG18ezXPtWQJhF1KVvEUbKRKsTFwFiNao4eKkkzM1CjAa/jlNfB4IYPmQiaGrSHXpecm1HcQ7+T\nEJDNZPsdzBx3hDK1mzggU0DUiGXdCABsHpel38HmxqhHsuZmFDMYCJkICpImSUk0D3gd/oCb9kBi\nnFC1YDFLxx1cqic5faOoSbyhihoBq4VHBOzOoCIoSJpEr0smiTsGY5EGd8yWyhJIfcLpG+XHC46Q\n+wP2akS26WLgrAMAa0c9mutUBAVJq+RmFNPu2kAgQZKl3yGNMF2IQzSpVfJhnMQDyxq7nD6m640I\n0oiv5ughNguPAKDbhfk6NUFB0iokSLJ21DMYS4wTStLMNUcPMRgrFKJJpvjY7Nc+ZTw0EopamToA\nqDl6qCIrj816uPZeC4ZH6oKCpGGYBUkAQPblZLDH+ThMQmyZ2VCabch+7VPVe7BGIGSxEaikRuR6\nYxYetfc0YnikLihIGoZxkFS1YHHtMTvjxB0Qj0OekfRgRU1iCfGVmIRYVdSIcbIOwyMewHVI06K5\nubmhoaGrq0sQhOzs7PLycpPJNPVLGhsb33vvvXEHk5OTt2zZouDEcjOKm+07FDzhFMiJu90LV7IZ\nMRSyPqmitY80Y2U/gUijVfIta+z6t3wjs66p46g5eqhqwWI2yToAaO9pvOu2ajZjIZcDBenKbNu2\nra6ububMmfPnzz99+vS+ffsOHDiwa9eu22+/fYpXWSyWgwcP6vX60IOpqanKzk0Okti0OSlJNds8\nLmbdLcdRlWesFzwVrX2l2Qa1viUjhHqHh2xGrpb2E1cnG2cdoLmOH4LIlFit1uzs7KVLl544cYIc\nefPNN3NycgoLC0dGRqZ44ZIlS+69996rHS47O/tqX+Ib+WL/B1W+kS+u9oXXxskzw6tbXvvILbEZ\nbiK9w2fNr35SbVNtAmFPeYvT/OonLSeH1ZrAR25p0Zt7Tp5hNAHfyBcvH6y8tk/QNXxgkSnAGtIV\neP311wFg8+bNaWlp5MiKFSvuvPNOl8v1/vvvX+5VZ86cOXHiRE5ODoMZslyTBCF9V9kXkwikNTgA\noM1BcYiFwekb7bxnvop50ZqjrSw7KLb3NGJ4xAkoSFegra0tOjq6qKgo9OCSJUsAwGq9bPOezs7O\nYDB4yy23UJ8fAFyy27Fz3KWZS9LMjJfKhhJqc8CVs0rRKvmyX/u0UBRUsTDIVB5pyjeIzEpHA15H\nt8uKjb05AWtIU3Hu3LlTp07Nnj1bp/tSM+a5c+cCwIkTJy73QtIA2Gg0Pv3000ePHo2Li5s3b15p\naelNN91EY56ku117jyWFVUfIklRzzdFDahWTCFV5xjLzxe3PsaR0PTh9o3UOT32nR8WiEYHc5bBs\n5tveY0GrNz9ghDQVp0+fHhsbS0hIGHecHBkaGrrcC4kgbdq0qa6uzuPxWK3W5557buXKlR988AGl\nqZLNZJkFSXL7BsZ9V8cRmr5rldRJIWodEhg5h1VO0wGAzeOq7WJ6izPgdfgDHtq7iyHTBwVpKs6d\nOwcAMTHj40hyhPx2Uj777LOoqKiKioo//elPf/jDHz766KNNmzadPn16y5YtPt8VvjfnXeKqpkqC\nJDZrkgiqF5MIJH1HNvfD9N1VQVoFEjcd470kJiJvvsUsWQcA7T2Wa0vWXduHFLkimLK7yObNm8+e\nPRt6pLq6Ojo6GiYTHnKE/HZStm/ffu7cOdnkHR0d/dBDD3V3d//+979/6623vv3tb08xk2ve7yvT\nWNAtWRlscC5TkmaWAr7KI43MNpa9HKVmQ6Eo1Dk82a99iqbw6UCM3YWiwMm+UyxbBBHaey0AcG2b\niskfUtQkZUFBusi777575syZ0COPPvro3/zN3wDAyMjIuCeTI3FxcZc728033zzx4PLly3//+987\nHBSzarfllDbbd7C0DJEES+WRJlVWy4ZCQiVSVarv9HC4FTonkP4LzuFR1StGMpVHmoBhiyAA8Afc\n7T2NS3AXPs5AQbqI3T65Zyw+Pv748eMXLlwIjYd6e3sBQBTFy51tbGwsKioqKioq9KAgCADgdlPc\nxEivS84UF7X3NLJ0Dam7WnYcpKpU5/Ass3RhqDQO2bxQmm2oKublnSFNexnf0BzuqM80FtDecxm5\nWrCGdAVycnJGR0c/+eST0IM2mw0A5s+fPNfR29ubk5Pz4x//eNxxEuZnZdH11GYaC1hawCHE4KCi\nETwUEirJZgcsLMGlchFpmt55z3x+dNrS77B5JMZqRLwMaPXmEBSkK7B8+XIAePrpp+UjkiS98sor\n0dHRd9xxBzni8Xjeeuutt956i9SWTCaTwWA4ePDgX/7yF/lVXq93z549MTExy5Ytozph9u4GABDj\nhN0Li0mcxHLcKZBlyTk8GsmyJEtRq+TjSooAwOZx1Rw9VLWgkPG4zFptIVdLVDAYVHsOXHPu3LnV\nq1d3dXV95StfKSkpGRgYsFgsX3zxxYYNGzZv3kye09bWVlZWBgAffvghcYS/9dZbGzdujIuLW7t2\n7bx58yRJevnllz///PNHHnmksrJyiuHmzZt3zaaGUIggMf7UEaNU1YJClqXp6eD0jdbYXK2SL6KS\neCRB9wubq1AUagvn8FZRs3lc7G11AGDtqPcF3EsVqh4p9YFFLqJ27yIN8Pnnn//oRz/KycnJzs7O\nzs7Oy8v7zW9+c/78efkJpN9ddna21+uVD7777rsrV64kx+fNm7ds2bK33377imMp1RqLNLhzDXYq\ncrbp85FbUrfT3RT0Dp8lXdrKW5wqNmpjQO/w2WqbFFtrL29x9g6fVXs6k0C61bG/TlyDndfctm5S\nsJedsmCExBcK3nB1u6yqdNQnxSSWvciuitC4ocxsKDUb1J6RkmgiFpRGfHe37mMfGwFAs317bkaJ\ngl4GjJCUBWtIYUumsUCvM5DFFiwpSTNXzM2rPNKo7oLZy0FqS533zC8zG8i6pRq7S+tdHkihaOae\n/1tm6TLFx/JWKwpFRTW6noVHCBvQ9h3OkGVJsxKzGX8I5QWz3MZJJiG21GwoNRtIwLSsscskxJZm\nG4qMAidLc6aDbOMGgNJsQ+c983krFI2DqBHLbfdkBrwO3IKPfzBlxxeKZwDUStwBQO0xu6Xfwa0m\nheL0jTqHR+scnnqHh39lGqdD6UKsJhKPshox23YvlAOHtxbklCp+Z4YpO2VBQeILGte3Ko47AtEk\nDn13l4MoU4vL1yr5nMOjhaJQJAomIVZ1cSIiBAC/sLn4l8yJqOWpIzTbtwOAUs66UFCQlAVTduFP\nbkZxs31Ht8uaaSxgPHTF3DxRJ9QcbdWKJpmE2IvykwdO32ir5GuRfCRsMsXHFopCkVEwxccyyIyF\nSmOr5COzIvUhzvNyE1FXjcgyWEzWaQKMkPiC0g2XP+Butu9YmveIKttikvVJxOzAfnRFkMWJPCD6\nZBJii0QBiIxdh0qRfW9bJV/vpQdkCAAozTaAxnd7UleN/AH3gcNbl+RtolRGxQhJWVCQ+ILe9d3e\na+mW2tS6T5RGfDVHD+UbjNrVpFBI+OL0jRKJAgBZQgDAFB8LAORH8vhLrx0elXdeJ4/lZxJh01Yu\nbmrIGgAV4+Nm+/aUJDO9/vcoSMqCKbtIIdNYMDDoYLk5RSik313lkUZg29