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Created April 20, 2017 14:27
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Alternating Direction Method of Multipliers (ADMM) for Lasso
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"'%.3f'"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import numpy.random as random\n",
"import scipy as sp\n",
"from pandas import Series,DataFrame\n",
"import pandas as pd\n",
"\n",
"# 可視化モジュール\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib as mpl\n",
"import seaborn as sns\n",
"%matplotlib inline\n",
"\n",
"# 小数第3まで表示\n",
"%precision 3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ADMM\n",
"ref. http://www-adsys.sys.i.kyoto-u.ac.jp/mohzeki/Presentation/lecturenote20160822.pdf"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"N = 100\n",
"M = 50\n",
"K = 10\n",
"# A = random.random((M, N))\n",
"A = random.random((N, N))\n",
"x0 = np.vstack((random.random((K, 1)), np.zeros((N-K, 1))))\n",
"random.shuffle(x0)\n",
"y = np.dot(A, x0)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# ADMM\n",
"# initialization\n",
"x = np.zeros((N, 1))\n",
"z = np.zeros((N, 1))\n",
"u = np.zeros((N, 1))\n",
"\n",
"# coefficient of the penalty term\n",
"mu = 1.0\n",
"lam = 1.0\n",
"\n",
"A1 = np.dot(A.T, np.linalg.inv(np.dot(A, A.T)))\n",
"A2 = np.eye(N, N) - np.dot(A1, A)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def soft_threshold(y, lam):\n",
" y[y > lam] -= lam\n",
" y[y < lam] += lam\n",
" return y"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 0.084 0.973 0.791 0.821 0.213 0.103 0.21 0.87 0.19 0.67 ]\n",
"[ 0.084 0.973 0.791 0.821 0.213 0.103 0.21 0.87 0.19 0.67 ]\n"
]
},
{
"data": {
