logistic regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating Fake Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, Y = make_blobs(n_samples=200, centers=2, n_features=2, cluster_std=5, random_state=11)\n",
    "m = 200"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from pandas import DataFrame \n",
    "df = DataFrame(dict(x=X[:,0], y=X[:,1], label=Y))\n",
    "colors = {0:'blue', 1:'orange'}\n",
    "fig, ax = plt.subplots()\n",
    "grouped = df.groupby('label')\n",
    "for key, group in grouped:\n",
    "    group.plot(ax=ax, kind='scatter', x='x', y='y', label=key, color=colors[key])\n",
    "plt.xlabel('X_0')\n",
    "plt.ylabel('X_1')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hx(w,X):\n",
    "    z = np.array(w[0] + w[1]*np.array(X[:,0]) + w[2]*np.array(X[:,1]))\n",
    "    return sigmoid(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cost Function - Binary Cross Entropy "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(w, X, Y):\n",
    "    y_pred = hx(w,X)\n",
    "    return -1 * sum(Y*np.log(y_pred) + (1-Y)*np.log(1-y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def grad(w, X, Y):\n",
    "    y_pred = hx(w,X)\n",
    "    g = [0]*3\n",
    "    g[0] = -1 * sum(Y*(1-y_pred) - (1-Y)*y_pred)\n",
    "    g[1] = -1 * sum(Y*(1-y_pred)*X[:,0] - (1-Y)*y_pred*X[:,0])\n",
    "    g[2] = -1 * sum(Y*(1-y_pred)*X[:,1] - (1-Y)*y_pred*X[:,1])\n",
    "    return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def descent(w_new, w_prev, lr):\n",
    "    print(w_prev)\n",
    "    print(cost(w_prev, X, Y))\n",
    "    j=0\n",
    "    while True:\n",
    "        w_prev = w_new\n",
    "        w0 = w_prev[0] - lr*grad(w_prev, X, Y)[0]\n",
    "        w1 = w_prev[1] - lr*grad(w_prev, X, Y)[1]\n",
    "        w2 = w_prev[2] - lr*grad(w_prev, X, Y)[2]\n",
    "        w_new = [w0, w1, w2]\n",
    "        print(w_new)\n",
    "        print(cost(w_new, X, Y))\n",
    "        if (w_new[0]-w_prev[0])**2 + (w_new[1]-w_prev[1])**2 + (w_new[2]-w_prev[2])**2 <pow(10,-6):\n",
    "            return w_new\n",
    "        \n",
    "        if j>100: \n",
    "            return w_new\n",
    "        j+=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initializing Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "w=[1,1,1] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 1]\n",
      "126.96627984087802\n",
      "[1.2539422898588644, -0.5512710240837779, 1.1843328109648115]\n",
      "112.81815690482537\n",
      "[1.2400289717256012, 1.3365539538600526, 1.3041857280167006]\n",
      "168.5749357223354\n",
      "[1.496038556709955, -0.26091766794801896, 1.498589948744304]\n",
      "75.77036936925771\n",
      "[1.552998152697941, 0.5805338886016641, 1.2059963033700993]\n",
      "67.88063552779857\n",
      "[1.7129970823802407, -0.12884219161477717, 0.9205552719943874]\n",
      "49.631255078140065\n",
      "[1.721522374547689, 0.8081464107255731, 0.784948881261807]\n",
      "84.65164447415044\n",
      "[1.9318934810214365, -0.5853214217947893, 0.9260582355386137]\n",