SZEiSzBwChbgIiM87h\nUflx7yXhCUUOqsiPYaM9E1G9gkh83rj/noZAQYoU9Lpk4gLX65LZF5PgUr+7yiONNo9L9b0qaHAx\n0NFagYcSZEcJFTfKGvA6VEwJINcGLoyNIPS65KV5j7T3NPoDFLfAmAKiSfkG492t+/hcNotcP9KI\nr/JIkxgnqHjb4Q+437Vvxw6qmgMFKbIgvcCb7TvUmgDZ+LwkzVx5pNHSz26PDIQNNo/r7tZ9+QZj\n1YLFKk7jcEc9jVVHCG0wZRdxZBoL/AG3uh34K+bm5SeJNUdbpYAvDEpKCKH2mL22y66WoU6GrDpS\nJS+NXCcYIUUimcYCX8DNvs1dKPkG4+6FxZZ+R+WRJkzfaR2SpiONOdRVI3JV01gDizAABSkSIQaH\nbqlNXU2SS0rE6aDiTJDrgaTpxDjhjcI16qoRMTKgGmkXTNlFKMTgoErr1VBISQkAao62anrlbMQi\ndyxUvRPHgNfxrn37ElQjLYMRUuQib3aululOpmJuHknfoftOQ/CTpoNLtjp6HRkQNqAgRTSZxoJM\ncVGzfYfqmkTSd8R9V3vMru5kkCtSe8xO3HRvFK5RvZu7P+BWx1YXwDyzwqAg8YTXDsD6Ks9NLyGa\nxHLQSSHpOwyVOCc0MOIkxXq4o15QY7n32GHVlv2GKyhIPJGYBwDBnhcYD3tJk7YzHndSMFTimdDA\nSPU0HYFct+zXMATtG6OMYdhwRF1QkPgjIAVdTYzHJHeXZOck1ZFDJWLfQgMeD3AYGAHNjY6mJuhq\nCgZcUTmPMh437EFB4o6onJ8Fe15gnLgjRnDVFyeFQvqxyqESZvDUQhrx1R6zVx5p5Cowgkv3TyqY\nvAOuYMdTM1CNKICCxB86Y5S4MtjxJONhOVmcFAoJlUiDTszgqQLJ0QHAG4Vr+AmMAMDaUT/gdaiy\n5CjY8WRUxnqSYEeUBQWJR0huOtjLuphEFidxpUkwIYOHHfDYIL/bXOXoCESNVOnkTT6VUenr2Q8d\nCeAGfXzx1/2+Aq4x+8YZOY+yvxEj28tmios43EiGbPgGAFrZE12L2DyumqOtAEDa4Ko9nfGoqEbg\ntY/ZH5mRt0P+VOIGfcqCnRp4RWeMylg/1vHUjNv2MR5ZbuIA/G1uVpJmzjeINo9EvjFRlpSFbOwr\njQxz2zVDTTUCGOt4KlSNEMXBCIkvxt1wBXtfgBF1zDw8x0kAII34LCcdJH2HsnT98C9FoLYaBe0b\nASAqb2foQYyQlAUFiS/GX98BV7DjSUjKUyVnzbkmAYA04rN5JJLE4zO/xD9ygo5nKQLV1aj3haDU\nNDFdgYKkLChIfDHJ9a1eMQkuNWURdMk8b75JZMlysovzG3yuCA0x+X/T1FpvdJEJpSMZFCRlQUHi\ni0mv76CrKdjzwoy8naBTITHlD7jbexpVvDmdPjaPy3LSYfNI+QaxJNWMebxJIVJU22WXd+9Ve0ZX\nQGU1mvKOEAVJWVCQ+OJy1/flMgZs8Afc3S5rt9S2NO8RvS5ZlTlMn9B7f0184bJBWyERgQTooOqG\ne0H7xily5ihIyoKCxBeXvb5VLSYR2nstWtEk+HIeL98g5icZI1aZQkMirUgR8JEuDva+AIP2cUaG\nUFCQlAUFiS+mur4DrjH7xihxpeqapEKf/+uAfB3bPC6iTJGTytOoDhHIbnu5GcVqGmq89iuuu0BB\nUhYUJL64wvWtqsGB0O2ytvc08my9uxzjlCksYyZpxCeN+GyDkqxDJalm1fcrulrkvV/VvO+5vJEh\nFBQkZUFB4osrXt/qGhwI/NvBpyY0myfGxecbjPlJoqbDJllrbR5JuzpE4CIKD7jGDq+ZzhpYFCRl\nQUHii+lc3+oaHAhEk/Q6g4rV5uuHKJNt0CWN+OSwiUiU2lO7MhNFCAC0lZebSLN9uz/gUd3PObWR\nIRQUJGVBQeKLaV7fV6y1MkBb1rsrMk6cAIA3fSIzlAI+WYTyDSKxbqs9NQXgwVBHmLQjw+VAQVIW\nFCS+mO71TUx3OlH1LcJIgkW76btJkSsxpOBEDhJ9AgAGEkU2fyLyc3EyHkmME8IjwTgRLiwMAAAQ\n7HgKAtL0b/VQkJQFBYkvruL65sB0R9B6SemKEEmQRoZJ/AQARB4AQIyLJw9krSIvufTb8VWc0G0G\nyWNpZFgK+ORRyMnJa2XlCz8FCoWLohEAXFMyHAVJWVCQ+OLqrm+eNIl0cwiP9N10kFUKAEgcAyEa\nA1/WnlBCVUrWs4v/6gR+MoQM4CdNB3DJ5H2VFlYUJGXB7Se0jM44I2/nmH0j6IxkTz+10OuSczOK\n9S5reIdKoYhxghgnAESKeCgOP2k6gOmavBHaoCBpnEuaFKUzqvtZ0uuSc9NLMo0FfG6khPCDHE+r\nvNJIBtWIG3ALc+1zaSs/8NrVnsrFzf0A4MDhrQNe3GscGc+A10FuWe66rZoLNQq4UI34ASOkcIDk\n68Y6nlJ3wSyBhEoAYO2oj5D0HTJN+PEvXGTaC2ARNmCEFCZEGVdGiSvH7Bsh4FJ7LgAAueklS/Me\nGRh0YKiEAIA/4D5weOvAoIOXwAhQjXgEBSl8iEpfz5Um6XXJS/M2ZYqLrB317b0WtaeDqEZ7r4W4\nXbhw0xECrrHDa6JUbQuJTARt33xx/S7Si2spOMjdycg9HXIzijONBWpPB2HHgNdh7ajnrsXUJTW6\nfm8q2r6VBWtI4QZZkzRm38iPJpGqkl6X3N7TeGrQkZtRHCFrlSIZ2UrHUcWIoJwaIYqDKbswhLfc\nHSHTWLA07xF9nKHZvgMzeOFNe6/lwOGt+jgDRxUjAqoR32DKji8UzABwmLsjkPX5/oAHM3jhh5yj\nuy2nlLs4mIIaYcpOWTBlF7ZwmLsjELMD2eivW7LmZpTwdRONXBO832dgbKQFUJDCmb9qEn9uokxj\nQUqiudtltXbUpySasbCkXWTTCr/LzrAXg0bAlB1f0MgAkE1meejBOika+DpDLgP527X3NPLSkm5S\naKoRpuyUBQWJL2hd39z0Bb8cKEvaIlSKMo0F/Ea3lGMjFCRlQUHiC4rXN/eaBChLWkAzUnQpN0A1\nX42CpCwoSHxB9/rWgibBl2WJ86+8iEJDUgQAwY6ngl477eopCpKyoCDxBfXrm+x9DjD9TZrVQpal\nlERzhliATjwV0ZYUAUDQvhGYXOQoSMqCgsQXLK7vgCvoauJzidJEZFkCAE79xGHNgNfR3mPxBzya\nSaKyveVCQVIWFCS+YHZ9c7tsdlL8AfeA19EtWbX0zahlQu8DtPSGe+1j9keiMtYzS0qjICkLChJf\nsLy+iSbxX1IKRe6Qhnk8SoRm52YlZmvpHVZjsREKkrKgIPEF6+tbIzaHcYy7f9dEVYNztBoSXeJi\nxM98ATgKkrKgIPGFCtd3wBXseSHotWslfRfKgNfRI1m7XVa9LlmLX6OqQ3RoYNBBcqEaC4kIqvp0\nUJCUBQWJL9S5vjVlc5gIqTCdGnQMeB16nSFTLEDvw9TIOnTK65iVaE5JMmtVy5kXjcaBgqQsKEh8\noeL1rcWS0jjGKVNKkhmzeaGEjw4BALlie15Qt0MdCpKyoCBRZ2ho6O67737ggQfWrVt3xSerfH2T\nkpLOyP8qpamRlYlk8yLcARFaH0pJNOvjDJrWIYCLabpgwKV612AUJGXBbt/Uqa2t7e/v9/v9ak9k\nGuiMM/J2Bl1NY4fXaDR9R9DrkjONyZnGgtyMYl/Ac8rb2d5jsQY8JGzSZKXkKgkNhkiBjbudW68Z\nctuUmDdD47dNyERQkKhw4cKF48ePO53O/fv3NzY2qj2dq0FnlDet0HT6jqDXJZMIKTf9r2FT+2AY\nipM/4CbSGypCKUnmpXmb1J6akpA0HW5rFK6gIFGhu7t71apVas/i2olKXx9lXDlm36hdp8NE5LAJ\n4Evi9K7XQURrVpKZPFB7ptPCH3ADQLfLCgDhLUIXkdN0t+3j5IIcCx5SewrhBgoSFURR3LnzYj7h\n448/rq2tnc6rgsE+ALgw9lT0jEcpTm6ayOk7aqGSivn3ceIEAESffAEr0Se9ziDokolECTrD9Tsj\nrvM/SwIgf8DtD7iJ/JD/xcWaEE+77tLa06vjqaiM9TO4CdkvjL18YewptWcRbqAgUUEQhBUrVpDH\nMTHTfZOjouYAwIWxlwGAE02SQyUYtEfl/IyTO1NlIWIzqT4RiSLBBwCQL/1ZSWb5VcrKABlaFh4A\nGBh0AIA8gYvWQbGAKwWiixwY8bTfK1GjmOhnASrUnktYgYLEHTdEN567UAwwJ3rGfWrPBQC+FCqF\nTfpuCsbpE0EOUADg1KADAHwBq//SEVktyJOFkHBKH2eQH7f3WgDAP+IhP/oC7ksnv3ie0FOlJJkB\nIFMs0FAWUXkCrrHDa7gKjAAgGOwjajQjarHacwk3UJC445ZblgEAQDVAtcpTmYQiZU83b948ZU/I\nM99Z8WO1p8AIpf+s/w/g/yl6QkXA2Eh5UJCui82bN589ezb0SHV1dVJS0jWfENc0IAgSsaAgXRfv\nvvvumTNnQo88+uij1yNICIIgEQsK0nVht9vVngKCIEiYMEPtCSAIgiAIAAoSgiAIwgkoSAiCIAgX\noCAhCIIgXIDbTyAIgiBcgBESgiAIwgUoSAiCIAgXoCAhCIIgXICChCAIgnABdmrglKGhobvvvvuB\nBx5Yt26d2nO5XpqbmxsaGrq6ugRByM7OLi8vN5lMU7+ksbHxvffeG3cwOTl5y5Yt1KZJhWv4v/NM\nJP8pJxJOH1JOQEHilNra2v7+fr/fr/ZErpdt27bV1dXNnDlz/vz5p0+f3rdv34EDB3bt2nX77bdP\n8SqLxXLw4EG9Xh96MDU1lfJkFeba/u/cEsl/ykkJmw8pRwQRbjh//nxPT88f//jHTZs2ZWdnZ2dn\nP/fcc2pP6rqwWq3Z2dlLly49ceIEOfLmm2/m5OQUFhaOjIxM8cIlS5bce++9TOZIi2v+v/NJJP8p\nQwm/DylXYA2JI7q7u1esWPGDH/ygsbFR7bkow+uvvw4AmzdvTktLI0dWrFhx5513ulyu999//3Kv\nOnPmzIkTJ3JychjNkg7X9n/nlkj+U4YSfh9SrkBB4ghRFHdeoqIiHLb/amtri46OLir60rZ+S5Ys\nAQCr1Xq5V3V2dgaDwVtuuYX6/Ghybf93bonkP2Uo4fch5QqsIXGEIAgrVqwgj2NiNP+nOXfu3KlT\np2bPnq3T6UKPz507FwBOnDhxuReSXQqNRuPTTz999OjRuLi4efPmlZaW3nTTTbTnrBTX/H/nk0j+\nU44jzD6kvIFvKEKL06dPj42NJSQkjDtOjgwNDV3uheRbbNOmTWfPnk1PTz9+/Ph77733yiuv7Nix\n4+tf/zrVOSvFNf/f+SSS/5QISzBlh9Di3LlzMNldJDlCfjspn/3/9u4gpMk/juP472FayGaR6MFA\nAwl0EnQULwaJSngQ3EUPiVBJEWqohO1i7BCKHjwI4sFCxRQVCp2HQdmhDqVlqAjGREYKQ7MhYXM6\n3P6HgQzT8D+ePc/vae/XSb7uGd8vP/Cz337P3LdviqLcvXv38+fPU1NTX758efTo0a9fv1pbW3d3\nd+Pas1pinl1OibyU0BI7JB20tLTs7+9HVxwOh6G/+PzEiUwmkzjpr1WkEvntibq7u4PB4NGdwSaT\n6cGDB2tra5OTky6Xy2azqdx9HMQ8u5wSeSmhJQJJB2/fvvX7/dGVJ0+eGDqQTpzowoULQoi9vb1j\nD45UUlJSTnu2jIyMP4ulpaWTk5Nut1uFduMvMl0Ms8sp5nH+gaWElggkHXz9+lXvFlR22kSpqanr\n6+uHh4fRL6I9Ho8QIjMz87RnC4VCiqIoihJdtFgsQoifP3+q0nC8WSyW2GaXU8zj/ANLCS1xhoQ4\nslqtBwcHy8vL0cX5+XkhRH5+/omXeDweq9Xa1NR0rB45Hr969Wp8OlVfDLPLLJGXEpohkBBHpaWl\nQojOzs6jitfrffnypclkunnzZqTi8/lcLpfL5YocSFy5ciUtLW1mZmZlZeXoqp2dnf7+/qSkpJKS\nEm0niN1ZZjeQRF5KaIa37BBHVVVVo6Ojs7OzlZWV5eXlm5ub09PTfr//3r17Rwfdbre7oaFBCDE7\nO3vx4kVFUZ4+fdrQ0FBVVVVdXZ2bm+v1eoeHh3/8+NHY2JiTk6PrQP/DWWY3kEReSmiGQEIcJScn\nDwwMOByON2/eRN7tMZvNzc3Nd+7c+ctVZWVlvb29XV1dz58/F0IoipKdnd3T02Os19SxzS6tRF5K\naEYJh8N694B/XzAY9Hg8ZrM5MzPz2BH3X+zs7Hi93uzs7GP/K9pYYptdWom8lIg3AgkAIAVuagAA\nSIFAAgBIgUACAEiBQAIASIFAAgBIgUACAEiBQAIASIFAAgBIgUACAEiBQAIASIFAAgBIgUACAEiB\nQAIASIFAAgBIgUACAEiBQAIASIFAAlTg8XiKi4uLiopmZmai6yMjI0VFRbdv3w4Gg3r1BhgF3xgL\nqOPFixft7e3p6elOp/PSpUtCCLfbbbPZwuHw2NiY1WrVu0FAduyQAHXU1tbeuHFje3u7ra1NCHFw\ncNDc3Ly/v2+320kj4CzYIQGq8fl8FRUVW1tbXV1dS0tLAwMDt27d6u7u1rsvwBgIJEBNnz59qq2t\nPX/+fCAQyMrKevXqlcVi0bspwBh4yw5QU0FBQU1Nzd7eXjgcttvtpBFwdgQSoKZAIPDhw4fIz/39\n/aFQSN9+AAMhkAA1dXR0rK6u2my2/Pz8ubm5vr4+vTsCDIMzJEA17969u3///uXLl51O58bGhs1m\nC4VCIyMj169f17s1wADYIQHq2N7ettvtiqI8e/bMbDbn5uY+fPjw8PCwpaXl9+/fencHGACBBKgg\nHA63trb6fL7q6urCwsJIsa6u7tq1a9+/f3c4HPq2BxgCgQSoYGho6P3791lZWY8fPz4qmkymjo6O\nc+fOvX792ul0Rj9+cXGxsLDQ7/dr3ikgL86QAK1tbm7W19cvLCzMz8+bzWa92wFkkaR3A0ACGR8f\nHxwcXF1d5XZw4E/skADtrKysuN1uIcTHjx8nJibYIQHR2CEB2gI0buIAAABRSURBVMnLy8vLyxNC\nBAKBiYkJvdsB5MJNDQAAKRBIAAApEEgAACkQSAAAKRBIAAApEEgAACkQSAAAKfDBWACAFNghAQCk\nQCABAKRAIAEApPAfxDaOYJc27CQAAAAASUVORK5CYII=\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ezcontour('sqrt(x.^2+y.^2)',[-1 1],[-1 1])\n",
