ex07.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Useful starting lines\n",
    "%matplotlib inline\n",
    "\n",
    "import random\n",
    "from datetime import datetime\n",
    "from helpers import *\n",
    "import numpy as np\n",
    "import copy\n",
    "import matplotlib.pyplot as plt\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Support Vector Machines\n",
    "## Classification Using SVM\n",
    "Load dataset. We will re-use the CERN dataset from project 1, available from https://inclass.kaggle.com/c/epfml-project-1/data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#from keras.datasets import mnist\n",
    "#(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "\n",
    "y, X, _  = load_csv_data('train.csv')\n",
    "\n",
    "#y, X, ids = load_csv_data(DATA_TRAIN_PATH, sub_sample=True)\n",
    "#print(y.shape, X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(250000, 30)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prepare cost and prediction functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def hinge_loss(y, X, w):\n",
    "    return np.clip(1 - y * (X @ w), 0, np.inf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calculate_primal_objective(y, X, w, lambda_):\n",
    "    \"\"\"compute the full cost (the primal objective), that is loss plus regularizer.\n",
    "    X: the full dataset matrix, shape = (num_examples, num_features)\n",
    "    y: the corresponding +1 or -1 labels, shape = (num_examples)\n",
    "    w: shape = (num_features)\n",
    "    \"\"\"\n",
    "    v = hinge_loss(y, X, w)\n",
    "    return np.sum(v) + lambda_ / 2 * np.sum(w ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def accuracy(y1, y2):\n",
    "    return np.mean(y1 == y2)\n",
    "\n",
    "def prediction(X, w):\n",
    "    return (X @ w > 0) * 2 - 1\n",
    "\n",
    "def calculate_accuracy(y, X, w):\n",
    "    \"\"\"compute the training accuracy on the training set (can be called for test set as well).\n",
    "    X: the full dataset matrix, shape = (num_examples, num_features)\n",
    "    y: the corresponding +1 or -1 labels, shape = (num_examples)\n",
    "    w: shape = (num_features)\n",
    "    \"\"\"\n",
    "    predicted_y = prediction(X, w)\n",
    "    return accuracy(predicted_y, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stochastic Gradient Descent for SVM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the (stochastic) subgradient for the n-th summand of the SVM optimization objective"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_stochastic_gradient(y, X, w, lambda_, n, num_examples):\n",
    "    \"\"\"compute the stochastic gradient of loss plus regularizer.\n",
    "    X: the dataset matrix, shape = (num_examples, num_features)\n",
    "    y: the corresponding +1 or -1 labels, shape = (num_examples)\n",
    "    w: shape = (num_features)\n",
    "    n: the index of the (one) datapoint we have sampled\n",
    "    num_examples: N\n",
    "    \"\"\"\n",
    "    # Be careful about the constant N (size) term!\n",
    "    # The complete objective for SVM is a sum, not an average as in earlier SGD examples!\n",
    "    def is_support(y_n, x_n, w):\n",
    "        \"\"\"a datapoint is support if max{} is not 0. \"\"\"\n",
    "        return y_n * x_n @ w < 1\n",
    "    \n",
    "    x_n, y_n = X[n], y[n]\n",
    "    grad = - y_n * x_n.T if is_support(y_n, x_n, w) else np.zeros_like(x_n.T)\n",
    "    grad = num_examples * np.squeeze(grad) + lambda_ * w\n",
    "    return grad\n",
    "\n",
    "def approximate_stochastic_gradient(y, X, w, lambda_, n, num_examples, diff_type='backward', h=0.005, last_w=None):\n",
    "    \"\"\"compute finite difference approximation of the stochastic gradient of loss plus regularizer.\n",
    "    X: the dataset matrix, shape = (num_examples, num_features)\n",
    "    y: the corresponding +1 or -1 labels, shape = (num_examples)\n",
    "    w: shape = (num_features)\n",
    "    n: the index of the (one) datapoint we have sampled\n",
    "    num_examples: N\n",
    "    \"\"\"\n",
    "    \n",
    "    if last_w is None :\n",
    "        last_w = np.array([(w_cur - random.random()) for w_cur in w])\n",
    "    \n",
    "    \n",
    "    hinge_diff =  hinge_loss(y[n], X[n], w) -  hinge_loss(y[n], X[n], last_w)\n",
    "    \n",
    "    sub = np.array(last_w) - np.array(w)\n",
    "    print(\"w=\"+str(w))\n",
    "    print(\"last_w=\"+str(last_w))\n",
    "    print(\"sub=\" +str(sub))\n",
    "    print(\"hinge_diff=\"+str(hinge_diff))\n",
    "    return(np.array([(hinge_diff / cur_sub) for cur_sub in sub ]))\n",
    "    \n",
    "                \n",
    "        \n",
    "def secant_method(w, last_w=None) :\n",
    "    calculate_stochastic_gradient()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement stochastic gradient descent: Pick a data point uniformly at random and update w based on the gradient for the n-th summand of the objective"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1.])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def newton_raphson(y, X, w, iters) :\n",
    "    for i in range(iters) :\n",
    "        \n",
    "         n = random.randint(0,num_examples-1)\n",
    "            \n",
    "        w = w - hinge_loss(y, w) / f_prime(w)\n",
    "        if i % 10 == 0 :\n",
    "            cost = calculate_primal_objective(y, X, w, lambda_)\n",
    "            acc = calculate_accuracy(y, X, w)\n",
    "            print(acc)\n",
    "            print(\"l=\" +str(cost)+\"acc=\"+str(acc))\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_support(y_n, x_n, w):\n",
    "        \"\"\"a datapoint is support if max{} is not 0. \"\"\"\n",
    "        return y_n * x_n @ w < 1\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     "name": "stdout",
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     "name": "stdout",
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    {
     "name": "stdout",
     "output_type": "stream",
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     "name": "stdout",
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      "   6829.1013952   25490.11333186]\n"
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    {
     "name": "stdout",
     "output_type": "stream",
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     "name": "stdout",
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    {
     "name": "stdout",
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     "text": [
      "  -308.9678409   -518.50948419]\n",
      "last_w=[ -410.13637821  -352.01968317  -312.37055048  -312.43985724\n",
      "  -305.84774393  -305.55087686  -370.91760389  -350.69078796\n",
      "  -305.83311907  -306.58294223  -308.41302209  -332.05162134\n",
      "  -314.41164177  -322.29701013  -313.84741169  -763.03085176\n",
      "  -303.59132725 -2362.53924475  -303.50895351  -317.46462061\n",