      "137.02236299684375\n",
      "[1.792209433897121, 2.259519445068961, 1.8717281361304319]\n",
      "296.375960910099\n",
      "[2.0717704014100984, 0.4671501798576154, 2.2375086018139254]\n",
      "96.21982855549399\n",
      "[2.2275891867070294, 0.17556932949773574, 1.7757719140648793]\n",
      "66.93614685472798\n",
      "[2.34635073219192, 0.10042351859759649, 1.3377088708014218]\n",
      "47.88369966457564\n",
      "[2.420814222298708, 0.2006649466226462, 0.9803329461122527]\n",
      "35.74059972551982\n",
      "[2.47109414690982, 0.15761477718705647, 0.7206148121331153]\n",
      "31.156227520259954\n",
      "[2.4669494157236738, 0.33368915465087157, 0.6530382051207929]\n",
      "31.825794017269445\n",
      "[2.5018185122166057, 0.052068234061564855, 0.5947139224875355]\n",
      "37.13648828690444\n",
      "[2.4168290256808196, 0.8618663362335011, 0.8721726092434906]\n",
      "77.31322559093016\n",
      "[2.596954895024072, -0.39576768312727784, 0.9305031886901464]\n",
      "97.53803980330012\n",
      "[2.4680716616586964, 1.8009384856190926, 1.4733863829082396]\n",
      "210.1650208652238\n",
      "[2.7256313646387795, 0.10398042243284711, 1.7582377785757068]\n",
      "60.930800473556\n",
      "[2.8139079434551295, 0.18042029298994794, 1.356581836503274]\n",
      "44.87910324512945\n",
      "[2.8764378665294585, 0.18788023515027294, 1.0240956114450044]\n",
      "35.1115767203633\n",
      "[2.9004091563475756, 0.25373283853477424, 0.8052448292395792]\n",
      "31.203934623682823\n",
      "[2.905564316215357, 0.23573784244902107, 0.6972405539065145]\n",
      "30.64594404630533\n",
      "[2.884978695284491, 0.3156866373830539, 0.7013654663287641]\n",
      "30.87299094573297\n",
      "[2.8899757309235032, 0.18571374355707734, 0.662108112619276]\n",
      "31.58765075793203\n",
      "[2.8456086105455767, 0.44695414312741255, 0.7472822400464028]\n",
      "34.997339236852504\n",
      "[2.8946903864992204, 0.0311385451581056, 0.652724208526957]\n",
      "41.16553917784135\n",
      "[2.78333314375564, 1.0205125031757631, 0.9858502424130702]\n",
      "90.41042650497221\n",
      "[2.970171901127539, -0.2925927602835001, 1.054289078329687]\n",
      "77.28627608547319\n",
      "[2.8765338440725268, 1.3870481637289969, 1.2593201244024514]\n",
      "137.884699579421\n",
      "[3.096205693561861, -0.09815951484676533, 1.3875700666825428]\n",
      "55.28433950652438\n",
      "[3.091222620686947, 0.691357878366354, 1.1851902704372872]\n",
      "54.56897648020144\n",
      "[3.197031648206172, 0.04853253754001363, 0.9522363399023503]\n",
      "38.879877723561194\n",
      "[3.152849114551307, 0.6705086356955698, 0.9042855300104767]\n",
      "47.42326651334623\n",
      "[3.249401718635574, -0.05586144519042935, 0.7968950006624693]\n",
      "50.77734982683568\n",
      "[3.1265348460183477, 1.2297186855362119, 1.1081714720550426]\n",
      "111.36985561835434\n",
      "[3.326563756861511, -0.1791741101134301, 1.2218462740483753]\n",