"axis equal, title('2-norm')\n",
"xlabel('x_1'), ylabel('x_2')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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4Imj+ezfm3rsx93pmyL1c92JK8eIdBUYtqZmcK7WDtmYI+hvIq6p++XTm0rS/i5jc4/EU\nucqXHn5H0HOv0lXy3Y9JR09tbvcM7X7BQqtwDKkNO3bsIITEx8f36dOHjsTGxk6YMOHChQuHDx9m\nbVVdXZ2fn+9wOHyzSOwbsci8b9QEx5M4cDzJVBCkNhw7dsxisYwePdp7cOzYsYSQ1NRU1lZnz571\neDyDBw8Wvj7UiE2JGlFoEgeaZB4IEo/b7S4qKurTp0+nTp28x2+66SZCSH5+PmtD+rZy7969ExMT\nZ8+evWDBgldffbWkpMTwFaJGLArViEKTONAkk0CQeCoqKhobG8PCwpqN05Hy8nLWhjRIcXFxmzdv\nLi0tTU1NfeuttyZOnHjkyBEDl4casShXIwpN4kCTzABB4nG73YSQwMDAZuN0hF7aqszMzICAgHnz\n5p04ceKzzz779ttv4+LiKioqVq5cWVnZxr8F9p/wr4YasShaIwpN4pCnSVf5IoVrhSDxWCwW0lp4\n6Ai9tFVr165NSUlZsGBBcHAwvebChQvvu+++ixcvJicn82808yec66BGLErXiEKTOCRp0tW8SKEd\nECSekJAQQojL5Wo2Tkfopa3q2bNnREREs8Hx48cTQs6dO3edq0KNWDSoEYUmcUjSJBABQeKxWq1d\nunRxOp0NDQ3e4zk5OYSQ8HDmJxkbGxs9LT5xbLVaCSGXLl26niWhRiza1IhCkzjQJF0hSG1wOBx1\ndXUZGRneg2lpaYSQ6OjoVjfJyclxOByPP/54s3G6gz9w4MB2LwY1YtGsRhSaxIEmaQlBagN9ny0x\nMbFppLCwcMuWLRaLZcyYMXSktLQ0OTk5OTmZHluKiorq1q1bSkrKmTNnmrYqKyvbuHFjYGDguHHj\n2rcS1IhFyxpRaBIHmqQf/Cy7Nrjd7smTJ2dlZQ0ZMuSee+65ePHirl27SkpK5s+fHx8fT69z7Nix\nWbNmEUKOHz9OzwhPTk5etmxZSEjIjBkz7HZ7YWHhBx98UFxcvHz58kWLFnFujvWjsVAjFo1r1AQ/\n747Dvz/vDj/LzlgIUttKSkoSEhL27t1LjySFhoYuWLBg7ty5TWfZtQwSISQlJeWVV1754YcfCCEB\nAQGRkZErVqxoc/eo1ec3asRihhpRaBKHH5uEIBkLQZJLy+c3asRinhpRaBKHv5qEIBkLx5Ckhhqx\nmK1GBMeTuHA8SQ8IkrxQIxYT1ohCkzjQJA0gSJJCjVhMWyMKTeJAk1SHIMkINWIxeY0oNIkDTVIa\ngiQd1IgFNWqCJnGgSepCkGSEGrWEGjWDJnGgSYpCkCRSVXOJoEatQY1ahSZx+KZJhs9scgiSREI7\ndRc0M2rEoWiNKDSJQ3STbu5/j+HTmhw+GCsXEZ+zQ404hNYor7j+0Omf/e6SkY6QyJ7Nf9+jATeE\nz8yyCf3MLD4YaywESS6GP79RIw6hNTp0umbS6oKRjp/90qy8Yvcbj/Ua6ehk+M2hSRzimoQgGcwD\nMrHZbAbOlnE5b/q+xIzLeQbO6W3yoaOTDx0VNPmBgitBG9IPFFwRNP+9G3Pv3ZgraPKDp1xhv/3h\n4ClXs/HcIvfNy3Nbjhsi93LdiynFi3cUiJjc4/HkXKkdtDVD0COSV1X98unMpWl/FzG5x+MpcpUv\nPfyO4a8FY1+wgGNI2sK+EYcP9o2SnolouScU2TMw6ZmIRW8XHTpdY/jt4ngSh9DjSWAUBElPqBGH\nv2pEoUksaBIgSBpCjTj8WyMKTWJBk0wOQdINasQhQ40oNIkFTTIzBEkrqBGHPDWi0CQWNMm0ECR9\noEYcstWIQpNY0CRzQpA0gRpxyFkjCk1iQZNMCEHSAWrEIXONKDSJBU0yGwRJeagRh/w1otAkFjTJ\nVBAktaFGHKrUiEKTWNAk80CQFIYacahVIwpNYkGTTAJBUhVqxKFijSg0iQVNMgMESUmoEYe6NaLQ\nJBY0SXsIknpQIw7Va0ShSSxokt4QJMWgRhx61IhCk1jQJI0hSCpBjTh0qhGFJrGgSbpCkJSBGnHo\nVyMKTWJBk7SEIKkBNeLQtUYUmsSCJukHQVIAasShd40oNIkFTdIMgiQ71IjDDDWi0CQWNEknCJLU\nUCMO89SIQpNY0CRtIEjyQo04zFYjCk1iQZP0gCBJCjXiMGeNKDSJBU3SAIIkI9SIw8w1otAkFjRJ\ndQiSdFAjDtSIQpNY0CSlIUjSQY1YUCNvaBILmqQuBEkixTUVhBDUqFWoUUtoEovPmiRicjNDkCTS\ns9MNhBDUqCXUiAVNYvFBk9bdPl/EzGaGIJkCasSidI0oNIlFdJPAcAEej8ffa4B/sdvtmZmZxs6J\nGrGIrlHCM0nffpPnPTJp8s3zF40ScVt5xfWTVhe88VgvEfclr8z9YXq587L79Snhhk9OCMmtrBu3\nK2tDTKSIZ5Gz2rU1z+l0udYNH2b45CJesGaGIMnF8Oc3asQiukYLHvmAEDJ/8c/yk/ZNbuH58udW\nTxJxi2gSi7gmIUjGQpDkYuzzGzVi8U2N3vrrb5uNF54vT/r0OzSpVSo2CUEyFo4haQs1YvFXjQgh\n4X3CJt3/7+F9whKeSRJx0ziexILjSUpAkPSEGrH4sUYUmsSBJpkcgqQh1IjF7zWi0CQONMnMECTd\noEYsktSIQpM40CTTQpC0ghqxSFUjCk3iQJPMCUHSB2rEImGNKDSJA00yIQRJE6gRi7Q1otAkDjTJ\nbBAkHaBGLJLXiEKTONAkU0GQlIcasShRIwpN4kCTzANBUhtqxKJQjSg0iQNNMgkESWGoEYtyNaLQ\nJA40yQwQJFWhRiyK1ohCkzjQJO0hSEpCjViUrhGFJnGgSXpDkNSDGrFoUCMKTeJAkzSGICkGNWLR\npkYUmsSBJukKQVIJasSiWY0oNIkDTdKSDkFqaGg4efJkUlJSRkZGs4vKysoOHTrkl1UZDjVi0bJG\nFJrEgSbpR/kgXb58+be//e20adOeeOKJKVOmzJw58/Lly02Xfv/993PnzvXj8oyCGrFoXCMKTeJA\nkzSjfJDWrl179uzZ1atX79y5c82aNT/88MP8+fPdbre/12Uk1IhF+xpRaBIHmqQT5YP05ZdfLlmy\n5MEHH7Tb7VOnTn333Xezs7PXr1/v73URQsjevXvj4uImTZo0ffr05557Ljc3tx2ToEYsJqkRhSZx\noEnaUDtIDQ0NZWVlNputaWTQoEFPPfXUhg0bsrOz/bgwQsjq1asXL16ckpJitVorKiq2b99+3333\nXesBLdSIxVQ1otAkDjRJD2oHyWKxDBgw4PDhw96Dv/71r2+99dYnn3yyrq7OXws7duzY5s2bIyMj\nP//8861bt+7evfu1115zu93PPPNMTc3VvtpRIxYT1ohCkzjQJA2oHSRCyEMPPbRp06ZVq1YdOXLE