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sRN4ya6U8n6FYK8JhsBZDWGdEnu+i9KVAVRTHKAWKgDC3VrZGw4ZHJexGml89FULetsXO\nkpC3rbH0LIiQOyBLvVP084W+OoTW2jfZdvjmT0J7sgQqIMi3tnYxEloUdnjkbY7I4+4dhyLkTkgn\nrJUkdW99FDnbKC+E3J4s5YhcrBWPUQmKkH7YVo+8HJF37zgUIXdAJqzjxc5aTpI81Q9PNt/Y3XMB\nQdGsoItpX4tCmuf89/KrxrZF5OWr4LZtdpoFEXIXFCdJ7pHXYq3ki52pHxH5KE/xUkoi8oUg98jH\n1krzx5BLkglrpXvHoQi5A6x/XVy21iG0eYaIL3VNRhMRuQi5zyRJUgh50cWqbUI+EZF37zgUIXfB\nVEZAHVkrTNT+bj790PqQAWExb1ns9JMoyTKMAsLSOk7LhFw8cmF+siqAdUbkKZ5F5HnUE6ig2NHa\nxRNoERhGmcgpFdAv1nHa5SOX7ca2pVbOggi5C6xHHlqPvIaIOY/6FQofNgRFcXaylIV82MFL2kXA\nVgMM2xyRl4R8lHbvOBQhd8C0R17LYqSt/e1J1kphraixpTTqYI2LRWA7TxUNyhG5BwvmLim3Goxk\nQ5BwKKxHXlO0MyrtosysleYj8vKGoMJakYjcS+wPbJs98nJwE0tELhyKPFruBSHZXiC3Qrs9GkdU\nvnnkoQqLTAjxyP3E5vcHKqSfNz9pX0QueeTCHNiMAGU/yhryvK2Q24hcqeYPVlsGNSxdrncx7WsR\nsNlE5e+qlsyqBplY7GzZQu4siJDPSZwv+ille1Ir54udw1Kqn61rMoqaPVittRKqsOg60/SPi1BN\ncfyosNT8pGVCriQiF+bACto4Indf1MoWyi+sFZovDGRPlkAF9POm0+KR+4k9Rnuq5JG3TMhREpEL\nc1De4Qig0hoi8mKxKijep+lO4VFSjsjFWvGZckRea2ZVk5SFXCJy4aDY3odFRI5ynh44jMaLnWNr\npVnRLIQ8CIuIvIuR0CIwyq/eeqo33uvQOo88JY3budlpFkTI52Schpd75Kn7DTtFpUEVFt14mi6e\nH5U88qVcyCUi9xN7/PSCsMis8qHMg1NUgkrbWWt9FkTI5ySa8sgVdXjkeUROySNvuK7JOCIPisv1\nLp5Ai0CU5FkrecaKL81JXBElMSpIUUl9zc99R4R8TuLSoh+QReSON+xEFd14ooZF04p2qEKWejYi\nFyH3kWFpsRPwphSyK2wGV0Be2ZHuHYci5HMynbWiakw/DFVI6En6oRXtXhAyCG0k1L0TaBGI7PGT\nR+TKkwqartiyG+bSfLNTB49DEfI5KdLwsHnk7ndeFhGHCgjyqGrky4agIGDQk8VOnxn/6Pbye9wv\nyDfJqAh0bETenrnNigj5nJRtD6CW6oSjqoi84e3w1ofsBWNrpYuR0CJg8/vtWka2IN8esbPrRT0G\ngFgrwiGw0Y6yQp66L2o1Kl0aFxF5w1krcclaWerl1koHT6BFYDoizxbk22OtbOfnRy+wAUV7fqRm\nRYR8TqYj8jq26I8j8qCIyJtO9bM2Si/oSUTuOfZYscXNSNtlrdhdziEhaaomStp2BRHyOYnyX/9Q\njdMPXXvkUSkP2C5YRQ1bK+X0w+V+dy9pFwH7XdmaONnCfHsicruGFKqwdRk5syJCPieFtVLKWqnN\nWlFh0ei46cXOpPDIe/R77axx3RZsRG4bgIDyohSyK4qIXIWoNCBp0dxmRYR8TsrlXIFaysyOStvh\ni8XOxrNWspOlH+a7BRMlEbmnWBvMVj70pTmJK2yefBiErdvsNCu9/Z8CWuu7gFvIrsfebIy5v+I5\nbwNuNcbc5nSEnhMl496VMC5nG8dJKQKa9z3GPxY2Im+6ndXYI6+v6qPghmKxMy+l0LY88lE8rrfe\n1eNw34hca/0q4IXGmFuBNwJ3VzznJcC3ux+e/8SlKoAwtlhcZpVEpYgjDPywMWyubpEJkQakSiJy\nHxlH5CWPvEX2w7BU9yfLGmvP3GZlFmvlduA9AMaYh4A1rfXJqee8HfgFx2NbCKKpLfpBHUJe8jh9\nWey04tBvaf2ONrFTyN2v4zRJVKQf9mqpdbQIzCLk1wMbpX9v5PcBoLV+A/BR4FGXA1sUrFccBqWs\nFdzWQrH2TS8Ii3oZTddasVcE/V45N7l7J9AikNislTxN1Jd2ga4YlgKdtl1tzMpMHvkUdi86Wuur\ngR8FXgPcOMuL19ZW6PUO7x2vr68e+rV1sLSczeXY8hLr66tFveeTJ5dZP+1mrHF+oJ48fozeKIBL\n0OuHjX4WKsgiuquvOsH6+iqKgETFTsfk23d9VDifd5h9V9eeXmV9fbW4qjt11TIrS8tu3+uQzDPn\nwSALnlaWlwkuhsQqWZhjx9U4ZxHyxyhF4MANwOP57e8A1oGPAUvA87XWdxljfnq3P3bu3OVDDjWb\n9MbG5qFfXwebl7YAiIYJGxubpAkQwpNnLrCUDJy8h42chtsJo1EWbVy6cqXRz2IUxdCDK5eGbGxs\nZrWgg6GzMfn4XR8Fdcx7OIqgD5c38+8nzWKxx5+8wMljzZZDhvnnfP7iFQDiUVJsdlqEY+eg895L\n9GexVu4B7gDQWt8EPGaM2QQwxvyRMeYlxphbgO8HPrGXiLeRwiPPrRXrlbtsN1WuNNgrOtY3vdg5\ntckkDUhb5Lu2Cftd2eJm43Wc5kXcBeM1pF7WeEWlJA2fH0fNvkJujLkPeEBrfR9ZxsqdWus3aK2/\nv/bRLQBHkbVS1DUJx81zm640WHjkxQJa2ElvchGwpROWSh45NF+vxxXlQKdt/v+szOSRG2PeMnXX\ngxXPeRS4bf4hLRbx1Bb9ovGDwwPJCnk/CBnlEXnTDWaL9MP8hyUgQAUJSZIUVyeCH9jvymat2GO0\n6QberihqyYS9oqjcdhQVVyBdQM64OZnOWrGXrS437NgMlV7YK/K2m47IbfPeJbtbULUrymsT1lpZ\n7ucReQ32X5OUI3J7/jXdCvGoESGfkySdtFZqicjTskduT8KmPXJrrVjfNZv/VjRsbExCNeNU0fHV\nE7TnR7fwyMNecf5tR91qBC5CPifjBgtT1orDk6Q4EYOwaA7QdF2T8WJnNp4wF/LtUbdOoEUgJSZN\nVLFQHnjSnMQV9hwc2MVO2vMjNSsi5HNiV8eDqZMkcriFvvDIw7BkrTQbkadplqFSRHn5FUnXLmkX\ngezqqdj+QWgj8pZkdlR75N06DkXI56ToJj/tkTu0VsoZInZLfOMeOQlpOi6Naq2lrY6dQItASpLV\nIMlRxVVjO76rcQmCfnEcdi2gECGfkySPTHtTHrnLhaSirknYK7bEN100KyWBkjgUEXlLLtfbRKom\nv6uigmZLIvJiDSkMSxk53ToORcjnxAqq3fZsI3OXJ8k4Ig+LiLzptmqZkJcu1zsaCS0CO39027XY\naRf+B+G4FlFb5jYrIuRzMl2Xu9aIvNcvIvLGPXI1ebneK+XvCp4x9V2FNWRWNUnZWunqlaEI+Zzs\niMiLy1b3HvkgCItNHUnDlQazxgTjiLyrJ9AikJIUuzmhnhTZJimEvNejp7Lzoy3lB2ZFhHxOxumH\n0x65Q2uFnYudvlkrtkP7sGMn0EKgJoXcBhtt2RBUrvtjrc227FqdFRHyOUmZzCOv47I1tbUy+mFR\nUzptutHxtDgE1puUiNw3pm2wojlJ0o7vykbkS6Wdz1HSrYBChHxOdovIXWaVjNuqjasfemGtVHjk\nIuQeopKsqFnO2FppR9aKDWoGvf648YpE5MJBsIJti0eNox2HEXlJyAc9P4R8OiLvBdmVglgrfpEk\nCSpIi/0N0D5rJcZesfbGV4YtmdusiJDPSToVkYc1ZK0kaUKaKIIgKBY7G7dWSLPejzn2h6xraV++\nYxef7SYgKKfItuO7soHOUq9fWCtduzIUIZ+TcUSee+S2qJVDoS3nAdvaJk33x5z2Xe1i56glvmtb\nGEZ545OStTKOyJsOBtyQlJpL94qIvFvHoQj5nBT+tZpMP3R5kmTpY1n0GwQBaaI8sFbSCWul39FI\nyHe2c6trQshbGJHbK9a+J/X6jxoR8jlJyLfoFx65Xex07JGn5a9KNR6RT3vktlNQWzIh2oLdoBWo\n8nqGrdfTkoh84orVHoci5MIBSEslZqEUkbu0VtRkznbWH7O5kzBKYpRiwiMXIfeTUV4ywW7YgvJV\nYzu+q3JRsF5Hj0MR8jmZbnlm88ldNn9NmbQxSJuNyG1qV3kBrR90MxLyHVvONSxZK22LyLOgJgsq\nejVkjS0CIuRzkpYKWsE4/dBlmdkd1koaQINCXrWANsjnHzW841SYZJhbK+GEtdKuVm8p8U5rpWPH\noQj5nExH5HVkrUz70Yogr3XSDLaORdlasY1uu3ZJ6zs2r3/CWmlZRI5KC2vFpue25UdqVkTI58QK\n6nREbjvoOEFN5myTqkY9cpsrXo7Ibe/OphteCJPY78paDuXbTde0d0W5KJiNyLt2HIqQz8n0hqBe\nLR18pjq8EECDEbktSFTOhLDWStciId+xQh6qspDbq8aWfFelK9ZBIEIuHILy9vns/+5rraRTOduK\nABqNyHemtC31BgDEqVgrPmGtlQkhL+yHlkTkpc1p43r9IuTCAUhJSdNsMwLU5D9Oe+RpQKqai8ht\nRkB5TANPGl4Ik9gf3TCo8shbInalomBFvf62zG1GRMjnZLout43MXaUHjnO2yxG5ajYir8iEWLYR\nOd06gXxnmC8+90oRed/xMdok00XBBuKRC4chK+daFnK3WSujaKcfnVkrDWatJHZMJXEomkKLteIT\nUR6R22JS2e321FoZTe1psNlTbVnInRUR8jlJVTJZBdBxRsCwSPWbFHKlUqebjg6CjcjLpVGXwm6e\nQL5TlbViM6war9fjgKIEQW6tFB55x64MRcjnZjoit+mHroTcpvqVhFzZdlbNRL9R0ad0PKZjg26e\nQL5j8/qrIvI2+MjjomDZsTgOKBZ/bgdBhHxOpndd2o1BriLTUUXRIxt92B2WR01UkUc+6OgJ5Dt2\nYXoiIi9ssObsOVeMz49sfks9P5qTHzUi5HMy3U3edSu2qs03NvpoqlO4rfU8mdIWkjZcA0bYiY3I\n7UYZKB+ji/+juz1VFGy570lP2yNGhHxepjxye8IkjjbsDKNqjxxgu6FuPDbKC4KpwycJWiEObaIq\nIm/Tzk5rL9qiYFlA0Y4fqYPQ2/8poLW+C7iFbDvhm40x95ceezXwNiAGDPAmY8ziHyEzkpKi0lKO\nbujWI7fFfyasFds8tykhL3YLTgp5lt/erRPIdwqPvBSRW2ulDVdPwwrrkTRoxdwOwr4Rudb6VcAL\njTG3Am8E7p56yjuBO4wxLwdWge92PkqvmayD0ndtrUQ7RdMetE1146mK8gBU0idR0nzZJ2we+VI4\nKO7rO17HaZIiIi/ZfCLk1dwOvAfAGPMQsKa1Pll6/GXGmC/ntzeA026H6Dk7usm7jcircratX96c\nkFecPECYLpEEwyaGJOzC5egyAGvHThT3DVqUfjiqEHLVcFG5JpjFWrkeeKD07438vgsAxpgLAFrr\nZwHfCfzSXn9sbW2FXi/c6yl7sr6+eujX1kJeB8WOa7CSi3rgZqzHzmSLN0v9fvH37KXxseODRj6P\nwVL2/ivLk+8/CJaJwnMcP9lnZWl57vfx7rs+IlzOe5hug4IX3Hhd8XePbWXHlFKpN5/xYcex9ER2\nLC4PSsdiHpH7Mre9cDXGmTzyKdT0HVrra4H3Az9pjHl6rxefO3f5EG+Zsb6+ysbG5qFfXwd2Z6cd\n15VhFpHGSexkrE8/cxGAJKb4e2kCBPD0uc1GPo/NS1cAiEbpxPv3WQLgoUcf59lXXzPXe/j4XR8F\nrud9JboMAwhGveLv2jWOOEm8+IztnL/8zFl+/xN/zJ3f9gOsLh+b6bVnz+fnRzQ+PxTZWo0Pc9uL\ng37Xe4n+LNbKY2QRuOUG4HH7j9xm+WPgF40x98w8qrYwVSs8DLLbzhY7k511Texl5KjhrJVwyiNf\nDrIo/OylC0c+JqGaUbpFmihOHRsLY6DyY9Qza+W9f3MvX+JBPviZv5r5NaOiBIF45PtxD3AHgNb6\nJuAxY0z5Z+TtwF3GmD+pYXz+MyXkzotmVVSvKxY7G+rGY+vITGetHOtlYnHuysUjH5NQTay2UfFg\nIlU0CALnmMWvAAATF0lEQVTSRHnnkV8YZsfN+a3Zj58i0CmdH03XImqCfa0VY8x9WusHtNb3kTWK\nvFNr/QbgPPCnwI8AL9Ravyl/yf8wxryzrgH7RJIkqKla4UEQ5Btj3BxIdrEznO6CnjYXkccV274B\njvdXYAjnRci9IQmGBEnVeoV/m7cuR5ehB5vD2Y+fYVFLZnwsBmlIIoudOzHGvGXqrgdLt5fcDWex\nqKrLDTjtcj/OWilbKwGkzXUKj5LJZhqW1aXjmZBvX2piWMIUURKThiN68akdj2WNGPyKWreTbO3l\nUjT7OlpUYa1kHnm3hFx2ds5BIeRqav3XYURuF6Z60xE544P4qLG1nm1dGcvJpSzF7eJQhNwHzl68\niFIwUBURuYcpesN0C4Ar8exCXlUuoukOWk0gQj4HRS3kqY9R4e4kSYpKg/50eEmKPqWT877q2HEA\nLo0On5kkuOPpy9mi81JQlQHin7USqUzIh8nW7K/Jz8F+OCnkSjW387kJRMjnIKooMQvkZW1dReQV\nrboa3qIfJzt9SYC1Y1l61JXoypGPSdjJ2UuZ12wXoSdIA2dXja5Iw20ARmr248eWsJjwyPPofNhQ\nUbkmECGfg90icpfpT8WBqnZG5E155IW1MuWRX30i2/C7dYCISqiPc1ey5LKVCiFvul3gNNujEYRZ\n0BKr7ZlfV1R3LAu5LSo36k63KhHyOYjiXTxyHHrkyc4mDlbIR40J+U67B+Ca45lHfpBLY6E+Lmxl\naxWrg+M7H/QsIn9y83xxOw2HM3e/Kur+hDtLWNgSt11AhHwOioySCo/cVbRTlepno/OmI/L+1GLn\ncn9AGveImD2iEurjQp49dHJpp5D7tiB45uJYyFWQcu7ybOsslRF5bj3aNnBdQIR8DgqPXFVZK24j\n8l7VYmdDQm4XO/vBzuzVIOkTByLkPnBplAn5qeUqIXe3juOCpy9PblXfuPjMTK+zV4eDcGdWV1NF\n5ZpAhHwOrH9dlbXi6iSpSvWzoh41lLWyW0QOECZSAdEXLueLzmsrO2t0ZLXj/YnIz+UZNmmSnUtn\nZizzUFyx5q0GobzYKUIuzEAUZyfCdETu8rI1ruq52HBEnqbVG4IAeiyhwpitkYh502zFmZCfPn5y\nx2O+bWM/v51l2PRH2Vht6uR+2GBmUGqcYSPyoXjkwixEFbsuM5Szk6QqQyRoWMjt5Wy/ohzxIC+c\ndeaSbNNvmu18g801J6qE3N0x6oLNfBPZiWANmL3MQ3F1WFGLaCgeuTALu+WRK4ceeVzhkRcReUMd\nXvbyyJfzzSdnL0oFxKaJ0i3SJOD4YGcVjWzTTDpzdkjdWD//muWs/PGs9VaSPJgZ9Coi8oaKyjWB\nCPkc7BaRu4x2bBPZfoVH3tjOzmJMO4Xcbj6ZXrwSjp6oovKhxa7rNJX5NI3dlv/VJ7OK2ZszlnmI\n8/0ag97YI+81XOa5CUTI58BmlFR75K6sFRuRl9IPcwFtzCPPT56qxc7j/RXgYKVIhXpIgxFhOqh8\nTBX2gx9it51mfv7zr7kRGLeo24+kyiPPz5VIdnYKs7BXRO7qsrXKA+z5Yq30dkbkJwaZkNvNKML8\n/Oa9/5Nf/8i7DvSaYTSC3oheWl2c1NqBvkStI7ZI4x5ftZZZK7YS4n6MM6jK1kr+I+XJ3I4CEfI5\niIta4RUROW4uW6tE00bCzVkrO3N3LafyzSdSAdEdD299gkfjTx6oto6ts1JZ+ZDxMepLrnWstgni\nAadXTpCmqojQ98OeH0ul88NevTbVeKUJRMjnYFdrRbkU8p0RuV1kTBqKyPeyVk7l3dqlAqIbnrxw\nHnojVJDyhTNPzvy6M/li81JY3fsycHiMzkuSJKThkF66TBAEqGhArGYr82DXa5bKHrndZyERuTAL\n8V6Lnbi5bI19jMiL3XT9HY+trWSpbpelAqITHn7qK8Xtz595bObXnc3T947tJuQeWSvnLl1CBQn9\n/OohTGffVGavDpf6EpEvBB95+K/5h7/3szz85OwHc93YzQjT1oo9SVxEBGMboyzkzUfkabqzsQTA\nNStZRL41o8cp7M2j54o+53zp/OwRua18aBefpyn6vnpgrTxx/hwwTl3tpcvQG2UVEfdhvNhZEZGL\nkPvHl88/RTLY5N5HHtz/yUeEzfEudyeBsbXiItqptFZyAW3UWkmnKz5mnM43n9huL8J8PHHxqeL2\nk5c3Zn6dXWw+UVX5kJJH7oHYPXkhK5i10st+dJbyTWUbl/ZPYa0KKqyQ+3C1cVQsjJC/eP3ZADy2\n+fg+zzw67GaE6TxdlxF5sR2+4kC1/uBRk5JCWn3oHBsMSOOQKJXCWS44Ozxb3D4fnZv5dRf3qHwI\n5eYkzW8I2tjMCmQd72VjXQ4yQT+zuX/hrJR4x7Fo15AkIveQl97wHNJUcS6aPSqpm6JW+C6LnS7q\nhSfFwuL40tEHa8WuA1QRJANiJbVWXHA5OZ8VkhotscX5/V+QczFfbL4qX3yexuWC/LyczeuqrOY9\nX62gz7KpLCXNG0mPKfZZNHR+NMHCCPmxwYDeaJXt3nkvDj4YLzYGU9ZKkIucU4+8VNfELnwmDfVc\nTFWya0QOEKQD0lCEfF6SJGHU26Q3WmUpOUnSv8yV4Wyf65V8Q83VFZUPoeSRe1CP5Jnczz+1nAm5\ntYPOzVA4K1E7I3KbFisRuadc1VtHhRFf2Jh90adO4oruPVCyVhxklaTpzsXOpfxATRuLOHb3yAH6\n6TKE0UyLVcLufOnc06gw5nhwitXwKpSCzz4122K/bbe3m5DbdZ3Ig6j1Qr4L+HQ+VrsX4Znt/XcH\nZ+s1UxF5kF29NrXzuQkWSshvWH0WAH/zxKPNDiSnaHk2nbXi0H+sytm2NktjETnpzj6lJQZBtpvw\n6RkWq4Td+exGlnq4NjjNNceyHY9fODvbGpHdULO+uktE7nAdZ15swazTeeqqTWG1Pv+eqJ02X7+I\nyJuf21GxUEKu158DwKPPfGWfZx4NyS69K51uCCIhTdTEgqq1WRpb7FR7R+RLeRqZCPl8fPGZJwB4\n1ol1bli9FoCvXJjtajRKt0njkJVB9c7OIiL3wH64HGWCvb56FQBXH8t+fC6O9hfylGSHR94vPHIR\nci952XNfAMBTV3yxVqq7yY8jcgfWCglMRRzWZmnMWlHJnhG53YRy7rIUzpoHm274nKuexfNPZ1ej\nG1fOzPTaONgmSKoLZsE406qpBt5ltpMt0hROn8g88vXVU8C4IuKeqATF5Pk3ECH3m69ZvxaiPhd5\nuumhAOOIfHpnZ+gwIk/VzogjCALSVBW2y9Gzt7VyvJ8L+ZZE5PPwzDBLN3zRtTfwoutuIE3hQjRb\nL8skGBHsUvkQxseoDz7yiC1UPCgCovUTmZDPUm8lVTuzVkTIPScIApbiNZL+Jc5fab4oU7xLyzMr\nci7Sn6oWc7IHmhPyqpOnzOogi6wuSCnbubjMeYj6XLt6ipXBMkF0jO1g/0yOrdEQFUbZovMuhA5T\nZOclCbYIknGVxhPLy6RxyGiWTWUVV4dirSwApwfXohR86it/1/RQSh55dUTuJtrZaa0A4LAL0YGp\nWGAqs5p3bb+4LYWzDsswGhH3LtKPVwsbZDk9Bf2tfYMY22bPLjpXYWt2xw13CBpGI9JwtONHJ0gG\nxMEMm8oqhNx2CxIh95ivyjNXPnvmiw2PpLqfJpQry7mIyKujX5WqBrugp+x16FxlhVwqIB6aR55+\nChWknAivKu472cv6We5Xb8hWPrS1S6rwxVo5c+kiSsFATY41TJZJwr2FPIpjlIJgF4+8qayuJlg4\nIX9xnrny5YvNb9XfLWtlnBHgxiOvjMhpxlpJkgQVpDv6lJZZy/OBr8RSOOuwfG4jE+vTS6eL+67N\nUxAf2ScF8Vy+I9K23asiDPxI0XtqM9utujxVpbGvllFBwoUrux9DW/k+BTW1RmVL2iYSkfvL19/4\nbNIUzo2a36o/boxcnUfuJtrZxY9Og0aE3BYi2mux025C2RIhPzS20qFNOwT4qlPXAfDY5lOVr7Gc\nLyofVtdZAX8i8rOXMiE/3pus0mivJp7ao97Kdr4rNZyKyG2TiS4J+c5eXRVore8CbiG7pn6zMeb+\n0mOvAX4NiIEPGmPeWsdALSuDZcLRKsPeMyRJUtlY9qjYNSIP7EniQGgrslaA7D5HfUEPwjAvezod\nBZWxm1CkAuLh2bhyBgJ47tqzivtecM0N8BQ8vb131tb5bVv5sLqELTg+RufAlts9MZisCbMSrnAO\nOHPpAi/gWRWvhO24OiJvesNcE+yrglrrVwEvNMbcCrwRuHvqKXcDrwdeDnyn1volzkc5xao6DWHE\n5zeeqPut9sQeKDs98rzxgxNrpTrVTzVkrdjc+L2slZWBzTqQCoiH5XyUVT180bU3Fvc975rrSBPF\nZrx3CqJts2drl1RhO803vSD4TJ7ZNF2l0V5NPH1p9yyd0X4ReUMb5ppgloj8duA9AMaYh7TWa1rr\nk8aYC1rr5wFnjTFfAtBafzB//mdqGzFw3bHrOB89yl1/fTd8avfsidoJEpTauUXf/vuejfdyz4fe\nP9dbqDBGxVWiGUB/m5/80M/N9fcPPqAUFewt5AAq6RMtnTv68bWFfowaLbF2fCxwg16fMDrOaOnp\nvT9XlaCCvYXcXkV+/OJH+PiHPups2AcmH+tVy5OlBFYHxyGCDzzxR3zg8f+1y2vzY3FHRJ7N7Ur/\nSe+Ov286/gp+/Nte6/zvziLk1wMPlP69kd93If9/2ax+Cnj+Xn9sbW2FXi/c6yl7sr6+yg/efBtv\nv/cR4rTh7cUxHAuOc9s3fB0nlsfpU9/zjTdj/vwhN+OL4ebrb2Z9ffJAv+mam3nwzCfn//uHQAGv\n+ppv3TGmMt9w1c08dO7TRzeothHD11399Ts+42+97lY+/uQDu7xozHKwwnd98zdxaqXaXvneb/4W\n7r/n44zS5qtUDoJlXvuyb2H95Hiur7vpVj7zkU8TpXsXXlMobte37Picnh1+A49f+XIt4z0sCnjO\n+vUTY93rHDrQ307TvX1WrfU7gQ8YY96b//vPgR8zxjystf424GeMMd+fP/Ym4HnGmJ/f7e9tbGwe\n2thdX19lY6N7uwW7OO8uzhm6Oe8uzhkOPu/19dVd7YdZVgofI4u8LTcAj+/y2I35fYIgCMIRMYuQ\n3wPcAaC1vgl4zBizCWCMeRQ4qbV+rta6B3xf/nxBEAThiNjXIzfG3Ke1fkBrfR/ZfvE7tdZvAM4b\nY94N/ATwrvzpf2iMebi20QqCIAg7mCmP3Bjzlqm7Hiw9di9wq8tBCYIgCLOzcDs7BUEQhElEyAVB\nEBYcEXJBEIQFR4RcEARhwdl3Q5AgCILgNxKRC4IgLDgi5IIgCAuOCLkgCMKCI0IuCIKw4IiQC4Ig\nLDgi5IIgCAuOCLkgCMKCM1PRLB/YqwF029Ba/zrwSrLv523A/cDvASFZLfh/ZIxpXUNMrfUx4G+A\ntwIfphtz/iHgZ4EI+GXgU7R43lrrE8DvAmvAEvCrZK0hWzlnrfVLgfcCdxljfktr/dVUzDU/Dn6K\nrMLsO40x//kg77MQEfkMDaBbg9b61cBL87l+N/AfgH8D/EdjzCuBzwE/1uAQ6+QXgbP57dbPWWt9\nGvjXwCvIavm/jvbP+w2AMca8mqzPwW/S0jlrrY8D7yALSiw75po/75eB1wC3AT+ttb76IO+1EELO\nVANoYE1rfbLZIdXGvcAP5refAY6Tfbnvy+97P9kX3iq01i8GXgJ8IL/rNlo+Z7I5/ZkxZtMY87gx\n5sdp/7zPAKfz22v5v2+jnXPeBr6Xya5pt7Fzrt8K3G+MOW+MuQL8BfDyg7zRogj5dJNn2wC6dRhj\nYmPMpfyfbwQ+CBwvXWo+BTyrkcHVy9uBf1H6dxfm/FxgRWv9Pq31x7TWt9PyeRtj/gB4ttb6c2RB\ny7+kpXM2xkS5MJepmmtVE/sDfQaLIuTT7NqEtC1orV9HJuT/bOqh1s1da/0jwF8aYx7Z5Smtm3OO\nIotOf4DMcvivTM61dfPWWv8w8EVjzAuA7wB+a+oprZvzHuw21wN/Bosi5Hs1gG4dWuvvAn4B+B5j\nzHngYr4QCO1scP1a4HVa6/8LvAn4Jdo/Z4AngfvyyO3zwCaw2fJ5vxz4UwBjzINk5/Klls+5TNVx\nPXcT+0UR8l0bQLcNrfUp4DeA7zPG2IW/PwNen99+PfAnTYytLowx/8AYc7Mx5hbgP5FlrbR6zjn3\nAN+htQ7yhc8TtH/enyPzhNFaPwe4CHyIds+5TNX3+/+Am7XWV+VZPS8HPnaQP7owZWy11v8e+Hby\nBtD5r3nr0Fr/OPArQLmJ9T8mE7hl4O+AHzXGjI5+dPWjtf4V4FGyqO13afmctdb/hMxCA/i3ZKmm\nrZ13LlT/BbiOLL32l4CHaOGctdYvI1v7eS4wAr4C/BDwO0zNVWt9B/AzZOnV7zDG/PeDvNfCCLkg\nCIJQzaJYK4IgCMIuiJALgiAsOCLkgiAIC44IuSAIwoIjQi4IgrDgiJALgiAsOCLkgiAIC87/B9XJ\naMOUScdOAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f68fc7f1c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def ADMM(T, x, z, u):\n",
" for t in range(T):\n",
" x = np.dot(A1, y) + np.dot(A2, z - u)\n",
" z = soft_threshold(x + u, 1/mu)\n",
" u = u + x - z\n",
" return x\n",
"\n",
"ans = ADMM(10, x, z, u)\n",
"\n",
"print(ans[ans > 0.01])\n",
"print(x0[x0 > 0.01])\n",
" \n",
"plt.plot(range(N), ans)\n",
"plt.plot(range(N), x0)\n",
"plt.grid(True)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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