      "62.108694704750796\n",
      "[3.269128921912794, 1.0293263482837012, 1.2008084141382773]\n",
      "82.99082598516479\n",
      "[3.433600163161756, -0.10416961202267583, 1.1426909126167342]\n",
      "53.969099415361306\n",
      "[3.372434392083106, 0.9606133194736919, 1.1258764505552485]\n",
      "73.24867011604414\n",
      "[3.5227671344926526, -0.10541269443776047, 1.0639829014706683]\n",
      "54.95877911862518\n",
      "[3.4402314176940667, 1.0678781146572354, 1.1359656744505753]\n",
      "84.39209613357035\n",
      "[3.6053162123525917, -0.1094419475498285, 1.1193961332548408]\n",
      "55.78053131843188\n",
      "[3.5284998867311446, 1.035838685329749, 1.1603344516799623]\n",
      "79.31512100875807\n",
      "[3.6850794814765253, -0.0823331021711422, 1.117327385696941]\n",
      "53.365825253435844\n",
      "[3.6094245208717335, 0.990136688364013, 1.1479057502919368]\n",
      "73.00073094363131\n",
      "[3.7550639240710013, -0.06190456364194685, 1.0874826200950347]\n",
      "51.85370536629623\n",
      "[3.6740149106228186, 0.9863883933259856, 1.1383256238195103]\n",
      "71.6077027550773\n",
      "[3.816365454730692, -0.053415680920452235, 1.079972647866281]\n",
      "51.512482717018116\n",
      "[3.7321415001226725, 0.9874518828741854, 1.1419582058166857]\n",
      "70.91147940312463\n",
      "[3.8721953817202945, -0.040975086743274325, 1.0817922008147334]\n",
      "50.68840558905084\n",
      "[3.7880511473342113, 0.9676622239349191, 1.1410140920986547]\n",
      "68.11602429098141\n",
      "[3.9218160093807857, -0.02032252700940551, 1.069864113475001]\n",
      "49.12965800771219\n",
      "[3.8372555826614154, 0.9397003151318558, 1.1301065005574003]\n",
      "64.66526827228455\n",
      "[3.963079147188273, 0.0015189750142303726, 1.048002481200122]\n",
      "47.55953959619178\n",
      "[3.8768575558853064, 0.9161026456599739, 1.116464165382025]\n",
      "61.870753988367085\n",
      "[3.995752432150913, 0.019597576030487285, 1.027414752411626]\n",
      "46.36190019402692\n",
      "[3.907745460549524, 0.89829389197684, 1.1055063163003485]\n",
      "59.82357707095895\n",
      "[4.0211666051250194, 0.03440304270300665, 1.0117153695411087]\n",
      "45.42762114954028\n",
      "[3.932061436494771, 0.8820448670623741, 1.0967233693735197]\n",
      "58.07265242127726\n",
      "[4.040538211472588, 0.0486222507940266, 0.9980600115598323]\n",
      "44.528626105329884\n",
      "[3.95104075816509, 0.8635822178845587, 1.087464778932447]\n",
      "56.25191093140636\n",
      "[4.0542064633885655, 0.06390897971924736, 0.9830845369826282]\n",
      "43.560297250359895\n",
      "[3.9647146116297285, 0.8419896969170714, 1.0762339319145042]\n",
      "54.28859760963312\n",
      "[4.061974777022511, 0.08010117719043697, 0.9658476947904583]\n",
      "42.55609321933739\n",
      "[3.9726570293297416, 0.8185528342778258, 1.0632653646122094]\n",
      "52.30757518813522\n",
      "[4.063741047353516, 0.09591304118161548, 0.9474917553090927]\n",
      "41.60869408164448\n",
      "[3.9746698824165576, 0.7955306511635729, 1.0497944865210715]\n",
      "50.49160062072334\n",
      "[4.0598875620346835, 0.10973094543337403, 0.929938489713735]\n",
      "40.807102034142616\n",
      "[3.9710681877912237, 0.7754202550430537, 1.0373138237663093]\n",
      "49.006821287773285\n",
      "[4.051367062032833, 0.120083598318384, 0.9149680408447317]\n",
      "40.21376802733146\n",
      "[3.9626934207233138, 0.7605664236412619, 1.027175552319945]\n",
      "47.97972673492794\n",
      "[4.03960146305846, 0.1258626202000106, 0.9038701158750538]\n",
      "39.8665848590012\n",
      "[3.9508175989838605, 0.7529117846030396, 1.0204483002710898]\n",
      "47.49986495259877\n",
      "[4.026319016314264, 0.12633822832598507, 0.8975122703008471]\n",
      "39.79309105387893\n",
      "[3.937022647315148, 0.7539702241394387, 1.0179583095352271]\n",
      "47.64232237902202\n",
      "[4.013431600037268, 0.12097838008325779, 0.8966869188055052]\n",
      "40.03060914399324\n",
      "[3.9231193858382776, 0.7650499798316024, 1.0204780871163988]\n",
      "48.50370516914084\n",
      "[4.0030116224672625, 0.10920033650354244, 0.9025652832558652]\n",
      "40.647028942768124\n",
      "[3.911168807082645, 0.7874617085157639, 1.0289496414232508]\n",
      "50.233655133405684\n",
      "[3.9973475854531766, 0.09037455328475408, 0.9170124097333662]\n",
      "41.74920834355003\n",
      "[3.9036347048532614, 0.8219989928942072, 1.0444815131818708]\n",
      "53.00756665023323\n",
      "[3.998896442510712, 0.06491278493707686, 0.9421306486550264]\n",
      "43.414481126056494\n",
      "[3.903578932273919, 0.8658652317559935, 1.0673333907773224]\n",
      "56.743118405663786\n",
      "[4.009605120891904, 0.03790132000571389, 0.9771595777097101]\n",
      "45.367245465512056\n",
      "[3.9142374607656074, 0.9053571447819756, 1.0933903406414625]\n",
      "60.26445149748922\n",
      "[4.028982704706953, 0.022311918251399665, 1.0115367561804436]\n",
      "46.56452396428107\n",
      "[3.936118279261484, 0.9161216408470005, 1.1107981056735687]\n",
      "61.119030592288695\n",
      "[4.05221859760455, 0.029367074818002936, 1.0249045662087954]\n",
      "46.03001820966252\n",
      "[3.962804479787527, 0.890313219168536, 1.1082732172211933]\n",
      "58.54793332826261\n",
      "[4.071694739617031, 0.05576987084898566, 1.0076561457699287]\n",
      "44.146310350361176\n",
      "[3.9843650919995444, 0.8441134205516451, 1.087132296857637]\n",
      "54.38313567139385\n",
      "[4.081221437775141, 0.08935078570508614, 0.9713207459960232]\n",
      "42.00179619891018\n",
      "[3.9945804561228613, 0.7946114356824799, 1.058305857789166]\n",
      "50.363531876210516\n",
      "[4.078719695444127, 0.11976411937445264, 0.9330027012706759]\n",
      "40.284159514532284\n",
      "[3.992398365094767, 0.7520453654158086, 1.0315755035230465]\n",
      "47.27452627208367\n",
      "[4.065870596044042, 0.14186053507189011, 0.9025860178561832]\n",
      "39.138492702670455\n",
      "[3.9799787694173245, 0.7210735715432988, 1.0111931600659616]\n",