\n5XLRwdWrVxcUFMybNy8zM9Mvq9qxYwchJD4+vk+fPnQkNjZ2woQJFy5caJZPFtSIxbQ1otAkDjRJ\ndcoH6eGHH166dOmnn376u9/97ty5c3QwIiLir3/9a3l5+csvv+yXVR07dsxisYwePdp7cOzYsYSQ\n1NTUNjdPPHOWCKtRbmWd0Bq9tL+ECKtRXnG90Br95Y2DROIaUT5rUl5xvfGT+6pJuZXGv0GCJomm\nfJAIIUuWLDl8+HBSUtJNN93UNDho0KCPP/5406ZNy5cv9/F63G53UVFRnz59OnX62T+adHn5+flt\nzrDVmb9u+DBBy/u6sHLmoG6CakQI2ZpW/vqUcEGTHzrtemhUF0E1IoQkffKP51dPEjS5gcL7hN1y\na9S33+QJmj+yZ2Bkz46HTruETH5jx5H9Ox/+sVrE5ISQKGtQVJcgETtJhJB+nUPu6NH9cMklEZOD\n7EFq8zhQUlISIaRz586DBg0KDQ31vqhDhw533HHHokWLBK6vNRUVFY2NjWFhYc3G6Uh5ebmP1wMA\noATZgzR37tzTp0+3elFVVdWTTz75xBNP+HhJbaKfggoMDGw2Tkc0+4wUAIBRmv+jKZvc3Nxp06Y9\n/fTTM2bM8B4/efJkfHx8Xl5eUFCQv9bGYrFYSGvhoSP0Ug673U4IuYsQf52RAQB8lUsW2v29Bi3J\nvoe0cOHCgICAVatWxcXFVVZWEkIaGxvffPPNGTNm5OXlDR069OOPP/b3GpsLCQkhhDSd8teEjtBL\nOTIzM62vv7k3/e+ClgcA18n6+puZmZn4ltFwsgdpxowZO3bssNvtn3/++QMPPPDVV1/Nnj177dq1\nHTp0iIuL2759+8CBA/29xuasVmuXLl2cTmdDQ4P3eE5ODiEkPLztA/4r7LbEzLOClhcTbv26sFLQ\nIV9CyB/G9Hg5pUTQ5CMdIYdOu0SckUzNXzSKnmgnv7+sPzhp8s2CJj90uubQaddIRxvfPLXbS/tL\npt/S/CCrUejTW9xpO4mZ56b36ytocpOTPUiEkEGDBn300UezZ892Op2PPfbY8ePHo6Ojd+zYsXDh\nwjbf/vIXh8NRV1fX7KePp6WlEUKio6Pb3PyOHt3FnVoq9LMahJA7BnQWd1Kv0E/JEEJ+eWukuNOp\nDUQ/LDV/0SgRkzd90iuyp5C39OnH1J68s4eIyZs+YxdlFfJmPv2A4IrBtjavCe2gQJAIIUFBQUOH\nDm06i9rhcPTtK/V3KOPHjyeEJCYmNo0UFhZu2bLFYrGMGTOmzc1Ff9xBaJNEf9BEaJNEf8THEEI/\nuiv6c8dCPzQt+hPfQj+uDkSJIF2+fHnZsmUrVqyora195JFHBg4cuGPHjkmTJh09etTfS2OaPn36\nwIEDjx8/PmXKlI0bN65Zs+bBBx+srq6eM2dORETE1cyAJvHmN3GTUCMW1EgHHrnt27fv9ttvt9ls\nI0eOTE1N9Xg8Lpdr1apVNpvNbrevWrWqurra32tsXXFx8dKlSx0Oh81ms9lsw4cPf/vtt+vr6/lb\n2Ww27z/mVVW/fDpzadrfBS0y50rtoK0ZBwquiJg893LdiynFi3cUiJjc4/HkFrlvXp578JRLxOQF\n+WXvrP/6j09/JmLydnts9vuPzX5f0OQHT7nCfvuDoL9Pj8dz78bcezfmCpr8QMGVoA3pgp7JHo9n\n8qGjkw8dbTne7AUL10n2II0aNcpms82fP7+0tNR7PCUlZcSIETabbezYsf5amwgtn99oEm9+MzUJ\nNWLxV408CJLRZH/LrmPHjitXrnz77be7du3qPX7nnXd+9tlno0aNcjqd/lqbb+C9O978pnnvDu/U\nseCdOp0EeDwef6+BJycnp3///qxLPR7Pe++9N2vWLB+uSCy73d7qhxuc1a6teU6nyyXoZ9zlVtaN\n25W1ISZSxKs6r8z9YXq587Jb0M+4oz9x9Y3Heon497TwfHnSp98Vni9/zn8/4w41YvF7jVgvWGgf\n2feQODUihAQEBOhUIw7sJ/Hm13o/CTVi8XuNwHCyBwmaoEm8+TVtEmrEghppCUFSCZrEm1+7JqFG\nLKiRrhAkxaBJvPk1ahJqxIIaaQxBUg+axJtfiyahRiyokd4QJCWhSbz5FW8SasSCGmkPQVIVmsSb\nX9kmoUYsqJEZIEgKQ5N48yvYJNSIBTUyCQRJbWgSb36lmoQasaBG5oEgKQ9N4s2vSJNQIxbUyFQQ\nJB2gSbz5pW8SasSCGpkNgqQJNIk3v8RNQo1YUCMTQpD0gSbx5peySagRC2pkTgiSVtAk3vySNQk1\nYkGNTAtB0g2axJtfmiahRiyokZkhSBpCk3jzS9Ak1IgFNTI5BElPaBJvfr82CTViQY1A9t8YazbG\n/gJK/J5Z3vw++T2z90z+d+/xv6w/SFCj1ihaI/zGWGMhSHIx/PmNJvHmF9+kpE/+4T0YHhGGGrWk\naI0IgmQ0BEkuIp7faBJvfpFN8hnUiEPoO3UIkrFwDEl/OJ7Em1/k8STfQI04hNaouKZCxLRmhiBJ\nhD6/T5U5DZ8ZTeLNr3KTUCMOoTU6VeZcduQdETObGYIkkZ6dbiCEvHXqCzSpGTSpVagRh+gavZC2\n7dlbfiNicjNDkKTz7C2/QZNaQpOaQY04fFOj6Bv7iZjfzBAk6fTsdAOa1Co0qQlqxIEaqQtBkhGa\nxIImEdSICzVSGoIkKTSJxeRNQo04UCPVIUjyQpNYTNsk1IgDNdIAgiQ1NInFhE1CjThQIz0gSLJD\nk1hM1STUiAM10gaCpAA0icUkTUKNOFAjnSBIakCTWLRvEmrEgRppBkFSBprEonGTUCMO1Eg/CJJK\n0CQWLZuEGnGgRlpCkBSDJrFo1iTUiAM10hWCpB40iUWbJqFGHKiRxhAkJaFJqI74kgAAFJFJREFU\nLBo0CTXiQI30hiCpCk1iUbpJqBEHaqQ9BElhaBKLok1CjThQIzNAkNSGJrEo1yTUiAM1MgkESXlo\nEotCTUKNOFAj80CQdIAmsSjRJNSIAzUyFQRJE2gSi+RNQo04UCOzQZD0gSaxSNsk1IgDNTIhBEkr\naBKLhE1CjThQI3NCkHSDJrFI1STUiAM1Mi0ESUNoEoskTUKNOFAjM0OQ9IQmsfi9SagRB2pkcgiS\nttAkFj82CTXiQI0gwOPx+HsN8C92uz0zM9PACYtrKl5I27YgeoKI16Gz2rU1z+l0udYNH2b45ISQ\n3Mq6cbuyNsREivgXMK/M/WF6ufOy+/Up4YZPTgjJK66ftLogsmdH78FDp12oUasUrZHhL1iTQ5Dk\nIuL5jSax+KBJh067vEdGOkIiewaKuC3UiEXovhGCZCwESS7int/IEovoLImGFLGIfpsu9fR7syf/\nCUEyEI4hSaSq5hIhJPX0eyImxyElFtGHlIRCjVhE12hv+trKmksiZjYzBEkioZ26E0JCQ7qhSS2h\nSS2hRiw+qBEh5K7hcSImNzMESTq/6D0CTWoVmuQNNWJBjdSFIEkntFN3NIkFTaJQIxbUSGkIkozQ\nJA40CTViQY1UhyBJCk3iMHOTUCMW1EgDCJK80CQOczYJNWJBjfSAIEkNTeIwW5NQIxbUSBv4YOxV\n2bt3b1JSUlZWltVqtdlsc+fOjYqK4m+ye/fu/fv3Nxvs3r37ypUrOVu