      "  -306.00266549  -303.58449339  -304.49221484  -336.78692834\n",
      "  -317.68623273  -304.76325908  -384.64995216  -750.63747925\n",
      "  -308.72215431  -518.44366186]\n",
      "sub=[0.09006668 0.11647448 0.15977414 0.15962569 0.17931358 0.18073574\n",
      " 0.1057595  0.1173511  0.23131124 0.17616474 0.24434235 0.13231971\n",
      " 0.26653995 0.14335044 0.15675423 0.04223577 0.21147429 0.013133\n",
      " 0.19780905 0.27594605 0.23231054 0.19632678 0.18697503 0.12793744\n",
      " 0.27659814 0.18514257 0.09949414 0.04299752 0.24568659 0.06582233]\n",
      "hinge_diff=1021.1556862224825\n",
      "grad=[11337.77461592  8767.20565673  6391.24490213  6397.18895264\n",
      "  5694.80409754  5649.99323338  9655.45100359  8701.71375972\n",
      "  4414.63921565  5796.59526883  4179.20051252  7717.33640586\n",
      "  3831.15439825  7123.49178168  6514.37391487 24177.50595676\n",
      "  4828.74631582 77754.91833856  5162.33045191  3700.56279714\n",
      "  4395.6494107   5201.30623268  5461.45485029  7981.67987699\n",
      "  3691.83863434  5515.50993247 10263.47594949 23749.17814745\n",
      "  4156.33459663 15513.81855126]\n",
      "w=[ -411.38336067  -353.03077047  -313.18249247  -313.25225731\n",
      "  -306.60815997  -306.30814252  -372.00861349  -351.69606904\n",
      "  -306.51490371  -307.35059629  -309.08381347  -332.97142435\n",
      "  -315.06911584  -323.16724749  -314.66889795  -765.54017998\n",
      "  -304.29553076 -2370.4865531   -304.23353097  -318.1181751\n",
      "  -306.68351169  -304.3115657   -305.23648118  -337.72932291\n",
      "  -318.33954909  -305.51120879  -385.79673977  -753.10386229\n",
      "  -309.39195668  -520.0925269 ]\n",
      "last_w=[ -410.22644489  -352.13615764  -312.53032463  -312.59948292\n",
      "  -306.02705751  -305.7316126   -371.02336339  -350.80813906\n",
      "  -306.06443032  -306.75910697  -308.65736444  -332.18394104\n",
      "  -314.67818172  -322.44036057  -314.00416592  -763.07308754\n",
      "  -303.80280154 -2362.55237776  -303.70676256  -317.74056666\n",
      "  -306.23497603  -303.78082017  -304.67918987  -336.91486578\n",
      "  -317.96283086  -304.94840165  -384.7494463   -750.68047676\n",
      "  -308.9678409   -518.50948419]\n",
      "sub=[1.15691578 0.89461282 0.65216785 0.65277438 0.58110246 0.57652992\n",
      " 0.9852501  0.88792998 0.45047339 0.59148931 0.42644903 0.78748331\n",
      " 0.39093412 0.72688692 0.66473203 2.46709244 0.49272922 7.93417534\n",
      " 0.52676841 0.37760845 0.44853565 0.53074553 0.55729131 0.81445713\n",
      " 0.37671823 0.56280714 1.04729346 2.42338553 0.42411578 1.58304271]\n",
      "hinge_diff=7718.739512077067\n",
      "grad=[ 6671.82491987  8628.02244867 11835.51066759 11824.51351341\n",
      " 13282.9235076  13388.27217907  7834.29455447  8692.95972117\n",
      " 17134.72914165 13049.66859168 18100.02822113  9801.78175995\n",
      " 19744.34840132 10618.90004743 11611.80617     3128.67867156\n",
      " 15665.27671387   972.84710517 14653.00370115 20441.11973369\n",
      " 17208.75350846 14543.20200244 13850.45730339  9477.15874153\n",
      " 20489.42402701 13714.71507521  7370.17825059  3185.10589077\n",
      " 18199.60483445  4875.88835517]\n"
     ]
    },
    {
     "data": {
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/bmYfA94be13t7nenGVMa1m7cxoU3vsDgsiJ++Yn9yMvTw3VERHqjnE34AO5+\nJ3Bn2nGkpbHR+epts1hRu4XbLziMAaV90g5JRES6Sc4lfDOrBbylQYC7e/luDik1v3/8DR6bv5Lv\nnzqV/Ub1TzscERHpRjmX8N1dj88F/vHGKn7x8Gucut9wzj5kTNrhiIhIN8vZq9JzWfX6LXzplhcZ\nP7gfP/yIXoojIpILcq6En+vqGhq56OYX2FzXwF/PnkZpkXYBEZFcoKN9jvnJ3+YxY+Fafn3m/kwY\notYNEZFcoSr9HPK3V5ZxzdNv8+lDx/ChfYenHY6IiOxGSvg54u1VG/n6HS+z36j+fPvkKWmHIyIi\nu5kSfg7YvK2BC2+cSWG+8buzptGnQF+7iEiuURt+L+fu/Ns9rzJ/eS3Xf+ZARvQvSTskERFJgYp6\nvdxfn1/EnS8s5uKjJ3LUpCFphyMiIilRwu/FXl2ynv+4dzZHTKzkkmMmph2OiIikSAm/l1q/uY4v\n3PQCg0r78KvT9yNfL8UREclpasPvhRobnUtve4ml6zbz188fyqB+RWmHJCIiKVMJvxe6+qm3+Pvc\n5Xz75L04YMyAtMMREZEsoITfy/zrrdX89IF5nLxPFZ85bGza4YiISJZQwu9FVtRs4aKbX2RsZSk/\n+dg+eimOiIg0UcLvIDMbZWaPmdkcM5ttZpekHVNSfUMjF93yIhu31vOHsw6gn16KIyIiCcoKHVcP\nXOruL5hZGTDTzB529zlpBwbw84de47m31/CLT+zLpGF6KY6IiOxIJfwOcvdl7v5C/FwLzAVGpBtV\n8PCc5Vz1xJt88uDRfHTayLTDERGRLKSEvwvMbCywP/BsC8PON7MZZjZj5cqV3R7LwtUb+epts3jP\niAr+4xS9FEdERFqmhN9JZtYPuBP4srvXNB/u7le7+3R3nz548OBujWVLXQMX3vgCeWb8/qxpFBfm\nd+vyRESk51IbfieYWSEh2d/k7nelHc8V985mzrIarvvMdEYN7Jt2OCIiksVUwu8gC/e4XQvMdfdf\npB3P7TMWcevzi/ji+/fg6MlD0w5HRESynBJ+x70X+BRwtJnNin8npRHI3GU1/Ns9r3Lo+EF85dg9\n0whBRER6GFXpd5C7Pw2k/iSbmi11XHjjTCpKCvn1mftTkK9zNhERaZ8Sfg/i7nzj9pdZtHYzt55/\nCIPL9FIcERHpGBUPe5Brn36bB2ZXc9kJkzlw7MC0wxERkR5ECb+HeH7BGn70t3kcP3Uo5x0xLu1w\nRESkh1Ed8ZZrAAAfMElEQVTC7wFWbdjKRTe/wKgBJfzs4/vqpTgiItJpSvhZrqHR+dItL7JuUx2/\nP+sAyosL0w5JRER6IF20l+V++fBrPPPman562j5MGV6edjgiItJDqYSfxR6dt5zfPvYGp08fxSem\nj0o7HBER6cGU8LPUojWb+MpfX2JKVTnfPXVq2uGIiEgPp4SfhbbWN/DFm1+g0Z0/nK2X4oiIyLun\nNvws9OO/zePlxeu5+lMHMGZQadrhiIhIL6CEn4XOOng0owb05bipw9IORUREegkl/Cw0YUgZE4aU\npR2GiIj0ImrDFxERyQFK+CIiIjnA3D3tGHotM1sJLNzFySuBVV0YTldRXJ2juDpHcXVetsb2buIa\n4+6DuzIYUcLPWmY2w92npx1Hc4qrcxRX5yiuzsvW2LI1rlymKn0REZEcoIQvIiKSA5Tws9fVaQfQ\nCsXVOYqrcxRX52VrbNkaV85SG76IiEgOUAlfREQkByjhi4iI5AAl/CxkZieY2Xwze8PMLksxjuvM\nbIWZvZroN9DMHjaz1+P/ASnENcrMHjOzOWY228wuyYbYzKzYzJ4zs5diXN/NhrhiDPlm9qKZ3Zct\nMcU4FpjZK2Y2y8xmZEtsZtbfzO4ws3lmNtfMDk07LjObFLdT5q/GzL6cdlwxtq/Eff5VM7sl/hZS\nj0t2pISfZcwsH/gdcCIwBTjTzKakFM4NwAnN+l0GPOLuE4FHYvfuVg9c6u5TgEOAL8ZtlHZsW4Gj\n3X1fYD/gBDM7JAviArgEmJvozoaYMt7v7vsl7tnOhtiuBB5w98nAvoRtl2pc7j4/bqf9gAOATcDd\nacdlZiOALwHT3X1vIB84I+24pAXurr8s+gMOBR5MdF8OXJ5iPGOBVxPd84Gq+LkKmJ8F2+x/gA9k\nU2xAX+AF4OC04wJGEg64RwP3ZdP3CCwAKpv1S3t7VQBvEy9qzpa4msVyHPCPbIgLGAEsAgYSXsh2\nX4wva7aX/sKfSvjZJ/PjyVgc+2WLoe6+LH6uBoamGYyZjQX2B54lC2KLVeezgBXAw+6eDXH9CvgG\n0Jjol3ZMGQ783cxmmtn5sV/asY0DVgLXx2aQa8ysNAviSjoDuCV+TjUud18C/Bx4B1gGrHf3h9KO\nS3amhC+7zMOpe2r3dZpZP+BO4MvuXpMcllZs7t7gocp1JHCQme2dZlxmdgqwwt1ntjZOyt/j4XF7\nnUhomjkyOTCl2AqAacAf3H1/YCPNqqPT3GZm1gf4EHB782FpxBXb5k8lnCgNB0rN7Oy045KdKeFn\nnyXAqET3yNgvWyw3syqA+H9FGkGYWSEh2d/k7ndlU2wA7r4OeIxwDUSacb0X+JCZLQBuBY42sxtT\njqlJLB3i7isI7dEHZUFsi4HFsXYG4A7CCUDacWWcCLzg7stjd9pxHQu87e4r3b0OuAs4LAvikmaU\n8LPP88BEMxsXz+TPAO5NOaake4FPx8+fJrSf71ZmZsC1wFx3/0W2xGZmg82sf/xcQriuYF6acbn7\n5e4+0t3HEvalR9397DRjyjCzUjMry3wmtPu+mnZs7l4NLDKzSbHXMcCctONKOJPt1fmQflzvAIeY\nWd/42zyGcJFj2nFJM3rSXhYys5MI7a75wHXu/oOU4rgFOIrwmsvlwHeAe4DbgNGEV/9+wt3X7Oa4\nDgeeAl5he7v0twjt+KnFZmb7AH8ifG95wG3u/j0zG5RmXIn4jgK+5u6nZENMZjaeUKqHUI1+s7v/\nIEti2w+4BugDvAV8lvidphxXKSHBjnf39bFfNmyv7wKnE+6geRE4D+iXdlyyIyV8ERGRHKAqfRER\nkRyghC8iIpIDlPBFRERyQEHaAfRmlZWVPnbs2LTDEBHpUWbOnLnK3QenHUdvo4TfjcaOHcuMGTPS\nDkNEpEcxs4Vpx9AbqUpfREQkB6iELyIiTdyd+kanodGpa2ikoTF01zc49Y2N8X/z4aF/Q6NT1+g0\nNDay94gKhpQVp706kqCELyLSAe5OXUxqycSXTHb1jY2J5BgSX2aa1pJnU7+meYZ5NDRsT54tJdkw\n3x2XV98Yl9HQcixN4zU07jy/2N3Q2DXPZrnq7GmcsHdVl8xLuoYSvojktC11DSyv2cKy9VtYXrOF\n6vXbP2f+r6zdSn0XJcLOKsw38vOMgrw8CvKNgvg5P8926M58Dv3zKMzPo6RPXlO/MJ88CpvG2T6f\nzLCC5Dzz83aYX1hOGJ6cT2F+jCWOl5nfmIGlqWwvaZ0Svoj0Su5OzeZ6qmu2sGz95pjMt1Jds3mH\npL52U91O05YVFTC0opiqimImDKlkSFkRRQX5MdlZIvklE2rLyXOnpNg8cedbIgnvOL88g/B4epF3\nTwlfRHqchkZn1YatLZbGq9dvoTr+31zXsNO0lf2KGFZRxMgBfZk+dgBVFSUMLQ/JfWh5McMqiulX\npEOj9D7aq0Ukq2Sq2JOJu3lSX1G7dae25sJ8Cwm7vJipw8s5ZvIQhlWEBJ5J5kPKiulToJuTJDcp\n4YvIbuPurNqwjaXrNrNk3WaWrtvM4rWbd+huqYq9X1FBSN7lxUyYUMmwWBJv+l9RzMC+fcjLU/W3\nSGuU8EWky2yrb2TZ+pC8l6zdzNJ1W1iyblP8H/pvq2/cYZp+RQWM6F/C8P7F7DeqP1UVxQyrKNkh\nmauKXeTd069IRDps/ea6UBpfu5ml68P/JYnS+YrarTR/4/aQsiKG9y9hyvByPjBlKCP6l8QEX8KI\nASWUFxfowjSR3UAJX0SAcCHcytqtLFm3KVazJ0rnsdq9dmv9DtP0yc9jeP9iRgwo4ciJgxkxoKQp\noY8YUMKwimKKCvJTWiMRSVLCF8kRjY1Odc0WFqzeyDurNzWVzDOl9WXrtux0r3lFSSEj+pcwamBf\nDt1j0A4l8+H9i6ksLVK7uUgPoYQv0os0JfVVG1mwehMLVm+MnzeycPUmtibaz/MMhpUXM7x/CdNG\nD2D4PttL5pnErrZzkd6jV/6azewE4EogH7jG3X/cbPipwPeBRqAe+LK7Px2H9QeuAfYGHDjX3f9p\nZvsBVwHFcZovuPtzu2mVRJo0NjrLarawcNVG3o6J/O1VG1nYQlLvk5/H6EF9GTuolCMnDmZsZSlj\nB5UyZlBfhlUUU5ivW9REckWvS/hmlg/8DvgAsBh43szudfc5idEeAe51dzezfYDbgMlx2JXAA+5+\nmpn1AfrG/j8FvuvufzOzk2L3Ud2/RpKLMkk9UzpvKrGv2sjCNZt2uNK9T0EeYwb2ZWxlKe/bczBj\nBpUyrjIk9aqKEvJV5S4i9MKEDxwEvOHubwGY2a3AqUBTwnf3DYnxSwklecysAjgS+EwcbxuwLTMZ\nUB4/VwBLu20NJCc0NjpL12/eoYT+9qpNoaTeQlIfOygk9fdPHsKYQX0ZN6iUMZWlVJUXqx1dRNrV\nGxP+CGBRonsxcHDzkczsI8CPgCHAybH3OGAlcL2Z7QvMBC5x943Al4EHzeznQB5wWEsLN7PzgfMB\nRo8e3RXrIz1YQ6OzbP1mFqzatGNJffVG3mmW1IsK8kIij0l97KDSpiQ/TEldRN6l3pjwO8Td7wbu\nNrMjCe35xxK2xzTgYnd/1sy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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b9a7475048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sgd_for_svm_demo(y, X, differentiate_method, h=0.0005):\n",
    "    #differentiate_method is 'classic' / 'forward' / 'backward' / 'central'\n",
    "    \n",
    "    max_iter = 100\n",
    "    gamma = 0.01\n",
    "    lambda_ = 0.01\n",
    "    data_interval = 10  \n",
    "    num_examples, num_features = X.shape\n",
    "    w = np.zeros(num_features)\n",
    "    \n",
    "    losses = []\n",
    "    accuracies = []\n",
    "    iters = []\n",
    "    last_w = None\n",
    "    \n",
    "    for it in range(max_iter):\n",
    "        # n = sample one data point uniformly at random data from x\n",
    "        \n",
    "        n = random.randint(0,num_examples-1)\n",
    "        not_support = is_support(y[n], X[n], w)\n",
    "        if not_support :\n",
    "        \n",
    "            grad = None\n",
    "\n",
    "            if differentiate_method == 'classic' :\n",
    "                grad = calculate_stochastic_gradient(y, X, w, lambda_, n, num_examples)\n",
    "            else :\n",
    "                grad = approximate_stochastic_gradient(y, X, w, lambda_, n, num_examples, differentiate_method, h, last_w)\n",
    "\n",
    "            print(\"grad=\" + str(grad))\n",
    "            #if np.sum(grad) == 0 :\n",
    "            #    return w\n",
    "\n",
    "            last_w = copy.deepcopy(w)\n",
    "            w -= gamma/(it+1) * grad\n",
    "            #w -= gamma * grad\n",
    "\n",
    "\n",
    "            if it % data_interval == 0:\n",
    "                cost = calculate_primal_objective(y, X, w, lambda_)\n",
    "                acc = calculate_accuracy(y, X, w)\n",
    "                print(acc)\n",
    "                print(\"l=\" +str(cost)+\"acc=\"+str(acc))\n",
    "                losses.append(cost)\n",
    "                iters.append(it)\n",
    "                accuracies.append(acc)\n",
    "        \n",
    "            #print(\"iteration={i}, cost={c}\".format(i=it, c=cost))\n",
    "    \n",
    "    #print(\"training accuracy = {l}\".format(l=calculate_accuracy(y, X, w)))\n",
    "    \n",
    "    # Two subplots, the axes array is 1-d\n",
    "    \n",
    "    fig = plt.figure()\n",
    "    ax1 = fig.add_subplot(211)\n",
    "    ax2 = fig.add_subplot(212)\n",
    "\n",
    "    ax1.plot(iters, losses)\n",
    "    ax2.plot(iters, accuracies)\n",
    "    \n",
    "    ax1.set_xlabel('iteration')\n",
    "    ax1.set_ylabel('loss')\n",
    "    \n",
    "    ax2.set_xlabel('iteration')\n",
    "    ax2.set_ylabel('accuracy')\n",
    "    \n",
    "    if differentiate_method == 'classic' :\n",
    "        ax1.set_title('evolution of loss and accuracy using classic differentiation method', y=1.08)\n",
    "        fig.savefig('plots/loss_acc_'+ differentiate_method + \"_i= \" + str(max_iter) + \".png\" )\n",
    "    else :\n",
    "        ax1.set_title('evolution of loss and accuracy using ' + differentiate_method + ' differentiation method (h=' +str(h) + ')', y=1.08)\n",
    "        fig.savefig('plots/loss_acc_'+ differentiate_method + '_h=' + str(h) + \"_i= \" + str(max_iter) +\".png\") \n",
    "    \n",
    "    #plt.plot(iters, losses, linewidth=2.0)\n",
    "    #plt.xlabel('iteration')\n",
    "    #plt.ylabel('loss')\n",
    "    #if differentiate_method == 'classic' :\n",
    "    #    plt.title('evolution of loss using classic differentiatation method', y=1.08)\n",
    "    #    plt.savefig('loss_'+ differentiate_method + \".png\" )\n",
    "    #else :\n",
    "    #    plt.title('evolution of loss using' + differentiate_method + ' differentiation method (h=' +str(h) + ')', y=1.08)\n",
    "    #    plt.savefig('loss_'+ differentiate_method + '_h=' + str(h) + \".png\" )\n",
    "                  \n",
    "\n",
    "sgd_for_svm_demo(y, X, 'backward')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Lucas\\Anaconda3\\lib\\site-packages\\matplotlib\\pyplot.py:524: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n",
      "  max_open_warning, RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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Ysa+LxmFqeXBwB5HhCMLsyYVMLckddw/I/oEQm5o6aNjfjQ6e5BkcqiqWp59E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\nhKrOA57wXqeba4D1Ea8zocy3AI+q6hH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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c601f6b438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9YTP7m4ORg6uYNztHXU2OubOqGTNsYLnDNLM+yInVeoV9TS0sfXHzgSre1Rt3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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c623fb57f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NDB44gPNmjee67A0j0yeMKHWYZmbd4sRpPS4iqN2y58hZ5TMbdxIBVaOGcMVp\nJ1BTPZEFsysZOcSbn5n1PT5yWY9441Azj61rZOma1Bbsll0HAHjLlDF8omY2i+flOO3EMW403cz6\nPCdOO2qbd6ZG05fWbuWXL23jYFMLIwanRtM/9bY5LJxbRW6UG003s/LixGnd1twSPLNhB0uyN4zU\nvb4HgOkThnPtudNYPC/HuTPHM6TCz1aaWfly4rRO7dp/mBUvNrC0divL1zawc/9hKgaIc2aM5/NX\nzqNmXo5ZlSP8bKWZ9RtOnPYmEcG6+r0syZ6tXPXqDppbgvEjBlNTnaOmOsfFc6oYPdSNpptZ/+TE\naRw43Myv1m878t7KTTveAOCUSaP500tOYlF1jjOmjnWj6WZmOHH2W1t3HziSKB99sZE3DjczdNAA\nFpxcyZ8uPIma6hyTxrjRdDOztpw4+4mWluDXm3ayrK6epWvqeW7zbgAmjx3Ge8+eQs28HBfMmsDQ\nQa7YY2bWGSfOMrbnwGEefbGRJXX1LF9TT+PeQwwQnDVtHJ+9fC6LqycyZ+JIV+wxMyuAE2eZeblx\nH0tqt7JsTT1Pvrydw83B6KEVXDI3d6TR9HEjBpc6TDOzPsuJs4871NTCU69sP/KGkZcbU6Pps3Mj\nueHCmSyeN5Gzpo2lwo2mm5n1CCfOPqhx70GW1dWzbE09D69tZO/BJgZXDOCCWROyN4zkmDp+eKnD\nNDMrS06cfUBE8Pxru1ma1YJ9dlNqNH3i6CG88/RJLJqbY8HsSoYP9tdpZlZsPtL2UvsPNfHoi40s\nzc4st+4+iASnTxnLpy6dQ011jlNPHO2KPWZmx5kTZy+ycfv+I/cqH1+/jUNNLYwaUsFFcypZNDfH\nouoclSOHlDpMM7N+zYmzhJqaW1j16g6WrqlnaW09L9bvBWBW5Qg+mL3g+ZwZ4xlc4Yo9Zma9hRPn\ncbZj3yFWrG1gSV09K9bUs/tAE4MGinNnjueac6dRU51jZuWIUodpZmYdcOIssohgzdY92Xsr63l6\nww5aAipHDuayU0+gpjpV7BnlRtPNzPoEJ84iOHC4mV++lFXsqWtg887UaPppk0dzU81saqpzvGXy\nGAa40XQzsz6n7BKnpMuBrwIDgTsj4ovHY7mv7XwjS5T1PPZSIwcOtzB88EAuPLmSj9eczKLqHBNH\nDz0eoZiZWRGVVeKUNBD4Z+BtwCbgKUn3R8QLPb2s5pZg9cYdWS3YBmq3pEbTp44fxtXzp7J43kTO\nmzWeIRVpUvRZAAAT1klEQVRuNN3MrJyUVeIEzgXWRcR6AEk/AK4CejxxXnvHr3jyle0MHCDOnj6O\nW6+o5tJ5OU6qcqPpZmblrNwS52RgY173JuC8YizogxdM57oLpnPJ7CrGDHfFHjOz/qLcEme3SLoR\nuBFg2rRpRzWPd55+Yk+GZGZmfUS5PVm/GZia1z0l6/cmEXFHRMyPiPlVVVXHLTgzM+v7yi1xPgXM\nljRT0mDgGuD+EsdkZmZlRBFR6hh6lKQrga+QHkf5ZkT8XRfjNwCvHuXiKoHGo5y2L+uP5XaZ+4/+\nWO6jKfP0iOiXl+zKLnEeT5JWRsT8UsdxvPXHcrvM/Ud/LHd/LPOxKLdLtWZmZkXlxGlmZlYAJ85j\nc0epAyiR/lhul7n/6I/l7o9lPmq+x2lmZlYAn3GamZkVwInTzMysAE6cR0HS5ZLWSFon6dZSx1Ms\nkqZKWibpBUnPS7o56z9e0s8lvZj9H1fqWHuapIGSnpH0s6y7P5R5rKQfS6qTVCvpgnIvt6RPZdv2\nc5LukTS0HMss6ZuS6iU9l9evw3JKui07vq2RdFlpou69nDgLlPfqsiuAU4BrJZ1S2qiKpgm4JSJO\nAc4HPpaV9VZgSUTMBpZk3eXmZqA2r7s/lPmrwAMRUQ2cTip/2ZZb0mTgE8D8iDiN1GjKNZRnme8C\nLm/Tr91yZvv4NcCp2TRfy457lnHiLNyRV5dFxCGg9dVlZScitkTE09nnPaQD6WRSeb+djfZt4N2l\nibA4JE0B3g7cmde73Ms8BrgY+AZARByKiJ2UeblJL7oYJqkCGA68RhmWOSIeBra36d1ROa8CfhAR\nByPiZWAd6bhnGSfOwrX36rLJJYrluJE0AzgTeAKYGBFbskGvAxNLFFaxfAX4LNCS16/cyzwTaAC+\nlV2ivlPSCMq43BGxGfjvwAZgC7ArIh6ijMvcRkfl7JfHuEI4cVqXJI0E7gU+GRG784dFep6pbJ5p\nkvQOoD4iVnU0TrmVOVMBnAX8S0ScCeyjzSXKcit3dk/vKtKPhhOBEZKuyx+n3Mrckf5Szp7ixFm4\nbr26rFxIGkRKmndHxH1Z762SJmXDJwH1pYqvCC4E3iXpFdJl+BpJ36O8ywzprGJTRDyRdf+YlEjL\nudyXAi9HRENEHAbuA95KeZc5X0fl7FfHuKPhxFm4fvPqMkki3fOqjYgv5w26H7g++3w98NPjHVux\nRMRtETElImaQvtulEXEdZVxmgIh4HdgoaW7WazHwAuVd7g3A+ZKGZ9v6YtJ9/HIuc76Oynk/cI2k\nIZJmArOBJ0sQX6/lloOOQqGvLuurJC0AHgF+w2/v932OdJ/zh8A00ivZ/iAi2lY86PMkLQQ+HRHv\nkDSBMi+zpDNIFaIGA+uBD5N+XJdtuSX9FXA1qQb5M8BHgJGUWZkl3QMsJL0+bCvwBeAndFBOSZ8H\nbiCtl09GxH+WIOxey4nTzMysAL5Ua2ZmVgAnTjMzswI4cZqZmRWgotQBlFplZWXMmDGj1GGYmfUp\nq1ataoyIqlLHUQq9LnFKupzUZuZA4M6I+GI74ywk1WodBDRGxCVZ/7GkWoGnkR7mvSEiHu9seTNm\nzGDlypU9WgYzs3In6dVSx1AqvSpx5jWg/jbSA9lPSbo/Il7IG2cs8DXg8ojYICmXN4vWRqrfmz1j\nOfw4hm9mZv1Ab7vH2Z0G1N8P3BcRGwAioh46baTazMysx/S2xNmdxoXnAOMkLZe0StKHsv4dNVL9\nOyTdKGmlpJUNDQ09XQYzMytjvS1xdkcFcDbptU+XAX8paQ7daKS6VUTcERHzI2J+VVW/vLdtZmZH\nqbclzu40LrwJeDAi9kVEI/Aw6aW7HTVSbWZm1mN6W+LsTgPqPwUWSKqQNBw4j9QIeUeNVJuZmfWY\nXlWrNiKaJN0EPMhvG1B/XtJHs+Ffj4haSQ8Az5IaHr8zIp7LZvFx4O4s6bY2Um1mZtZj+n0j7/Pn\nzw8/x2lmVhhJqyJifqnjKIXedqnWzMysV3PiNDMzK4ATp5mZWQGcOM3MzArgxGlmZlYAJ04zM7MC\nOHGamZkVwInTzMysAE6cZmZmBXDiNDMzK4ATp5mZWQGcOM3MzArgxGlmZlYAJ04zM7MCOHGamZkV\nwInTzMysAE6cZmZmBXDiNDMzK4ATp5mZWQF6XeKUdLmkNZLWSbq1g3EWSlot6XlJK9oMGyjpGUk/\nOz4Rm5lZf1K0xCnpPklvl9TtZUgaCPwzcAVwCnCtpFPajDMW+Brwrog4FXhfm9ncDNQeU/BmZmYd\nKOYZ59eA9wMvSvqipLndmOZcYF1ErI+IQ8APgKvajPN+4L6I2AAQEfWtAyRNAd4O3NkTBTAzM2ur\naIkzIn4RER8AzgJeAX4h6ZeSPixpUAeTTQY25nVvyvrlmwOMk7Rc0ipJH8ob9hXgs0BLjxTCzMys\njYpizlzSBOA64IPAM8DdwALgemDhUc62AjgbWAwMAx6X9CtSQq2PiFWSOp23pBuBGwGmTZt2lGGY\nmVl/VLTEKenfgbnAd4F3RsSWbNC/SVrZwWSbgal53VOyfvk2AdsiYh+wT9LDwOmkM9t3SboSGAqM\nlvS9iLiu7UIi4g7gDoD58+fHURXQzMz6pWLe4/yfEXFKRPxDXtIEICLmdzDNU8BsSTMlDQauAe5v\nM85PgQWSKiQNB84DaiPitoiYEhEzsumWtpc0zczMjkUxE+cpWQ1YACSNk/RnnU0QEU3ATcCDpJqx\nP4yI5yV9VNJHs3FqgQeAZ4EngTsj4rliFcLMzCyfIopzpVLS6og4o02/ZyLizKIs8CjNnz8/Vq7s\n6MqxmZm1R9KqTq4elrVinnEOlKTWjuwZzcFFXJ6ZmVnRFbNW7QOkikD/K+v+k6yfmZlZn1XMxPnn\npGT5p1n3z3HDBGZm1scVLXFGRAvwL9mfmZlZWSjmc5yzgX8gtTk7tLV/RMwq1jLNzMyKrZiVg75F\nOttsAhYB3wG+V8TlmZmZFV0xE+ewiFhCeuTl1Yi4ndQAu5mZWZ9VzMpBB7NXir0o6SZS03kji7g8\nMzOzoivmGefNwHDgE6RG2a8jNe5uZmbWZxXljDNr7ODqiPg0sBf4cDGWY2ZmdrwVJXFGRLOkBcWY\nd2/xV//7eV54bXepwzAzOyqnnDiaL7zz1FKH0ScV8x7nM5LuB34E7GvtGRH3FXGZZmZmRVXMxDkU\n2AbU5PULoCwSp3+pmZn1T8VsOcj3Nc3MrOwUs+Wgb5HOMN8kIm4o1jLNzMyKrZiXan+W93ko8PvA\na0VcnpmZWdEV81Ltvfndku4BHi3W8szMzI6HYjaA0NZsIHccl2dmZtbjinmPcw9vvsf5OukdnWZm\nZn1WMS/VjirWvM3MzEqlaJdqJf2+pDF53WMlvbsb010uaY2kdZJu7WCchZJWS3pe0oqs31RJyyS9\nkPW/uedKY2ZmlhTzHucXImJXa0dE7AS+0NkEWRu3/wxcQXoB9rWSTmkzzljga8C7IuJU4H3ZoCbg\nlog4BTgf+Fjbac3MzI5VMRNne/Pu6tLwucC6iFgfEYeAHwBXtRnn/cB9EbEBICLqs/9bIuLp7PMe\noBaYfAzxm5mZ/Y5iJs6Vkr4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c6289a7a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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z6z2cOO2YOtTSyopXth9+FddLjXsBOLFyBB++YAa11ZOomTGOQQPdaLqZ9U5O\nnFZ0W/ccYNnqRpasbuChNY3s3t/M4IEDOHfWeK7N3jAyfcKIUodpZtYtTpzW4yKCus27D59VPr1h\nBxFQOWoIV5x6HLXVk5g/eyIjh3jzM7O+x0cu6xFvHGzh0bVNLFmd2oLdvHM/AG+ZMoZP1c5m0bwq\nTj1hjBtNN7M+z4nTjtimHanR9CV1W/jlS1s50NzKiMGp0fTPvHUOC+ZWUjXKjaabWXlx4rRua2kN\nnl6/ncXZG0bqX98NwPQJw3nfOdNYNK+Kc2aOZ0iFn600s/LlxGmd2rnvEMtfbGRJ3RaWrWlkx75D\nVAwQZ88YzxevnEftvCpmTRzhZyvNrN9w4rQ3iQjWNuxhcfZs5cpXt9PSGowfMZja6ipqq6u4eE4l\no4e60XQz65+cOI39h1r41bqth99buXH7GwCcfPxo/uiSE1lYXcXpU8e60XQzM5w4+60tu/YfTpSP\nvNjEG4daGDpoAPNPmsgfLTiR2uoqjh/jRtPNzNpz4uwnWluDZzbuYGl9A0tWN/Dcpl0ATB47jPec\nNYXaeVWcP2sCQwe5Yo+ZWWecOMvY7v2HeOTFJhbXN7BsdQNNew4yQHDmtHF8/vK5LKqexJxJI12x\nx8ysAE6cZeblpr0srtvC0tUNPPHyNg61BKOHVnDJ3KrDjaaPGzG41GGamfVZTpx93MHmVp58Zdvh\nN4y83JQaTZ8zaSTXz5/JoupJnDltLBVuNN3MrEc4cfZBTXsOsLS+gaWrG3hoTRN7DjQzuGIA58+a\nkL1hpIqp44eXOkwzs7LkxNkHRATPv7aLJVkt2Gc3pkbTJ40ewjtOO56Fc6uYP3siwwf76zQzKzYf\naXupfQebeeTFJpZkZ5Zbdh1AgtOmjOUzl86htrqKU04Y7Yo9ZmbHmBNnL7Jh277D9yofW7eVg82t\njBpSwUVzJrJwbhULq6uYOHJIqcM0M+vXnDhLqLmllZWvbmfJ6gaW1DXwYsMeAGZNHMEHsxc8nz1j\nPIMrXLHHzKy3cOI8xrbvPcjyNY0srm9g+eoGdu1vZtBAcc7M8VxzzjRqq6uYOXFEqcM0M7M8nDiL\nLCJYvWV39t7KBp5av53WgIkjB3PZKcdRW50q9oxyo+lmZn2CE2cR7D/Uwi9fyir21DeyaUdqNP3U\nyaO5sXY2tdVVvGXyGAa40XQzsz6n7BKnpMuBbwADgTsi4ivHYrmv7XgjS5QNPPpSE/sPtTJ88EAu\nPGkin6wdjawJAAAUFklEQVQ9iYXVVUwaPfRYhGJmZkVUVolT0kDgH4C3AhuBJyXdFxEv9PSyWlqD\nVRu2Z7VgG6nbnBpNnzp+GFfXTGXRvEmcO2s8QyrcaLqZWTkpq8QJnAOsjYh1AJJ+AFwF9HjifN/t\nv+KJV7YxcIA4a/o4brmimkvnVXFipRtNNzMrZ+WWOCcDG3K6NwLnFmNBHzx/OteeP51LZlcyZrgr\n9piZ9Rfllji7RdINwA0A06ZNO6J5vOO0E3oyJDMz6yPK7cn6TcDUnO4pWb83iYjbI6ImImoqKyuP\nWXBmZtb3lVvifBKYLWmmpMHANcB9JY7JzMzKiCKi1DH0KElXAl8nPY7ynYj4chfjNwKvHuHiJgJN\nRzhtX9Yfy+0y9x/9sdxHUubpEdEvL9mVXeI8liStiIiaUsdxrPXHcrvM/Ud/LHd/LPPRKLdLtWZm\nZkXlxGlmZlYAJ86jc3upAyiR/lhul7n/6I/l7o9lPmK+x2lmZlYAn3GamZkVwInTzMysAE6cR0DS\n5ZJWS1or6ZZSx1MskqZKWirpBUnPS7op6z9e0s8lvZj9H1fqWHuapIGSnpb0s6y7P5R5rKQfS6qX\nVCfp/HIvt6TPZNv2c5LuljS0HMss6TuSGiQ9l9Mvbzkl3Zod31ZLuqw0UfdeTpwFynl12RXAycD7\nJJ1c2qiKphm4OSJOBs4DPpGV9RZgcUTMBhZn3eXmJqAup7s/lPkbwP0RUQ2cRip/2ZZb0mTgU0BN\nRJxKajTlGsqzzHcCl7fr12E5s338GuCUbJpvZsc9yzhxFu7wq8si4iDQ9uqyshMRmyPiqezzbtKB\ndDKpvN/LRvse8K7SRFgckqYAbwPuyOld7mUeA1wMfBsgIg5GxA7KvNykF10Mk1QBDAdeowzLHBEP\nAdva9c5XzquAH0TEgYh4GVhLOu5ZxomzcB29umxyiWI5ZiTNAM4AHgcmRcTmbNDrwKQShVUsXwc+\nD7Tm9Cv3Ms8EGoHvZpeo75A0gjIud0RsAv4nsB7YDOyMiAcp4zK3k6+c/fIYVwgnTuuSpJHAPcCn\nI2JX7rBIzzOVzTNNkt4ONETEynzjlFuZMxXAmcA/RsQZwF7aXaIst3Jn9/SuIv1oOAEYIena3HHK\nrcz59Jdy9hQnzsJ169Vl5ULSIFLSvCsi7s16b5F0fDb8eKChVPEVwYXAOyW9QroMXyvp+5R3mSGd\nVWyMiMez7h+TEmk5l/tS4OWIaIyIQ8C9wAWUd5lz5StnvzrGHQknzsL1m1eXSRLpnlddRHwtZ9B9\nwHXZ5+uAnx7r2IolIm6NiCkRMYP03S6JiGsp4zIDRMTrwAZJc7Nei4AXKO9yrwfOkzQ829YXke7j\nl3OZc+Ur533ANZKGSJoJzAaeKEF8vZZbDjoChb66rK+SNB94GPg1v7nf9wXSfc4fAtNIr2T7/Yho\nX/Ggz5O0APhsRLxd0gTKvMySTidViBoMrAM+QvpxXbbllvQXwNWkGuRPAx8DRlJmZZZ0N7CA9Pqw\nLcCXgJ+Qp5ySvghcT1ovn46I/y5B2L2WE6eZmVkBfKnWzMysAE6cZmZmBXDiNDMzK0BFqQMotYkT\nJ8aMGTNKHYaZWZ+ycuXKpoioLHUcpdDrEqeky0ltZg4E7oiIr3QwzgJSrdZBQFNEXJL1H0uqFXgq\n6WHe6yPisc6WN2PGDFasWNGjZTAzK3eSXi11DKXSqxJnTgPqbyU9kP2kpPsi4oWcccYC3wQuj4j1\nkqpyZtHWSPV7smcshx/D8M3MrB/obfc4u9OA+vuBeyNiPUBENECnjVSbmZn1mN6WOLvTuPAcYJyk\nZZJWSvpQ1j9fI9W/RdINklZIWtHY2NjTZTAzszLW2xJnd1QAZ5Fe+3QZ8OeS5tCNRqrbRMTtEVET\nETWVlf3y3raZmR2h3pY4u9O48EbggYjYGxFNwEOkl+7ma6TazMysx/S2xNmdBtR/CsyXVCFpOHAu\nqRHyfI1Um5mZ9ZheVas2Ipol3Qg8wG8aUH9e0sez4d+KiDpJ9wPPkhoevyMinstm8UngrizptjVS\nbWZm1mP6fSPvNTU14ec4zcwKI2llRNSUOo5S6G2Xas3MzHo1J04zM7MCOHGamZkVwInTzMysAE6c\nZmZmBXDiNDMzK4ATp5mZWQGcOM3MzArgxGlmZlYAJ04zM7MCOHGamZkVwInTzMysAE6cZmZmBXDi\nNDMzK4ATp5mZWQGcOM3MzArgxGlmZlYAJ04zM7MCOHGamZkVoNclTkmXS1otaa2kW/KMs0DSKknP\nS1rebthASU9L+tmxidjMzPqToiVOSfdKepukbi9D0kDgH4ArgJOB90k6ud04Y4FvAu+MiFOA97ab\nzU1A3VEFb2Zmlkcxzzi/CbwfeFHSVyTN7cY05wBrI2JdRBwEfgBc1W6c9wP3RsR6gIhoaBsgaQrw\nNuCOniiAmZlZe0VLnBHxi4j4AHAm8ArwC0m/lPQRSYPyTDYZ2JDTvTHrl2sOME7SMkkrJX0oZ9jX\ngc8DrT1SCDMzs3YqijlzSROAa4EPAk8DdwHzgeuABUc42wrgLGARMAx4TNKvSAm1ISJWSup03pJu\nAG4AmDZt2hGGYWZm/VHREqek/wDmAv8KvCMiNmeD/l3SijyTbQKm5nRPyfrl2ghsjYi9wF5JDwGn\nkc5s3ynpSmAoMFrS9yPi2vYLiYjbgdsBampq4ogKaGZm/VIx73H+74g4OSL+NidpAhARNXmmeRKY\nLWmmpMHANcB97cb5KTBfUoWk4cC5QF1E3BoRUyJiRjbdko6SppmZ2dEoZuI8OasBC4CkcZL+uLMJ\nIqIZuBF4gFQz9ocR8bykj0v6eDZOHXA/8CzwBHBHRDxXrEKYmZnlUkRxrlRKWhURp7fr93REnFGU\nBR6hmpqaWLEi35VjMzPriKSVnVw9LGvFPOMcKEltHdkzmoOLuDwzM7OiK2at2vtJFYH+Kev+w6yf\nmZlZn1XMxPmnpGT5R1n3z3HDBGZm1scVLXFGRCvwj9mfmZlZWSjmc5yzgb8ltTk7tK1/RMwq1jLN\nzMyKrZiVg75LOttsBhYC/wJ8v4jLMzMzK7piJs5hEbGY9MjLqxFxG6kBdjMzsz6rmJWDDmSvFHtR\n0o2kpvNGFnF5ZmZmRVfMM86bgOHAp0iNsl9LatzdzMyszyrKGWfW2MHVEfFZYA/wkWIsx8zM7Fgr\nSuKMiBZJ84sx797iL/7P87zw2q5Sh2FmdkROPmE0X3rHKaUOo08q5j3OpyXdB/wI2NvWMyLuLeIy\nzczMiqqYiXMosBWozekXQFkkTv9SMzPrn4rZcpDva5qZWdkpZstB3yWdYb5JRFxfrGWamZkVWzEv\n1f4s5/NQ4PeA14q4PDMzs6Ir5qXae3K7Jd0NPFKs5ZmZmR0LxWwAob3ZQNUxXJ6ZmVmPK+Y9zt28\n+R7n66R3dJqZmfVZxbxUO6pY8zYzMyuVol2qlfR7ksbkdI+V9K5uTHe5pNWS1kq6Jc84CyStkvS8\npOVZv6mSlkp6Iet/U8+VxszMLCnmPc4vRcTOto6I2AF8qbMJsjZu/wG4gvQC7PdJOrndOGOBbwLv\njIhTgPdmg5qBmyPiZOA84BPtpzUzMztaxUycHc27q0vD5wBrI2JdRBwEfgBc1W6c9wP3RsR6gIho\nyP5vjoinss+7gTpg8lHEb2Zm9luKmThXSPqapBOzv68BK7uYZjKwIad7I7+d/OYA4yQtk7RS0ofa\nz0TSDOAM4PGOFiLpBkkrJK1obGzsZnHMzMyKmzg/CRwE/p105rgf+EQPzLeC9H7PtwGXAX8uaU7b\nQEkjgXuAT0dEh68viYjbI6ImImoqKyt7ICQzM+svilmrdi/QYeWeTmwCpuZ0T8n65doIbM3mv1fS\nQ8BpwBpJg0hJ8y6/hcXMzIqhmLVqf55V5GnrHifpgS4mexKYLWmmpMHANcB97cb5KTBfUoWk4cC5\nQJ0kAd8G6iLiaz1XEjMzs98oZlu1E7OatABExHZJnbYcFBHNkm4EHgAGAt+JiOclfTwb/q2IqJN0\nP/As0ArcERHPZS/O/iDwa0mrsll+ISL+qwhlMzOzfqqYibNV0rS22q9ZhZ3feltKe1mi+692/b7V\nrvurwFfb9XsE0NGFbGZm1rliJs4vAo9kDRQIuAi4oYjLMzMzK7piVg66X1INKVk+DfwEeKNYyzMz\nMzsWitnI+8eAm0g1Y1eRWvN5DKgt1jLNzMyKrZjPcd4EnA28GhELSQ0S7Oh8EjMzs96tmIlzf0Ts\nB5A0JCLqgblFXJ6ZmVnRFbNy0MbsOc6fAD+XtB14tYjLMzMzK7piVg76vezjbZKWAmOA+4u1PDMz\ns2OhmGech0XE8mOxHDMzs2Ir5j1OMzOzsuPEaWZmVgAnTjMzswI4cZqZmRXAidPMzKwATpxmZmYF\ncOI0MzMrgBOnmZlZAZw4zczMCuDEaWZmVgAnTjMzswI4cZqZmRWg1yVOSZdLWi1praRb8oyzQNIq\nSc9LWl7ItGZmZkfjmLwdpbskDQT+AXgrsBF4UtJ9EfFCzjhjgW8Cl0fEeklV3Z3WzMzsaPW2M85z\ngLURsS4iDgI/AK5qN877gXsjYj1ARDQUMK2ZmdlR6W2JczKwIad7Y9Yv1xxgnKRlklZK+lAB0wIg\n6QZJKyStaGxs7KHQzcysP+hVl2q7qQI4C1gEDAMek/SrQmYQEbcDtwPU1NREj0doZmZlq7clzk3A\n1JzuKVm/XBuBrRGxF9gr6SHgtKx/V9OamZkdld52qfZJYLakmZIGA9cA97Ub56fAfEkVkoYD5wJ1\n3ZzWzMzsqPSqM86IaJZ0I/AAMBD4TkQ8L+nj2fBvRUSdpPuBZ4FW4I6IeA6go2lLUhAzMytbiujf\nt/hqampixYoVpQ7DzKxPkbQyImpKHUcp9LZLtWZmZr2aE6eZmVkBnDjNzMwK0O/vcUpqBF49wskn\nAk09GE5f0R/L7TL3H/2x3EdS5ukRUVmMYHq7fp84j4akFf3x5nh/LLfL3H/0x3L3xzIfDV+qNTMz\nK4ATp5mZWQGcOI/O7aUOoET6Y7ld5v6jP5a7P5b5iPkep5mZWQF8xmlmZlYAJ04zM7MCOHEeAUmX\nS1otaa2kW0odT7FImippqaQXJD0v6aas/3hJP5f0YvZ/XKlj7WmSBkp6WtLPsu7+UOaxkn4sqV5S\nnaTzy73ckj6TbdvPSbpb0tByLLOk70hqkPRcTr+85ZR0a3Z8Wy3pstJE3Xs5cRZI0kDgH4ArgJOB\n90k6ubRRFU0zcHNEnAycB3wiK+stwOKImA0szrrLzU2k19W16Q9l/gZwf0RUk95xW0cZl1vSZOBT\nQE1EnEp6q9I1lGeZ7wQub9evw3Jm+/g1wCnZNN/MjnuWceIs3DnA2ohYFxEHgR8AV5U4pqKIiM0R\n8VT2eTfpQDqZVN7vZaN9D3hXaSIsDklTgLcBd+T0LvcyjwEuBr4NEBEHI2IHZV5u0qsVh0mqAIYD\nr1GGZY6Ih4Bt7XrnK+dVwA8i4kBEvAysJR33LOPEWbjJwIac7o1Zv7ImaQZwBvA4MCkiNmeDXgcm\nlSisYvk68HnS+17blHuZZwKNwHezS9R3SBpBGZc7IjYB/xNYD2wGdkbEg5RxmdvJV85+eYwrhBOn\ndUnSSOAe4NMRsSt3WKTnmcrmmSZJbwcaImJlvnHKrcyZCuBM4B8j4gxgL+0uUZZbubN7eleRfjSc\nAIyQdG3uOOVW5nz6Szl7ihNn4TYBU3O6p2T9ypKkQaSkeVdE3Jv13iLp+Gz48UBDqeIrgguBd0p6\nhXQZvlbS9ynvMkM6q9gYEY9n3T8mJdJyLvelwMsR0RgRh4B7gQso7zLnylfOfnWMOxJOnIV7Epgt\naaakwaSb6PeVOKaikCTSPa+6iPhazqD7gOuyz9cBPz3WsRVLRNwaEVMiYgbpu10SEddSxmUGiIjX\ngQ2S5ma9FgEvUN7lXg+cJ2l4tq0vIt3HL+cy58pXzvuAayQNkTQTmA08UYL4ei23HHQEJF1Jug82\nEPhORHy5xCEVhaT5wMPAr/nN/b4vkO5z/hCYRnol2+9HRPuKB32epAXAZyPi7ZImUOZllnQ6qULU\nYGAd8BHSj+uyLbekvwCuJtUgfxr4GDCSMiuzpLuBBaTXh20BvgT8hDzllPRF4HrSevl0RPx3CcLu\ntZw4zczMCuBLtWZmZgVw4jQzMyuAE6eZmVkBnDjNzMwK4MRpZmZWACdOsx4i6ZfZ/xmS3t/D8/5C\nR8sys2PPj6OY9bDc5z8LmKYiIpo7Gb4nIkb2RHxmdnR8xmnWQyTtyT5+BbhI0qrsfY8DJX1V0pOS\nnpX0h9n4CyQ9LOk+Uis9SPqJpJXZOyJvyPp9hfQGj1WS7spdlpKvZu+T/LWkq3PmvSzn/Zp3Za3j\nmNlRqih1AGZl6BZyzjizBLgzIs6WNAR4VNKD2bhnAqdmr28CuD4itkkaBjwp6Z6IuEXSjRFxegfL\nejdwOun9mROzaR7Khp1Beqfia8CjpHZ4H+n54pr1Lz7jNCu+3wU+JGkVqbnCCaT2PwGeyEmaAJ+S\n9AzwK1JD27Pp3Hzg7ohoiYgtwHLg7Jx5b4yIVmAVMKNHSmPWz/mM06z4BHwyIh54U890L3Rvu+5L\ngfMjYp+kZcDQo1jugZzPLXh/N+sRPuM063m7gVE53Q8Af5S9og1Jc7KXRLc3BtieJc1q4LycYYfa\npm/nYeDq7D5qJXAxfpOFWVH5F6hZz3sWaMkuud4JfIN0mfSprIJOI/CuDqa7H/i4pDpgNelybZvb\ngWclPRURH8jp/x/A+cAzpBcRfz4iXs8Sr5kVgR9HMTMzK4Av1ZqZmRXAidPMzKwATpxmZmYFcOI0\nMzMrgBOnmZlZAZw4zczMCuDEaWZmVoD/CxI9PlYePVNlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c600d6c0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+JNfWzaCuJsObxo+knxvcN7M+wEnW+rxXtu5JzlbrN/CnFzaxr6mFIQMqOGtG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\nhwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c600d73cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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t14oIlr+x/cCzq0+s3kwEjB06gAuPP4q6mhznzKxm6AAf5mZWGj77WK+ye18z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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c629225208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UkknYSltE8Oymnc1Hu09s2E4EVI4YxIV/MoHquZUsmFnOsEH+ephZ93ItYyXh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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c668ddbac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YZlaCyjIJW3mLCJ59dSuLltWzaEU9T6zdTARUjRrCOX80ibq51Zx2eCUjhvjr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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c6002d0128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6wmYWLk+v4FzZuAOAqdVD+MBZk6mryVE7ZTT9q9zoy8x6lpO0VaTNO1OHFQsa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\nmZmVKCdpMzOzEvV/AR+nZXTTyapeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c62cb65748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lnJhiuigiVqVpLge+kML5SkT8IPU/CrgVGAMsBd4XEXsPaq2YdWFV0w4W1GWP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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c62c312d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Wkn5cbVXX3gv8gnSWt470PRZX430lW/d9wE5SAhiU7YxvIP2ANpFaoy7Ilvku6SzxhWy5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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c600d762b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c60069cfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HzJw76TezN5JzTsfmzp0by5YtK3UYVkIRwUsNu9oeiL7slS00tQQjB/dj3qyx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c6007ae860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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jqanOcerU0fRzIy0zO0K9PilL2kVKqG+YBEREDG9n8QbgsxHxVNar1FJJ90fE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\ndKD8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c6008d17b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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eRWjgQZW0RKQtPSIpu/sXzewvgbNir9vd/dftjN9gZtcBDxIeibozNmJxbRx+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\nQ8srNPvkMR4REZGcStM95Qe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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c6009d83c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Ap9392dgq2DIze9jdX+qOWCV/bdhxoOXZ6SfXbqe+oYmSfkWcP72MqpkZ5paX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\nxPImIcxc+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c600aeca20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hkUvR2bL7AI8vC5e9n1hew64DdfTs3o0zjx3G1WeOo7J8OGOH9U07TBHJE3mX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\nChzsMgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c600bfec50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+eNZUqiozHDVyoCq5iUiHpSGpP2BmDwJ3xe4LgT+0M81zwBQzm0BI5hcRKts1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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c601da6198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c601df8898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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D7CdphqSZkn5bKP98LntQ0pWS1m9czc3MrF2stYlU0hDgh8D7gHHARySNqxhm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\nz04AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c601fb8668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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atoUT2A2YFxEPRsRLwGXA5IphDgamRcR8gIhYUujXBawnqQtYH3i0CTGbmVmb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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c6020dbf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OiXMMsLDQvSiXFW0HjJR0q6SZkg4DiIjFwLeBBcAS4NmIuLFyBpKOktQrqXfZ\nsmUNCcLMzNrLcE6c9egCdgMOAPYD/lXSdpJGkq5OxwNbARtIOrRy5Ig4JyJ6IqJn9OjRzay3mZmt\nobpaXYEaFgPjCt1jc1nRIuCpiHgBeEHSbcBOud/DEbEMQNI1wFuASxpbZTMza3fD+YrzLmCCpPGS\n1iY17pleMcx1wNskdUlaH9gDmEu6RbunpPUlCdgnl5uZmQ3KsL3ijIiVko4FZpBaxZ4fEbMlfTr3\n/0FEzJV0A3Av8CpwbkTcDyDpKuBuYCVwD3BOK+IwM7P2oohodR2GhZ6enujt7W11NczM1iiSZkZE\nT6vr0UzD+VatmZnZsOPEaWZmVoITp5mZWQlOnGZmZiU4cZqZmZXgxGlmZlZCUxKnpGskHSDJidrM\nzNZozUpkZ5F+yeRBSadJ2r5J8zUzMxtSTUmcEfHziPgosCvwCPBzSb+VdLiktZpRBzMzs6HQtFun\nkjYHPg58gvQKvDNJifSmZtXBzMxssJryrlpJPwG2By4G3h8RS3KvKyT5PXdmZrbGaNZL3r8bEbf0\n16PT3nFoZmZrtmbdqp0oadO+DkkjJR3dpHmbmZkNmWYlzk9GxDN9HRHxNPDJJs3bzMxsyDQrcY7I\nPygNgKQRwNpNmreZmdmQadYzzhtIDYH+O3d/KpeZmZmtUZqVOL9ESpb/nLtvAs5t0rzNzMyGTFMS\nZ0S8CpydP2ZmZmusZr2rdoKkqyTNkfRQ36eO8SZJmidpvqQTqgyzt6RZkmZL+mWhfNM8zwckzZW0\n11DGZGZmnalZt2p/CJwMfAd4F3A4AyTt3IDo+8B7gUXAXZKmR8ScwjCbkt6DOykiFkh6bWESZwI3\nRMSHJK0NrD+UAZmZWWdqVqva9SLiF4Ai4tGIOAU4YIBxdgfmR8RDEfEycDkwuWKYQ4BrImIBQEQs\nBZC0CfAO4Lxc/nLx32HMzMxWV7MS50v5J8UelHSspA8CGw4wzhhgYaF7US4r2g4YKelWSTMlHZbL\nxwPLgB9KukfSuZI2GII4zMyswzUrcU4j3Sr9LLAbcCgwdQim25WndwCwH/CvkrbL5bsCZ0fELsAL\nwN88I5V0lKReSb3Lli0bguqYmVm7a3jizM8qD46I5yNiUUQcHhH/GBG3DzDqYmBcoXtsLitaBMyI\niBci4kngNmCnXL4oIu7Iw11FSqSriIhzIqInInpGjx69GtGZmVmnaXjjoIh4RdLbVmPUu4AJksaT\nEuYU0jOa0lG9AAAJ8UlEQVTNouuA70nqIr2JaA/gOxHxuKSFkraPiHnAPsAcGuQr/zubOY8916jJ\nm5k11MStNubk9+/Q6mqsMZrVqvYeSdOBH5NumwIQEddUGyEiVko6FpgBjADOj4jZkj6d+/8gIuZK\nugG4F3gVODci7s+T+AxwaW5R+xCpJa+ZmdmgKCIaPxPph/0UR0Qc0fCZ16mnpyd6e/3ToGZmZUia\n2Wk/D9msNwf5as/MzNpCUxJnvuL8m0vb4XTFaWZmVo9mPeP8aeH7usAHgceaNG8zM7Mh06xbtVcX\nuyVdBvy6GfM2MzMbSs16AUKlCcBrBxzKzMxsmGnWM84VrPqM83HSb3SamZmtUZp1q3ajZszHzMys\n0Zr1e5wfzL9Y0te9qaSDmjFvMzOzodSsZ5wnR8SzfR35J75ObtK8zczMhkyzEmd/82nWv8KYmZkN\nmWYlzl5Jp0t6Q/6cDsxs0rzNzMyGTLMS52eAl4ErgMuBF4FjmjRvMzOzIdOsVrX9/pC0mZnZmqZZ\nrWpvkrRpoXukpBnNmLeZmdlQatat2lG5JS0AEfE0fnOQmZmtgZqVOF+VtHVfh6Ru+vm1FDMzs+Gu\nWf8S8i/AryX9EhDwduCoJs3bzMxsyDSrcdANknpIyfIe4FrgT82Yt5mZ2VBq1kvePwFMA8YCs4A9\ngd8B727G/M3MzIZKs55xTgPeDDwaEe8CdgGeqT0KSJokaZ6k+ZL6/XcWSXtLmiVpdr4VXOw3QtI9\nkn7a37hmZmZlNesZ54sR8aIkJK0TEQ9I2r7WCJJGAN8H3gssAu6SND0i5hSG2RQ4C5gUEQskVbbU\nnQbMBTYe0mjMzKxjNeuKc1FOctcCN0m6Dnh0gHF2B+ZHxEMR8TLpjUOTK4Y5BLgmIhYARMTSvh6S\nxgIHAOcOUQxmZmZNaxz0wfz1FEm3AJsANwww2hhgYaF7EbBHxTDbAWtJuhXYCDgzIi7K/c4AvpjL\n+yXpKHLr3q233rraYGZmZn/R9F8oiYhfDjxU3bqA3YB9gPWA30m6nZRQl0bETEl716jLOcA5AD09\nPf6/UjMzG9Bw/mmvxcC4QvfYXFa0CHgqvwv3BUm3ATsBuwIfkLQ/sC6wsaRLIuLQJtTbzMzaWLOe\nca6Ou4AJksZLWhuYAkyvGOY64G2SuiStT7qVOzciToyIsRHRnce72UnTzMyGwrC94oyIlZKOBWYA\nI4DzI2K2pE/n/j+IiLmSbgDuBV4Fzo2I+1tXazMza3eK8KM9SM84e3t7W10NM7M1iqSZEdHT6no0\n03C+VWtmZjbsOHGamZmV4MRpZmZWghOnmZlZCU6cZmZmJThxmpmZleDEaWZmVoITp5mZWQlOnGZm\nZiU4cZqZmZXgxGlmZlaCE6eZmVkJTpxmZmYlOHGamZmV4MRpZmZWghOnmZlZCU6cZmZmJThxmpmZ\nleDEaWZmVoITp5mZWQmKiFbXYViQtAx4dBCTGAU8OUTVWVN0YszQmXF3YszQmXGXjXmbiBjdqMoM\nR06cQ0RSb0T0tLoezdSJMUNnxt2JMUNnxt2JMZflW7VmZmYlOHGamZmV4MQ5dM5pdQVaoBNjhs6M\nuxNjhs6MuxNjLsXPOM3MzErwFaeZmVkJTpxmZmYlOHEOkqRJkuZJmi/phFbXp1EkjZN0i6Q5kmZL\nmpbLN5N0k6QH89+Rra7rUJM0QtI9kn6auzsh5k0lXSXpAUlzJe3V7nFL+lzetu+XdJmkddsxZknn\nS1oq6f5CWdU4JZ2Yj2/zJO3XmloPL06cgyBpBPB94H3AROAjkia2tlYNsxI4PiImAnsCx+RYTwB+\nERETgF/k7nYzDZhb6O6EmM8EboiINwI7keJv27gljQE+C/RExI7ACGAK7RnzBcCkirJ+48z7+BRg\nhzzOWfm419GcOAdnd2B+RDwUES8DlwOTW1ynhoiIJRFxd/6+gnQgHUOK98I82IXAQa2pYWNIGgsc\nAJxbKG73mDcB3gGcBxARL0fEM7R53EAXsJ6kLmB94DHaMOaIuA1YXlFcLc7JwOUR8VJEPAzMJx33\nOpoT5+CMARYWuhflsrYmqRvYBbgD2CIiluRejwNbtKhajXIG8EXg1UJZu8c8HlgG/DDfoj5X0ga0\ncdwRsRj4NrAAWAI8GxE30sYxV6gWZ0ce4wbixGmlSNoQuBo4LiKeK/aL9L9NbfP/TZIOBJZGxMxq\nw7RbzFkXsCtwdkTsArxAxS3Kdos7P9ObTDpp2ArYQNKhxWHaLeZqOiXOwXDiHJzFwLhC99hc1pYk\nrUVKmpdGxDW5+AlJW+b+WwJLW1W/Bngr8AFJj5Buw79b0iW0d8yQrioWRcQdufsqUiJt57jfAzwc\nEcsi4s/ANcBbaO+Yi6rF2VHHuHo5cQ7OXcAESeMlrU16iD69xXVqCEkiPfOaGxGnF3pNB6bm71OB\n65pdt0aJiBMjYmxEdJPW7c0RcShtHDNARDwOLJS0fS7aB5hDe8e9ANhT0vp5W9+H9By/nWMuqhbn\ndGCKpHUkjQcmAHe2oH7Dit8cNEiS9ic9BxsBnB8RX29xlRpC0tuAXwH38dfnfSeRnnNeCWxN+lm2\nD0dEZcODNZ6kvYHPR8SBkjanzWOWtDOpQdTawEPA4aQT7baNW9