      "45.255334753917104\n",
      "[4.0460976445817955, 0.15448991706397763, 0.8819752531296552]\n",
      "38.48142071458852\n",
      "[3.960514974560398, 0.7030948526309135, 0.9977984989102618]\n",
      "44.1983732970012\n",
      "[4.022890960756249, 0.1583065776331426, 0.8696992149881329]\n",
      "38.21770810120381\n",
      "[3.937085053426291, 0.6982103483166531, 0.9909832248890901]\n",
      "43.98944447469072\n",
      "[3.937085053426291, 0.6982103483166531, 0.9909832248890901]\n"
     ]
    }
   ],
   "source": [
    "w = descent(w,w,.0099)\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the Result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MHtKXqkoPX5hWyoA+Qc7FVFZ2TTWxmikCI6tCkd0X6D5rggoknsHeLfc6mdVaOIV4eDOs+1T03yJWhZoJitdBONoM5VMW07XWB6N9N5PNUJFo6+jixe37WF7TxKbGI+TlZHH9hSNYNKucKWUDeib7pZujMB4zRSjzUOA+VzxrRAYVlJjjJ3HyvTbDDxB8j/xKNlaTUaz3WCraJk1a+CxEWZjLu/uOs6K2kWc27+HUmS4uGFFM1SwPN04eRd98Ry8yEyMe/0C4CJ2sApj1eO8ByImDvRkymekHCJTnVEP438L/eaIVaZ34W7iIdFEWu4EjGBVyHtVaPxbuu6IsYudkeyer3zKS/d7dd5yi/BxumjKKqlkezh9ebLd45hHvwNewEmpuDzBtZMOM/4Kxd6VC2rMkMvgluhoIPpdVDvhwv0UykWWCKaSLshiptd6rlBoKvALco7XeEPD5ncCdAB6PZ1pjY6NNkroTrTVbmo+yvKaRNW/v40xnN9PLB1I1y8OnJ46gIDcN+ojHY6Zo88Kznt6hsqmMrvHLq3KMwXPaL6Mrq6Sr7KagFlSP8yVomgqHrCySIi2URSBKqR8AJ7XWPw31uawskuPIqTM8tbmFFbVN7D54ioF9crllehkLZ3qoGNI3voM57Z83VnnsDmsNZwqbsTSywkhE7kgKJlrp9GSI1TQV6/2WPIukcX3orFKqL5CltT7he30N8O82i5W2DOybx5cvH8Mdl47mjQ8PsaK2kWV/281jGz7i8rFDqKosZ+74GJL9nPjPG2uXPbuja041GCuKYDZ9HcpuNrfMR6SwU6vqaoVS2snc70i1wZwwSUkzHKssgGHAM75onRygWmu91l6R0p+sLMVlY4dw2dgh7D/e9kmy393LNzGsOJ/5MzwsmOlheP8QyX5u/+e1O6w11KAP0XMHEpE7moJJpI1tJMJNIpK535JnkVJcY4aKhpihrKOzq5tX3zvAitomNnzgJUsp5o4fSlVlOZedO+Rssp/dZhyzsNOM9sGjUHd3z22x2vHjlTtVYafRfCqJ3m/J4DYF15uhBOeQk53FNROGc82E4TQdOk31xiaeqG/mpR37KR/ch4UzPdwyvYxBdptxzMLsWXU8+H0Tm75uDOK6K/JsO3igjUfuVJVxj7YCSPR+270SzDBkZSEkRHtnF2u3f8yKmiY2NhwmLyeLz0waQZXnfaY13o7KliSppIg02463UrDdAQdWrwDsvj6Xk3bRUNEQZWEf7+8/wYqaRp7evIcT7Z2cP7SQqguzuXH6OPoNGG63eOlFYGht54men4UagJ0ScJCoyUsUgeWIshBSzqn2Tv6ydS/LaxvZvuc4ffOyuWHKKKoqPUwY2d9u8SLjhEEpmgyR+kBAb/+QFTP6QBkhvnuWsE/FQZF1aYj4LISU0zc/h/kzPXxxRhlbW46xvKaRpza1UF3bxBTPAKoqy7n+Qgcm+zlhUIolGS+U7T+QYP+Q2dFCgfep8zQoZSifWO9ZPL4Jt0fWpSHSVlUwHaUUk8sG8NNbLqL2gTn82/UXcKy1g289uZVZP17P/13zDrsPnop8kGRamcZD4KDUccx4rl2c2taygTJ0njDKn9fdbURGBRIutDanKHS7UzMDDoLvk+4wjp3MPYv0G0drmSukHFEWgqUM6JPH4stGs/6fP0X1Vyq59Jwh/O6NBq766WtU/XcNL27bR0dXUOOIhpWG+eTVq43nhpXWCeiEQSlSMl7gQBqqJ/eMpTDnVcO0FDyzj7eHdzQZw/XNhvjvWbTf2KrIulRNQtIQ8VkIKefA8TaeqG9m5cZm9hxtZWi/fObPKGP+TA8jC05aa2cPFVlkd6x+mxeeLevZUAkgpx/MWR+6Qq6VvoJwx4jkL4nnnsV6z83OA3GCudGBiINbcDxd3ZrXdh5geU0jr73vRQGzz8ljEQ9yReHfyFK+v81kEvtiGSA+8RdkG4OS31+QSqd3Msl4obBC9sDBu7PV57MoiH8gj7d0vBnX4YRJgUMRB7fgeLKzFHPGD2PO+GE0Hz7Nyo1NPFHXyLpT91KWdxsLB73IrYNeYXC2CXb2SE7SigXQcdyXCJdn5C4c3Q4fLUvdLLRHMl4e6M7ETUZWzaCDk/ggsYE8HhOTWQmSUhokaWRlITiKM53dvPTaUyyv2U3tyQnkqQ6uPQcWzbmCGRUDe3b2i0asM9hoJhZI3Sw02Zm0W2bQqe5w55b7YgOyshBcSV5OFp+dewufvczLrqZdLN+Ry1NbD/Hco29y3rAiqirLuWnqKIoLcqMfLNYZbLSQVEjdLDTZmbRbZtCpKjXiR0qDJI2sLATH03qmi79s3cuK2ka2thyjMDebGyaPpKqynEmlUZL9YpnBHnsXXpzS28EciKws0gMnJF86DHFwC2nJNl+y3+qte2jr6Oai0v5UVZbz2YtGUpgXJtkv0gDhVyYa6G41BlaAMYt9PosU1rgyy9eQahOP4GpEWQhpzbHWDp7xdfb74MBJigty+Py0UqoqPZw7tF9sBwk1C8/Kh09vgf7jUzsLNXNF0OaFI1sMBThoisygQVYUERCfhZDW9C/M5fZLR3PbJRVs3H2Y5bVNLK9p5Ld/b2DWmEFUVZYzb8Jw8nIi5J2Gsu9n50PnSeN1KkuVm+VrCF6dTF0Cg6Zm1iAZrBgkv8IURFkIrkYpReWYwVSOGczBkxfwRH0z1bVN3LNyC0OK8vnijFLmz/BQNqhP751DOcC72o3yGanGjIzlUKHCdXcbyX3+UNx0HyRDKcvN35QaUybg6HIfSqlrlVI7lVK7lFL32S2P4GyGFOXzj1eey4ZvX8VvvzSDyWX9eeS1D7niJ3/ljt/V8ep7++nqDjC7BpbD8PsqyIK106wtMRIKM0pzhCvJ0XnCnppXqSZUna9NX+9dSkVqTCWEY30WSqls4H3gaqAFqAMWaK3fCfV98VkIodhztJVVG5tYVdeM90Q7owYUsrDSw63Tyyjpl298KVQ0lJURRLE0NkrEbBRvCfN0I1ReTU6RsUJL1W/rQmL1WTh5ZTET2KW1/khrfQZYBdxgs0yCyxg1oJB/uWYcb9w3m19XTaV8cB9+8tJOLnloPV+t3sybHx5Cd5wwylYEYtXsM1oBvYISYzBPps1odqFhegrGjS1u4yGUKU93GeVbzCimmOE42WcxCmgOeN8CVNoki+Bm2rzknmrgurEVXDdpFh96T1Jd28SfN7Xw/Nv7OGdIAVX5c/n8gLX0z/aVTrdiYI1QfsR7ooSGBqiogJJkxrHAZLdP2q5mSBJauMS7igVQdrNEQyWJk81QtwDztNZf9r3/B2Cm1vqegO/cCdwJ4PF4pjU2Ntoiq+BgIkTCtHV0sebtfSyvaeSt5qMUqHbm9XuThQPW0jngAS5dGOQMTsBE5PVyVglkhS4/8lLHOm768gzy8uDMGVi2DBbE64cOJ1smhoxm4jUngevzLJRSFwM/0FrP872/H0Br/eNQ3xefhdCLNi/62XJUd+TcBa8Xzpl+jH4X7iR33EHI0XTs788PFnmounwkffJyEgq/XLkSFi/mEyWw/L+93Jzd06egswop/6dGmr1n5SkshMbGOFYYEhoqJEE6+CzqgLFKqdFKqTxgPvCczTIJLuKlpxs4fjJ6Y6OGBsg61p+9a2bS9KurOfTyBLJyuvnhK9uo/OF6vv90He+/9v24uul5vYaiaG2FY8eM50VfLuH4+J4RTx+VLOP4mZ5aITfXkCkmUtHpTxoGCTjYZ6G17lRKfQ14CcgGHtda77BZLMFphDE5eL3wlW9U8N5/9HR46q4OVJAvoqLCmPkD6DO5nNxSQdd75az++xGe39nIyk17+X3XEmb23UbVoBe5tv8b5OdGTphraDBWFK0Bi5rcXNjZvoAZN5wtoFd8ouSTc/vp6DBkigmTkvl6mMsCd5NVi+DDySsLtNYvaK3P01qfo7X+od3yCA4jQmRRQwMcP1PCHY8t43R7IcdOF3P6jDGTDx5ES0oMP0FhIRQXG8/LlimunjKIX8yfwpv/PIX7Rv6RjzuG8PXm73DJu7/jP1puofnMiLCiBSogP58ogYCIp9DnjsMEZUIy38qVUF4OV19tPK/030Yn9CcXHINjfRbxIj6LOEgHB2CUWkperzHwtbbCkH5eKkoa2H+igk07SsIOxGFn1wANK+mu+TL/c3IqK7yzWXd8BhrFp84roaqynNnnDyU7q2evDb/PIjfXUBSRHNcRzx2NBAsHer2wZQvceGPPFdAnPpMwDvm0ztXIQFzv4I4XURYxki5mhRgaG8UzWMdEgJLd117Eqo3NrKprYv/xdkb2L2DBTA9fnFHG0OKzORuBSgCSUAhxyBbLBMB/b7Ky4NSpnp8VF8O6dTBjkpQ7zwREWQi9cXivg3Cz61DbD+7xMnBDOdk6eqSTZQM00NHVzfp397Oiton/+eAgOVmKayYMo6qynEvOGfxJZ7/Awbm72wTFlQSBq65Q9IjGknLnaY9UnRV64+AuasFhpv7BNNR2gMWLS5h/8TIeXrSYnPxc8rJDJ52VlMSpJOKcoedmZ3HtxBFcO3EEuw+eorq2kSc3tfDCto8ZM6QvCys9XFleyu235/XwYdx+O8yda40Ci0Yo5ztA375nFdkncqW6o53gWGRlkSF4vdCyy8vkxuh5B3bIFjzTLSyETZtg2rSe2wsKQKmz24b083J+aQPPvFLBkFFJXoNJJrq2ji5e2GYk+21uOkpuVhZHto7kxFsezuwdABirjZdegmuuCXUAa31Koe53QQGsXg1TptijwMKSDv41hyMrC+ETzs7OS/jcRct4/K7F5OQ6pwREuDDTjRt7b88OaoZ38EQJb+8pYfdeGDIqCSFCleKouQPyBsfdQKggN5ubp5Zy89RS3tl7nP94qpG/tu6haFILZ/YXc2JLOafeGUnIf78U+JT8EVjB/pyQiisVhFMI0pvDUcjKIs0JNYssK/Gy9Y0GBpZWOOKfLpmVhf+7cWU8hyKUwxzozu6L7u7m1IRlFF+Y2KDt9UJpRSd55+2h35RG8oaeoLs9h1tnjuIrV5Uzbriv6F+KfUpW+3NiIpxyDFdBN5N6c6SIdMjgFkzAP2sP5Fh7CbuOJFjZ1ALC5RqMH997++OPJ5mXEI5Q+QpAVtcpsnUrOZsW83R1YvkFJSXwu//OofO9co4/cTmH/3QJ04YP47kdzcz7xQa+8MgbPLtlD23HdvfuR2Fh74WSEpgxw0ZFESmPI9N7czgQWVmkGf7YeTDszxB61p70TNwC4omGsmRW7J/lkoXuOkVg1sSx08Vc//N1PP36jITPFyzzkVNn+POmFlbUNtJw6DSD+uRwS9FTLBz4F8rzPzZ2coBPyTIihT/3rcjs3hwpxPLQWaXU1VrrVxLa2QJEWRi+idtvP5s5nJsLv/+98drUfIN0ps0LR7bQ/dqNZAWE5Z4+U8jCR57l