1+sHYqppL2RdSq1ylIxwz\n27H4NuEzsyzyfGYWNWLxb43wkxqMhSC1bfXq1Zs3bw4ODo6Ojq6oqMjOzg4ODl6/fv3IkSM5Wy1e\nvDglJSU0NNR7MCIiYufOnZytWM9vNIlD+yahRix+3zdCkAzmAa7U1FSbzXbXXXfl5+fTkS+++MLh\ncMTExLhcLs6GY8eOfeihh6715mw2G+uiSlfJdz8mHT21+VrnvEpFrvKlh9/JuJwnYvK8quqXT2cu\nTfu7iMk9Hk/OldpBWzMOFFwRMXnu5boXU4oX7ygQMXmb7t2Ye+/GXEGTHyi4ErQhXdDfm8fjmXzo\n6ORDRwVNnnE5b/q+REHPWI/Hsyft1T1pr/Kvw3nBQjvgGFIbduzYQQiJj4/v06cPHYmNjZ0wYcKF\nCxcOHz7M2qq6ujo/P9/hcBi4EhxP4tD1eBL2jVj8vm8EIiBIbTh27JjFYhk9erT34NixYwkhqamp\nrK3Onj3r8XgGDx5s7GLQJA79moQasaBGukKQeNxud1FRUZ8+fTp1+tkvsLnpppsIIfn5+awN6dvK\nvXv3TkxMnD179oIFC1599dWSkpLrXxKaxKFTk1AjFtRIYwgST0VFRWNjY1hYWLNxOlJeXs7akAYp\nLi5u8+bNpaWlqampb7311sSJE48cOXL9q0KTOPRoEmrEghrpDUHicbvdhJDAwOa/UY2O0EtblZmZ\nGRAQMG/evBMnTnz22WfffvttXFxcRUXFypUrKyvb+IfS/hPOddAkDtWbhBqxyFOjq3mRQjvgtO9/\nio+Pr62t9R5JSEior68fOXLk0KFD6akNTQoKCu68887hw4dv3bq11dmKi4vdbndERIT34IoVK3bu\n3LlmzZqpU6eylnFNZ5HiXHAORc8FR41Y5KmRN5z2bSzsIf3Tvn37vvw5l8sVEhJCCHG5XM2uTEfo\npa3q2bNnsxoRQsaPH08IOXfunFFrxn4Sh4r7SagRi5w1AsMhSP+Unp6e+XMRERFWq7VLly5Op7Oh\nocH7yjk5OYSQ8HDmd8eNjY0tdz2tVish5NIlI3/LJJrEoVaTUCMW1Mg8EKQ2OByOurq6jIwM78G0\ntDRCSHR0dKub5OTkOByOxx9/vNk43bUfOHCgsStEkzhUaRJqxIIamQqC1Ab6PltiYmLTSGFh4ZYt\nWywWy5gxY+hIaWlpcnJycnIyPc0hKiqqW7duKSkpZ86cadqqrKxs48aNgYGB48aNM3yRaBKH/E1C\njVhQI7PBSQ1tcLvdkydPzsrKGjJkyD333HPx4sVdu3aVlJTMnz8/Pj6eXufYsWOzZs0ihBw/fpye\nEZ6cnLxs2bKQkJAZM2bY7fbCwsIPPviguLh4+fLlixYt4tzc9RwjxTkOHNKe44AasShRI5zUYCwE\nqW0lJSUJCQl79+6lR5JCQ0MXLFgwd+5ci8VCr9AySISQlJSUV1555YcffiCEBAQEREZGrlixos3d\no+t8fqNJHBI2CTViUaJGBEEyGoIkl+t/fqNJHFI1CTViUaVGBEEyGo4h6QbHkzjkOZ6EGrEoVCMw\nHIKkITSJQ4YmoUYsqJHJIUh6QpM4/Nsk1IgFNQIcQ5KLsW9J43gSh2+OJ80Y/rOfzPvS/hKCGrVG\n0RrhGJKxECS5GP78RpM4fNCkrWk/+5Hw/bp2RI1aUrRGBEEyGoIkFxHPbzSJQ2iTfAY14hD6Th2C\nZCwcQ9IfjidxCD2e5BuoEYfQGtW7ikRMa2YIkkTo87vmckab17xWaBKH0k1CjTiE1qjmckbBwYUi\nZjYzBEkigSG9CCGl37+OJjWDJrUKNeIQXaOib57rdWuCiMnNDEGSTq///COa1BKa1AxqxOGbGnXq\nOkTE/GaGIEknMKQXmtQqNKkJasSBGqkLQZIRmsSCJhHUiAs1UhqCJCk0icXkTUKNOFAj1SFI8kKT\nWEzbJNSIAzXSAIIkNTSJxYRNQo04UCM9IEiyQ5NYTNUk1IgDNdIGgqQANInFJE1CjThQI50gSGpA\nk1i0bxJqxIEaaQZBUgaaxKJxk1AjDtRIPwiSStAkFi2bhBpxoEZaQpAUgyaxaNYk1IgDNdIVgqQe\nNIlFmyahRhyokcYQJCWhSSwaNAk14kCN9IYgqQpNYlG6SagRB2qkPQRJYWgSi6JNQo04UCMzQJDU\nhiaxKNck1IgDNTIJBEl5aBKLQk1CjThQI/NAkHSAJrEo0STUiAM1MhUESRNoEovkTUKNOFAjs0GQ\n9IEmsUjbJNSIAzUyIQRJK2gSi4RNQo04UCNzQpB0gyaxSNUk1IgDNTItBElDaBKLJE1CjThQIzND\nkPSEJrH4vUmoEQdqZHIIkrbQJBY/Ngk14kCNIMDj8fh7DfAvdrs9MzPTwAnrXUVFJ57vNnSJiNdh\nVc2l7AupVa7SEY6Zhk9OCCmuqXghbduC6Aki/gV0Vru25jmdLte64cMMn5wQkltZN25XVlSXIO/B\nrwsrUaNWKVojw1+wJocgyUXE8xtNYvFBk5rtJMWEW6OsQazrXw/UiEXovhGCZCwESS6Cnt9oEovo\nJvkGasQi+p06BMlYOIZkCjiexCL6eJIPoEYsomvUmPusiGnNDEGSSV0BEfYsR5NYlG4SasQiukYN\n5+Z46s6LmNnMECSZBEXQ/6NJLaFJLaFGLD6oESHEMmiTiMnNDEGSTofu96NJrUKTvKFGLKiRuhAk\n+QRFoEksaBKFGrGgRkpDkKSEJrGhSagRC2qkOgRJVmgSm5mbhBqxoEYaQJAkhiaxmbNJqBELaqQH\nBEluaBKb2ZqEGrGgRtpAkKSHJrGZp0moEQtqpBMESQVoEpsZmoQasaBGmkGQFIEmsendJNSIBTXS\nD4KkDjSJTdcmoUYsqJGWECSloEls+jUJNWJBjXSFIKkGTWLTqUmoEQtqpDEESUFoEpseTUKNWFAj\nvSFIakKT2FRvEmrEghppD0FSFprEpm6TUCMW1MgMECSVoUlsKjYJNWJBjUwCQVIcmsSmVpNQIxbU\nyDwQJPWhSWyqNAk1YkGNTAVB0gKaxCZ/k1AjFtTIbBAkXaBJbDI3CTViQY1MCEHSCJrEJmeTUCMW\n1MicECS9oElssjUJNWJBjUwLQRKuvLx8zJgx77//vo9uD01ik6dJqBELamRmCJJwGzZsOH/+fFVV\nle9uEk1ik6FJqBELamRyCJIQDQ0NOTk5Bw4c+P3vf//OO+/4YQVoEpt/m4QasaBGgCAJkZ2dHRsb\n++ijj+7evdtvi0CT2HzWpCMll7z/Q41YUCMgCJIg4eHh634yb948v61D7ibZ7XbOpXo0aWn6Sfrf\n7+64fWn6SWKCGvEf1lahRkAF+nsBerJarbGxsfTrwEC//iUHRXTofn/jpU8bc5/tEPWC4dPTJhWd\neL7b0CWG/2tCm5R9ITX19HsjHDONnZz81KQX0rYtiJ5g+L/j/TqHrBhsWzHYRv9oJ+TbcWOMvYkm\n8tSoHVAjaII9JBNo2k8qfFPE9E37SfWuIsMnb9pP+kfOLsMnJ177ScU1FSLm94HimgqhNaJ7qIJq\nVO8qEloj+t4AaqQK7CFJpx3veFyLtSInT7nWDa7xzj5+rfNfvWTyirjJKaGP7APkL+ImJ4QQcg3f\nzVz7PZ1yjde/VkJfU2AYBOm6xMfH19bWeo8kJCR07dq13RNmZmZe96IAAJSEIF2Xffv2VVdXe488\n9dRT1xMkAADTQpCuS3p6ur+XAACgCZzUAAAAUkCQAABACggSAABIAUECAAApBHg8Hn+vAQAAAHtI\nAAAgBwQJAACkgCABAIAUECQAAJACflKDpMrLyx944IE5c+Y8/PDD/l7L9dq7d29SUlJWVpbVarXZ\nbHPnzo2KiuJvsnv37v379zcb7N69+8qVK4UtU4h23HeZmfmhbEmnF6kkECRJbdiw4fz581VVVf5e\nyPVavXr15s2bg4ODo6OjKyoqtm/f/umnn65fv37kyJGcrXbt2pWSkhIaGuo9GBERIXixBmvffZeW\nmR/KVmnzIpWIB6RRX1//448/fvXVV3FxcTabzWazvfXWW/5e1HVJTU212Wx33XVXfn4+Hfniiy8c\nDkdMTIzL5eJsOHbs2IceesgnaxSl3fddTmZ+KL3p9yKVCo4hSSQ7Ozs2NvbRRx/dvXu3v9dijB07\ndhBC4uPj+/TpQ0diY2MnTJhw4cKFw4cPs7aqrq7Oz893OBw+WqUY7bvv0jLzQ+lNvxepVBAkiYSH\nh6/7ybx58/y9HAMcO3bMYrGMHj3ae3Ds2LGEkNTUVNZWZ8+e9Xg8gwcPFr4+kdp336Vl5ofSm34v\nUqngGJJErFZrbGws/TowUPmHxu12FxUV9e3bt1OnTt7jN910EyEkPz+ftSH9LYW9e/dOTEz8/vvv\nQ0JC7Hb7zJkze/ToIXrNRmn3fZeTmR/KZjR7kcoGf6EgSkVFRWNjY1hYWLNxOlJeXs7akP4rFhcX\nV1tb279/f6fTuX///i1btrz22mu333670DUbpd33XU5mfijBl/CWHYjidrtJa99F0hF6aasyMzMD\nAgLmzZt34sSJzz777Ntvv42Li6uoqFi5cmVlZaXQNRul3fddTmZ+KMGXsIfkB/Hx8bW1td4jCQkJ\nSv/i81bvkcViIa39a0VH6KWtWrt2rdvtbjoz2GKxLFy4MDs7e+fOncnJyVOnTjV49QK0+77LycwP\nJfgSguQH+/btq66u9h556qmnlA5Sq/fohhtuIIS4XK5mV6YjISEhrNl69uzZcnD8+PE7d+48d+6c\nAcsVj967dtx3ObX77mjwUIIvIUh+kJ6e7u8lGIx1j7p06eJ0OhsaGry/ic7JySGEhIeHs2ZrbGwM\nCAgICAjwHrRarYSQS5cuGbJg0axWa/vuu5zafXc0eCjBl3AMCQRyOBx1dXUZGRneg2lpaYSQ6Ojo\nVjfJyclxOByPP/54s3F6eHzgwIFiVmq8dtx3mZn5oQSfQZBAoPHjxxNCEhMTm0YKCwu3bNlisVjG\njBlDR0pLS5OTk5OTk+kBiaioqG7duqWkpJw5c6Zpq7Kyso0bNwYGBo4bN86396D9rua+K8TMDyX4\nDN6yA4GmT5++devW48ePT5ky5Z577rl48eKuXbuqq6vnz5/fdKD73Llzy5YtI4QcP348LCwsICBg\n1apVy5Ytmz59+owZM+x2e2Fh4QcffFBcXLx8+fJf/OIXfr1D1+Bq7rtCzPxQgs8gSCBQx44d3333\n3YSEhL1799J3e0JDQ5944om5c+dytoqNjX3zzTdfeeWVTZs2EUICAgIiIyNff/11tb6nbt99l5aZ\nH0rwmQCPx+PvNYD+3G53Tk5OaGhoeHh4s0PcHGVlZYWFhZGRkc1+VrRa2nffpWXmhxJEQ5AAAEAK\nOKkBAACkgCABAIAUECQAAJACggQAAFJAkAAAQAoIEgAASAFBAgAAKSBIAAAgBQQJAACkgCABAIAU\nECQAAJACggQAAFJAkAAAQAoIEgAASAFBAgAAKSBIAAAgBQQJwAA5OTljx46NiYlJSUnxHv/www9j\nYmJmzpzpdrv9tTYAVeA3xgIY43//939ffPHFHj16JCUlde3alRBy7ty5qVOnejye7du3OxwOfy8Q\nQHbYQwIwxiOPPDJ69OiSkpLnn3+eEFJXV/fEE0/U1tY+/fTTqBHA1cAeEoBhSktL77///qKiolde\neeUf//jHu+++O3HixLVr1/p7XQBqQJAAjHTs2LFHHnkkODi4pqamX79+H3/8sdVq9feiANSAt+wA\njPTf//3fs2bNcrlcHo/n6aefRo0Arh6CBGCkmpqaQ4cO0a83btzY2Njo3/UAKARBAjDSSy+9lJWV\nNXXq1Ojo6G+++ebtt9/294oAlIFjSACG2b9//4IFCyIiIpKSkvLz86dOndrY2Pjhhx8OGzbM30sD\nUAD2kACMUVJS8vTTTwcEBKxZsyY0NNRuty9evLihoSE+Pr6qqsrfqwNQAIIEYACPx7Ny5crS0tIZ\nM2bcdtttdPDRRx8dOnRoXl5eQkKCf5cHoAQECcAA77333sGDB/v16/eHP/yhadBisbz00ktBQUGf\nfPJJUlKS9/W/++672267rbq62ucrBZAXjiEB+NrFixeXLl168uTJtLS00NBQfy8HQBaB/l4AgIn8\n7W9/27x5c1ZWFk4HB2gJe0gAvnPmzJlz584RQlJTUz/66CPsIQF4wx4SgO8MHjx48ODBhJCampqP\nPvrI38sBkAtOagAAACkgSAAAIAUECQAApIAgAQCAFBAkAACQAoIEAABSQJAAAEAK+GAsAABIAXtI\nAAAgBQQJAACkgCABAIAU/h8htLvnB6DrMwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ezcontour('abs(x)+abs(y)',[-1 1],[-1 1])\n",
"axis equal, title('1-norm')\n",
"xlabel('x_1'), ylabel('x_2')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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JACAFCgkAIAUKCYDTqK2vVDsCHIi7faNlt3UbfLi+Mis/Se0gwC9q6yt13j1u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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ezcontour('max(abs(x),abs(y))',[-1 1],[-1 1])\n",
"axis equal, title('\\infty-norm')\n",
"xlabel('x_1'), ylabel('x_2')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Induced matrix norms"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A matrix norm is the maximum of $\\|Ax\\|$ over all unit vectors $x$. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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2j1Iw0jqHuKB2H4WePZ1BxI+CsmTXQ20kbyi7h19tsQ6RDKWlxGLWIcSYP9br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\nEREnqJBERMQJKiQREXHC/wefhAgrwLN8DwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"A = [-2 0; -1 3];\n",