JXgINJLcjvAT4BbEibxSzpMmBv\n0s+HPQGcDFxLlTgl/QtwBGm5HBcR17eg2sOKE6eZmVkJvlVrZmZWghOnmZlZCU6cZmZmJThxmpmZ\nleDEaWZmVoITp1kDSPpt/tst6ZAhnvZJ/c3LzJrD/45i1kDF//8sMU5XRKys0f/5iNhwKOpnZuX5\nitOsASQ9n7+eBrxd0qz8e48jJH1L0l2S7pX0qTz83pJ+JWk66S09SLpW0sz8G5FH5bLTSL/gMUvS\npcV5KflW/j3J+yQdXJj2rYXf17w0vx3HzFZDV6srYNbmTqBwxZkT4LMR8WZJ6wC/kXRjHnZXYMf8\n800AR0TEcknrAXdJujoiTpB0bETs3M+8/gHYmfT7maPyOLflfruQflPxMeA3pPfw/nrowzVrf77i\nNGuufYHDJM0iva5wc9L7PwHuLCRNgM9K+j1wO+lF2xOo7W3AZRHxSkQ8AfwSeHNh2osi4lVgFtA9\nJNGYdSBfcZo1l4DPRMSMVQrTs9AXKrrfA+wVEX+UdCuw7iDm+1Lh+yt43zdbbb7iNGusFcBGhe4Z\nwD/nn2hD0nb5R6IrbQI8nZPmG4E9C/3+3Dd+hV8BB+fnqKOBd+BfsjAbcj7rNGuse4FX8i3XC4Az\nSbdJ784NdJYBB/Uz3g3ApyXNBeaRbtf2OQe4V9LdEfHRQvlPgL2A35N+iPiLEfF4TrxmNkT87yhm\nZmYl+FatmZlZCU6cZmZmJThxmpmZleDEaWZmVoITp5mZWQlOnGZmZiU4cZqZmZXw/wExW5L6XUpI\nNwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c60223b390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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zMyuJk6qZmVlJnFTNzMxK4qRqZmZWEidVMzOzkjipmpmZlcRJ1czMrCROqmZm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\noF3PEhCEbfcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c602355e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MzEripGpmZlaS1T6pSpogabakOZKOrzHNHpKmS5oh6beF8s/nsvslXSpp7da1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\nSZxUzczMSuKkamZmVhInVTMzs5L8f0+XxX01KWGfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c60246d400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SNTMzK4mTrpmZWUnaqg5gbTZ06NBob2+vOgwzs35l+vTpT0XEsKrjWBs56TbR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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c602588ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KiGFVx7EuctJtor29nc7OzqrDMDPrVyQ9VnUM6yo3L5uZmZXESdfMzKwkTrpm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\nzEry/wEOzQbK/2ZtiwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c6026a1470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MrAJckM3MzCrABdnMzKwC2soOYDAZOXJktLe3lx2GmdmgMnPmzMcjYlTZcVSd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c6027bcf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dckgDQtI7gd8D9/Lq/dzjSfexLwc2J/006cciovaBlsqTtBvwpYjYR9LGtHnO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c6028d44e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for method in ['classic', 'forward', 'backward', 'central'] :\n",
    "    if method == 'classic' :\n",
    "        sgd_for_svm_demo(y, X, method)\n",
    "    else :\n",
    "        for h in [10, 5, 1, 0.5, 0.1, 0.05, 0.01, 0.001, 0.0001] :\n",
    "            sgd_for_svm_demo(y, X, method, h)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coordinate Descent (Ascent) for SVM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the closed-form update for the n-th variable alpha, in the dual optimization problem, given alpha and the current corresponding w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calculate_coordinate_update(y, X, lambda_, alpha, w, n):\n",
    "    \"\"\"compute a coordinate update (closed form) for coordinate n.\n",
    "    X: the dataset matrix, shape = (num_examples, num_features)\n",
    "    y: the corresponding +1 or -1 labels, shape = (num_examples)\n",
    "    w: shape = (num_examples)\n",
    "    n: the coordinate to be updated\n",
    "    \"\"\"        \n",
    "    # calculate the update of coordinate at index=n.\n",
    "    x_n, y_n = X[n], y[n]\n",
    "    old_alpha_n = np.copy(alpha[n])\n",
    "    \n",
    "    g = (y_n * x_n.dot(w) - 1)\n",
    "\n",
    "    if old_alpha_n == 0:\n",
    "        g = min(g, 0)\n",
    "    elif old_alpha_n == 1.0:\n",
    "        g = max(g, 0)\n",
    "    else:\n",
    "        g = g\n",
    "    if g != 0:\n",
    "        alpha[n] = min(\n",
    "            max(old_alpha_n - lambda_ * g / (x_n.T.dot(x_n)), 0.0),\n",
    "            1.0)\n",
    "    \n",
    "        # compute the corresponding update on the primal vector w\n",
    "        w += 1.0 / lambda_ * (alpha[n] - old_alpha_n) * y_n * x_n\n",
    "    return w, alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calculate_dual_objective(y, X, w, alpha, lambda_):\n",
    "    \"\"\"calculate the objective for the dual problem.\"\"\"\n",
    "    return np.sum(alpha)  - lambda_ / 2.0 * np.sum(w ** 2) # w = 1/lambda * X * Y * alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration=0, primal:6003.21766, dual:-80.21761, gap:6083.43528\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Lucas\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:22: RuntimeWarning: divide by zero encountered in double_scalars\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration=10000, primal:6003.21766, dual:-71.97291, gap:6075.19057\n",
      "iteration=20000, primal:6057.86750, dual:-125.33057, gap:6183.19807\n",
      "iteration=30000, primal:6057.86750, dual:-120.11498, gap:6177.98248\n",
      "iteration=40000, primal:6057.86750, dual:-116.88346, gap:6174.75096\n",
      "iteration=50000, primal:6057.86750, dual:-114.61378, gap:6172.48128\n",
      "iteration=60000, primal:6057.86750, dual:-114.38160, gap:6172.24910\n",
      "iteration=70000, primal:6057.86750, dual:-114.13428, gap:6172.00178\n",
      "iteration=80000, primal:6057.86750, dual:-111.87311, gap:6169.74061\n",
      "iteration=90000, primal:6057.86750, dual:-111.66917, gap:6169.53667\n",
      "iteration=100000, primal:6057.86750, dual:-110.43385, gap:6168.30135\n",
      "iteration=110000, primal:6057.86750, dual:-110.19085, gap:6168.05835\n",
      "iteration=120000, primal:6057.86750, dual:-108.92677, gap:6166.79427\n",
      "iteration=130000, primal:6057.86750, dual:-108.69608, gap:6166.56358\n",
      "iteration=140000, primal:6057.86750, dual:-108.45988, gap:6166.32738\n",
      "iteration=150000, primal:5923.49990, dual:26.14640, gap:5897.35350\n",
      "iteration=160000, primal:5923.49990, dual:26.39153, gap:5897.10837\n",
      "iteration=170000, primal:5923.49990, dual:27.62433, gap:5895.87557\n",
      "iteration=180000, primal:8753.65378, dual:-2802.24103, gap:11555.89481\n",
      "iteration=190000, primal:8753.65378, dual:-2801.99275, gap:11555.64653\n",
      "iteration=200000, primal:8753.65378, dual:-2801.76178, gap:11555.41556\n",
      "iteration=210000, primal:6105.64247, dual:-153.51537, gap:6259.15784\n",
      "iteration=220000, primal:6105.64247, dual:-153.25915, gap:6258.90162\n",
      "iteration=230000, primal:6105.64247, dual:-153.01283, gap:6258.65530\n",
      "iteration=240000, primal:6105.64247, dual:-151.77417, gap:6257.41665\n",
      "iteration=250000, primal:6105.64247, dual:-151.54629, gap:6257.18877\n",
      "iteration=260000, primal:5927.72599, dual:26.61276, gap:5901.11323\n",
      "iteration=270000, primal:5927.72599, dual:26.84007, gap:5900.88592\n",
      "iteration=280000, primal:5927.72599, dual:27.10421, gap:5900.62178\n",
      "iteration=290000, primal:5927.72599, dual:27.35536, gap:5900.37063\n",
      "iteration=300000, primal:5927.72599, dual:27.57463, gap:5900.15136\n",
      "iteration=310000, primal:5927.72599, dual:27.84527, gap:5899.88071\n",
      "iteration=320000, primal:5927.72599, dual:28.14447, gap:5899.58152\n",
      "iteration=330000, primal:5927.72599, dual:28.35262, gap:5899.37336\n",
      "iteration=340000, primal:5931.54093, dual:24.79982, gap:5906.74111\n",
      "iteration=350000, primal:5940.85059, dual:15.68792, gap:5925.16267\n",
      "iteration=360000, primal:5931.67852, dual:25.07493, gap:5906.60359\n",
      "iteration=370000, primal:5931.67852, dual:25.35460, gap:5906.32392\n",
      "iteration=380000, primal:5931.67852, dual:25.58373, gap:5906.09479\n",
      "iteration=390000, primal:6146.20950, dual:-188.71583, gap:6334.92533\n",
      "iteration=400000, primal:6146.20950, dual:-188.46944, gap:6334.67895\n",
      "iteration=410000, primal:6146.20950, dual:-188.23106, gap:6334.44057\n",
      "iteration=420000, primal:5929.27659, dual:28.93928, gap:5900.33731\n",
      "iteration=430000, primal:5929.27659, dual:29.17661, gap:5900.09998\n",
      "iteration=440000, primal:5929.27659, dual:29.43124, gap:5899.84535\n",
      "iteration=450000, primal:5929.27659, dual:29.70839, gap:5899.56821\n",
      "iteration=460000, primal:5929.27659, dual:29.95484, gap:5899.32175\n",
      "iteration=470000, primal:5929.27659, dual:30.18338, gap:5899.09321\n",
      "iteration=480000, primal:5929.27659, dual:30.42525, gap:5898.85134\n",
      "iteration=490000, primal:5929.27659, dual:30.64489, gap:5898.63170\n",
      "iteration=500000, primal:5929.27659, dual:30.90708, gap:5898.36951\n",
      "iteration=510000, primal:5929.27659, dual:31.14968, gap:5898.12691\n",
      "iteration=520000, primal:5929.27659, dual:31.39135, gap:5897.88525\n",
      "iteration=530000, primal:5929.27659, dual:31.63380, gap:5897.64279\n",
      "iteration=540000, primal:5929.27659, dual:31.93084, gap:5897.34576\n",
      "iteration=550000, primal:5929.27659, dual:32.14777, gap:5897.12883\n",
      "iteration=560000, primal:5929.27659, dual:32.41562, gap:5896.86097\n",
      "iteration=570000, primal:5929.27659, dual:32.67035, gap:5896.60624\n",
      "iteration=580000, primal:5929.27659, dual:32.89306, gap:5896.38354\n",
      "iteration=590000, primal:5929.27659, dual:33.18614, gap:5896.09045\n",
      "iteration=600000, primal:5938.00314, dual:24.66035, gap:5913.34279\n",
      "iteration=610000, primal:5938.00314, dual:24.90433, gap:5913.09881\n",
      "iteration=620000, primal:5938.00314, dual:25.14366, gap:5912.85947\n",
      "iteration=630000, primal:5938.00314, dual:25.43368, gap:5912.56946\n",
      "iteration=640000, primal:5938.00314, dual:25.68989, gap:5912.31325\n",
      "iteration=650000, primal:5938.00314, dual:25.92202, gap:5912.08112\n",
      "iteration=660000, primal:5938.00314, dual:26.14166, gap:5911.86148\n",
      "iteration=670000, primal:5982.01312, dual:-17.59203, gap:5999.60516\n",
      "iteration=680000, primal:6035.22577, dual:-70.55441, gap:6105.78018\n",
      "iteration=690000, primal:6035.22577, dual:-70.31069, gap:6105.53646\n",
      "iteration=700000, primal:6035.22577, dual:-70.06837, gap:6105.29414\n",
      "iteration=710000, primal:6035.22577, dual:-69.84503, gap:6105.07080\n",
      "iteration=720000, primal:6035.22577, dual:-69.59357, gap:6104.81934\n",
      "iteration=730000, primal:6035.22577, dual:-69.34639, gap:6104.57215\n",
      "iteration=740000, primal:6035.22577, dual:-69.08971, gap:6104.31547\n",
      "iteration=750000, primal:6035.22577, dual:-68.83261, gap:6104.05838\n",
      "iteration=760000, primal:6035.22577, dual:-68.62242, gap:6103.84819\n",
      "iteration=770000, primal:6209.08551, dual:-242.20914, gap:6451.29465\n",
      "iteration=780000, primal:6209.08551, dual:-241.92717, gap:6451.01268\n",
      "iteration=790000, primal:6209.08551, dual:-241.63650, gap:6450.72201\n",
      "iteration=800000, primal:6209.08551, dual:-241.41854, gap:6450.50405\n",
      "iteration=810000, primal:6209.08551, dual:-241.20779, gap:6450.29330\n",
      "iteration=820000, primal:6209.08551, dual:-240.97824, gap:6450.06376\n",
      "iteration=830000, primal:6209.08551, dual:-240.70407, gap:6449.78958\n",
      "iteration=840000, primal:6209.08551, dual:-240.46845, gap:6449.55396\n",
      "iteration=850000, primal:6209.08551, dual:-240.24716, gap:6449.33267\n",
      "iteration=860000, primal:6209.08551, dual:-239.99625, gap:6449.08176\n",
      "iteration=870000, primal:6209.08551, dual:-239.77131, gap:6448.85682\n",
      "iteration=880000, primal:6209.08551, dual:-239.52939, gap:6448.61490\n",
      "iteration=890000, primal:6209.08551, dual:-239.33729, gap:6448.42280\n",
      "iteration=900000, primal:6209.08551, dual:-239.08506, gap:6448.17057\n",
      "iteration=910000, primal:5948.00442, dual:22.23185, gap:5925.77257\n",
      "iteration=920000, primal:5948.00442, dual:22.48476, gap:5925.51966\n",
      "iteration=930000, primal:5948.00442, dual:22.75065, gap:5925.25377\n",
      "iteration=940000, primal:5948.00442, dual:23.00101, gap:5925.00341\n",
      "iteration=950000, primal:5948.00442, dual:23.25221, gap:5924.75220\n",
      "iteration=960000, primal:5948.00442, dual:23.52044, gap:5924.48397\n",
      "iteration=970000, primal:5948.00442, dual:23.72277, gap:5924.28165\n",
      "iteration=980000, primal:5948.00442, dual:23.96550, gap:5924.03891\n",
      "iteration=990000, primal:5943.37065, dual:28.80268, gap:5914.56798\n",
      "training accuracy = 0.11236666666666667\n"
     ]
    }
   ],
   "source": [
    "def coordinate_descent_for_svm_demo(y, X):\n",
    "    max_iter = 1000000\n",
    "    lambda_ = 0.01\n",
    "\n",
    "    num_examples, num_features = X.shape\n",
    "    w = np.zeros(num_features)\n",
    "    alpha = np.zeros(num_examples)\n",
    "    \n",
    "    for it in range(max_iter):\n",
    "        # n = sample one data point uniformly at random data from x\n",
    "        n = random.randint(0,num_examples-1)\n",
    "        \n",
    "        w, alpha = calculate_coordinate_update(y, X, lambda_, alpha, w, n)\n",
    "            \n",
    "        if it % 10000 == 0:\n",
    "            # primal objective\n",
    "            primal_value = calculate_primal_objective(y, X, w, lambda_)\n",
    "            # dual objective\n",
    "            dual_value = calculate_dual_objective(y, X, w, alpha, lambda_)\n",
    "            # primal dual gap\n",
    "            duality_gap = primal_value - dual_value\n",
    "            print('iteration=%i, primal:%.5f, dual:%.5f, gap:%.5f'%(\n",
    "                    it, primal_value, dual_value, duality_gap))\n",
    "    print(\"training accuracy = {l}\".format(l=calculate_accuracy(y, X, w)))\n",
    "\n",
    "coordinate_descent_for_svm_demo(y_train, x_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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