"t = linspace(0,2*pi,300);\n",
"x1 = cos(t); x2 = sin(t);\n",
"Ax = A*[x1;x2];\n",
"subplot(121), scatter(x1,x2,4,t,'.'), axis equal, axis off, title('x')\n",
"subplot(122), scatter(Ax(1,:),Ax(2,:),4,t,'.'), axis equal, axis off, title('Ax')\n",
"colormap(hsv)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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kq2MitS2vyvA1RtxaG3v0LSFEGksvWwLhZ0uSCb827pBMjHCrrKxct25dYmIi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\nJeXq2s6/fwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(t,sqrt( sum(Ax.^2,1) ))\n",
"xlim([0 2*pi])\n",
"xlabel('angle'), ylabel('||Ax||_2')\n",
"hold on, plot([0 2*pi],[norm(A),norm(A)],':')\n",
"text(6.4,norm(A),'||A||_2')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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GS5qOpHUGccpzJA/7stu3FjXkOEcXNfhbSPnEio0jiFvOo9ibEdI2HrWOIJYu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\nAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t = linspace(-1,1,100); o = ones(size(t));\n",
"x1 = [t,o,t,-o]; x2 = [o,t,-o,t];\n",
"Ax = A*[x1;x2];\n",
"subplot(121), scatter(x1,x2,4,1:400,'.'), axis equal, axis off, title('x')\n",
"subplot(122), scatter(Ax(1,:),Ax(2,:),4,1:400,'.'), axis equal, axis off, title('Ax')\n",
"colormap(hsv)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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B8qAHeDidNAUPQL/Ok/htnqMgNUPKkLtBkHjzVaBlB3YVnLyGfp1WOBqxIyhIzYLlkexC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\nYAIKEgAAMAEFCQAAmICCBAAATPh/5dFs/8D+EegAAAAASUVORK5CYII=\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(max(abs(Ax),[],1))\n",
"ylabel('||Ax||_\\infty')\n",
"hold on, plot([1 400],[norm(A,inf),norm(A,inf)],':')\n",
"text(402,norm(A,inf),'||A||_\\infty')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `max` and `sum` functions can operate along a specified dimension of a matrix, making the matrix norm easy to compute directly."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"onenorm =\n",
"\n",
" 3\n"
]
}
],
"source": [
"onenorm = max( sum(abs(A),1), [],2)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"infnorm =\n",
"\n",
" 4\n"
]
}
],
"source": [
"infnorm = max( sum(abs(A),2), [],1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Unitary matrices"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A unitary (or real orthogonal) matrix preserves the 2-norm---i.e., Euclidean distances. So they represent rotations and reflections. "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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+ZpU31iY5GkoKHb5tQF28f/qn7+w8AD89eDXbtHy6DRM7XPXv/E4OM4CDgUSl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\nYII=\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"[Phi,Theta] = ndgrid(linspace(0,1.5*pi,60),linspace(0.25*pi,pi,50));\n",
"x = [ cos(Phi(:)).*sin(Theta(:)) sin(Phi(:)).*sin(Theta(:)) cos(Theta(:)) ];\n",
"[Q,~] = qr(magic(3));\n",
"Qx = (Q*x')';\n",
"\n",
"colr = sum(x,2);\n",
"subplot(121)\n",
"scatter3(x(:,1),x(:,2),x(:,3),40,colr,'.')\n",
"axis equal, title('x')\n",
"subplot(122)\n",
"scatter3(Qx(:,1),Qx(:,2),Qx(:,3),40,colr,'.')\n",
"axis equal, title('Qx')\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Matlab",
"language": "matlab",
"name": "matlab"
},
"language_info": {
"codemirror_mode": "octave",
"file_extension": ".m",
"help_links": [
{
"text": "MetaKernel Magics",
"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
}
],
"mimetype": "text/x-octave",
"name": "matlab",
"version": "0.11.0"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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