+7+YwpSLzR24u7s1b3x4iBW1jby8Yx9dWnF58dssGryWOVffTc6YNP2xopnd/Mpb5RgrikDSWYmmmFQoiyattSehnS0g05VFuNj5ggJoajJe226fdhHH315JzqbFdHTlUpDbBmjaOvpQXHQGNcs6e/n+422seuM9Vtbv4+OT3QwvLmD+zDLmz/AwvH9B9AO4jWh5HH6TVKjeHOKzMAVTlIVSKlyVVwXM1lr3TVA+08l0ZVFXB1dd1Tsbt29f+OtfDdu0EB9PV3t5/GdbeOKeG+iT13b2A7NntSGigTq7uln/3gFW1Dax4X0v2VmKueOHUlVZzmXnDiErqLSIq4k1PDaW70mobdyYFTp7ObAIOBl8fIy2p4JDqKgwEqqC6eqKo4Kp0IObF5Zw1cyB5NXnQ3eAsog3kTHSABYmGignO4t5E4Yzb8JwGg+donpjE0/UNfPSjv1UDO7DwkoPt0wrY2DfEE5gt1FQEtu9jPa9dCll41CirSxeBP5Ta/3XEJ9t0FpfYaVw8ZDpKwsI77MQ/0QSJBvOGmkAi/PYbR1drN3+MStqG6lrOEJeThafmTSCRbM8TPUM/KS0SEbi8FI2TsaUlYXW+tMRPnOMohAMFiwwSkgERkOJfyJJwvV1jmUAitBzm4KSuMuvFORmc+OUUdw4ZRTvfXyc6tomnt68h2csAd6bAAAduklEQVS27OH84f2omlXOTVNGUZSfgbm2Di5lky6YEjqrlHpTa32xCfIkjKwsBEtJxBYerTJutNlwDOc81d7Jc1v3srymkR17j9M3z1AoVZXlXDCyOMGLdSGyskiYVJf7SMMwDUEIIFa7eiDRGhNFWrXEaH/vm5/Dgpke5s8oY2vLMZbXNPpyN5o4b9AAqirL+eIlIyjIze61b1qRzApQiAmzVhabtdZTTZDHf7wfAF8B/CmaD2itX4i0j6wsBEcSS4nvNi8c3mKEjQz0ZVImMUte9sczfOeRPfSZ1Ej2wFMUZuey6JJSFlaWM3qIYwIYrUGioeImHQoJLtFa/9RuIdyII2r+mIjZ15PS+xNLie+P1/VcRVzwQML2d68X7rkrj9bW0Rx+s4ICzyH6T2/icd3Ab/5nN5edO4SqSg9zLxhGbnYaVPsJVg6JrACFmIj416KUKovw2eWBb02TSEiKsP2UXYrZ12PL/Qnoud2LUPWRdvww4b7aPWuBKdqahtC6biqPXDubf7n6PD7ynuR/r9jMpQ+9ys9f3sneo2HKabiBCD3YBfOJFjr7EbAU+LnWutO3bRjwM2Cc1nqGb9tErfV204QyzFC3A8eBeuBftNZHIu3jRjOUFTNmt9SBigWzr8eR9yecE3z8t2HHjxLqqx3pGru6NX997wAraht57X0vCpgzfhhVlR6uGFvinmQ/cWibhllVZ6cB5wBblFKzlVJfBzYCbwKV/i8loiiUUuuUUttDPG4AHvGddzKwD0M5hTrGnUqpeqVUvdfrrgqUVsxwQ1WYzc01tieC12tkhqf61vrPu2WLuddj9v0xhXBO8HPvMga+2euM5xiTy8JV8PUrw+wsxdwLhvHbL81kw7ev4q5PncPmxiPc/ts6rvzpayx9/UMOnWw39xqtIFRVWgsr9AoxOrh9SmIJsBeYpbVusVqwgHNXAGu01hMjfc9NKwurZrhmHjdcm1OrCTxve7uRlR7YjjTtVhZgSZ/reFat7Z1dvLRjPytqGqndfZi87Cw+PWk4VZXlzKhwaLKfrCxMI9aVBVrrsA9gAPAo8BZwDfALYBtGXaiI+ybzAEYEvP4msCraPtOmTdNuYeNGrfv31xrOPoqLje3JUl2tdWGhcbzCQuN9vBw4YOwbKF9hobHdSkKdNzc3+esJxIz7YwmtB7Q+uNF4tvGc7398XH9/9XY98ftrdfm9a/Q1P39d//6N3fp465nUyRUru6u1XlWo9RPFxvNup/yY7gKo1zGMy7H4LH4N/EKf9VlM9m1r1FpbMtdUSv0RwwSlgQbgLq31vkj7yMqi5/GT8YXU1RnmsWMBZvTiYli3zpyChOHkC3feJ5+EgQPdEw3limi0KHkcp8908pete1le08S2Pcfok5fNDZNHUlVZzsRR/W0UPAgJlU0as6rOluowJiel1Fe01r9JQkZTcZOygLPmFif2mLBSmUUybznWTBQHdpnv4iJOE87bLUdZXtPIc1v30tbRzUVlA1hU6eH6C0dSmJfmyX4ZgOX9LJyG25QFOHsGaoUyi0UZOFmJRsM1yi5aGZIwHDvdwdNbWlhe08iH3lMUF+TwhWllVM3ycE5JUQoEF6wgHZLy0p6SEocNIgH4ixKaqcz80UiBg6k/Gsl//HjO6zRlG8v1OYJoZUjC0L9PLl+6dDS3X1JB7e7DLK9p5I81DTz+991cPGYwi2aVc82ENEn2E3ohykIIi9nKrKKiZ2QTGKuH4H4bsZzXieaecNdXVGT4Y5JVaqYpxyTrKCmlmDVmMLPGDMZ7op0n6puprm3iq9WbKemXzxenl7Gg0sOoAYVJCCk4DTFDCSklmpkplgHRyeae4OtbvNi4xmSVmiXK0UTncFe3ZsP7XpbXNPLqzgNGK83zjc5+V5xXQrZbkv0yEPFZCI4lnEKIdUC0OlorXoKvx/++qAimTUteqTlZOYai5chpVm1sZlVdMwdPtlM6sJAFMz3cOr2Mkn75dosnBGFWBrcgmE5JiTGoBw50Xq+hKFpbDSXQ2mq8D5U9Hqs5KxWEysT3X9/Jk+ZkjIfKPM/OtjnzPAKlA/vwrXnjeOO+2fzXwqmUDezDT17aySUPredr1Zup+egQ6TJJzSTEZyE4gnicw/6SFsHmrMBZfSqc3oEKzi/34sUwebKhKIqKzFFqoZTjyZOwebM1Kymz7mFeThafuXAEn7lwBLsOnKS6tok/b2pmzdv7OHdoEVWVHm6eWkr/wlyzRBesJJbMPTc83JTBLfQmkazxAweMrHf/d5Yu1To/X+t+/VKTnR0qE7+w0JChf3/j9de+Zk7G+NKlPc9jVVa9P8PdL7/Z9/B0e6f+U12T/tzDf9Pl967R4/71Bf3tJ9/SW5uPmHsiIWYwI4PbTYjPwt14vfDoo/CjHyWWY/Hoo3D33T23WW3X93ph1ChD1nAUFsKmTcZKIJmZel0dzJkDJ06c3Wa2nybVvpFtLcdYUdvI6rf20trRxaRR/Vk0y8NnLxpJnzwxeqQK8VkIrsFv9//pT40587e/bQxQsSoKrxe+/vXe23NyQtv1zaymG63GXm6uoSiCfTTxUlEBnZ09t5ntp0l1Vd5Jpf156PMXUvvdOfyfz02graOLe5/aRuWP1vOD53aw68CJ6AcRUoYoizTFrvLi8RLs2G5rM1YX8RBqkAPDzh88mJpZGr6hwXA0R8KsAT1a6XEzsCtwoLggl9suqeDlb17BE3ddzFXjhrKitpG5P9/AFx99k79s3cuZzm5rhRCiImu9NMSJCWvhMCPrOdSsG+CXvwwfcRXokJ47N/S5ojl6i4p6yu2noMC4pkDHuxlYkVUfSKTAgVSglGLm6EHMHD2Igycv4Mn6Fqo3NnLPyi0MKcrj1ullLJjpoWxQn9QIJPRAfBZphpl251REFoWSt6AAVq+GKVNiP+/KlXD77Wdnxjk58Ic/9FSS8eRnBCvcJUtg6tSe96KuDj71qdCyB1bJdVpZkmg4Sd7ubs2GD7ysqG1i/bv70cCV55WwaFY5V44bKsl+JmBKPws3PSQaysCsXhlWR8WEOldxsdG/Ii8v/vMeOKB1QUHkaKFYIq4OHND6pZd6HwuMKKuCAq0ffND4XizHS+V9THf2HDmtf/byTj3j/76iy+9doy/58Xr9q/Xv6/3HW+0WzdUQYzSU7YO8WQ9RFgZmNC6yo/mRf5BO9LwbNxqDeTQl6R+8i4qMENelS3t/1rdvb0URKmy1ujp8M6VwSifU9QSHAAuROdPZpV/ctldX/aZGl9+7Rp9z//P6H5dv0n//wKu7u7vtFs91xKosxGeRZphhd7ajempJiWG6SfS8mzf3DCuF0M7ZBQvg+HEjeiovD775TcMUNXfuWX9GLPgzzBsbjUeg2cZvwsrKMhz2gQReT2C4sBv8S04hNzuLayeO4NqJI9h98BTVtY08uamF57ftY8yQviys9PCFaaUM6BMi6kFIGPFZpCnJ2J3D+RGamqy1YSfqbwm1H8DSpXDXXbGd49ln4dZbe/oz/J+FUyCh/B3hZAm+nnXr4I47eisTJ9d8cjJtHV28sG0fy2sa2dx0lPycLK6/cCSLZnmYXDbAmX3EHYLj8yyUUrcopXYopbqVUtODPrtfKbVLKbVTKTXPLhndTKj6S36ihdX6Vye5AVUYuruNAS4ZYj1vYHjokiWG0osUAhwqdLZfP8MhHct3/dcZHDbqVyJLlxrKMphQK5dwYbx9+54NdwVj5RGsKPyyOLXmk1lYEdZdkJvNzVNLefofL+WFf7qcz08r5cXt+7jp129w/a/+RnVtE6faQ4TMCbETi63KigcwHhgHvAZMD9h+AbAVyAdGAx8C2dGOJz6L2IjV4WqW78Nvi4/H0evfb+lS82WN9N1w/gf/fg8+GN4/4b/OcMd/6aWz8oQKQvA/8vLS23eRSof/8dYz+g9vNuh5S17X5feu0RO+t1b/6zPb9Hv7jlt3UheCWxzcIZTF/cD9Ae9fAi6OdhxRFtGJZ1BNNKoq3ECfmxuf4olXWUUa6OP5bjRnc/DnoQa/aLKEujb/Izc3fZWFHYETWmvd3d2t6xsO6W+s2qLHPvCCLr93jf78r/+un9ncots6Oq09uQuIVVk40cE9CqgJeN/i2yYkSTyO60Syef2O3Zycs87mcLb7SI5rrxdeeKF3dnSkfeJJWIv03Whd+gI/D5fkF8rpHXyMZcvgS1+C9vaenxUWOrANq0nY1XZWKcW08kFMKx/Ev11/AX/e1MyK2ia+8ae3+Pc1edwyvZSFMz2UD+5rnRBpgKXKQim1Dhge4qPvaq1Xh9stxLaQXnil1J3AnQAejychGTOJeBRAvFFVgQNnLIQ7r1/haN3bph9NWcXTBtaMlrGRBr9otaAWLDBKmU+Z0lNh2NWXIxU4oQ/JoL553HnFOXz5sjH8/cODLK9p5L//ZzePvv4RV5xXwqJKD7PPH0qO9BHvhaXKQms9N4HdWoCygPelwN4wx38MeAyMaKgEzpVRxKsA4pmthxo4A8nLM0JJI5XBiKZwlixx1ow72cFv/Hj47W/tK6+RauwuJxJIVpbi8rElXD62hI+PtbGqrolVG5u584+bGNG/gPkzPMyfWcaw4hCRDRmK7aGzSqnXgG9pret97ycA1cBMYCSwHhirte6KdBwJnY0dK8o5hAsZLSqCri5jUIimeF5+GW6+GU6d6v1ZURG8+qo9bVMjEa2neCw4qbxGKnDq9XZ2dbP+vQOsqG1iw/tesrMUV48fxqJZ5VxyzmCy0rS0iON7cCulbgJ+BZQAR4G3tNbzfJ99F7gD6AS+obV+MdrxRFnYT/DAGaqeUqR9Q+Ud+Ek2/8DKASpVg59TB9l0pPHQKaprm3iivpkjpzsYPaQvC2cayX4D+6ZXsp/jlYXZiLJwBokMaJES2QoLjedkMpvdVIU3HOlwDW6kraOLtds/ZnlNI/WNR8jLyeL6SSOomuVhqmdgWiT7ibIQXEOoarB9+8Ljj8Po0bEpnnBKKtXd36wgHa4hHXjv4+OsqGnimS17ONneyfnD+7FoVjk3ThlFUb4TA0tjw/EZ3IK7sLKZUihHcXc3XHVVbB3mwjU08ofg5gT9H7stSzrVHeyE0Jw/vJgHb5xI7QNz+NFNk8hSin99djuVP1zHd5/Zxrv7jtstoqXIykKISqwmkGRs6ok6isPNupcsMYoEBuZ8BH7uplm5rCycidaat5qPsrymiTVv76W9s5upngEsmlXOdZNGUJAbpY2iQxAzlGAKsQ5UZtjUI5mSwimhujqYM6enQujXz5AhOOGtXz+jo54b7f1mRF0J1nH09Bn+vKmF6tomPjp4igF9crllWikLK8sZPcTZyX6iLARTiKW7nJUz32hK6NFH4e67e+6Tn298P1CBFBXBww/Ddde5dzYu0VDOR2vNmx8eYnltIy/v2E9nt+ayc4ewaJaHueOHOTLZT5SFYAqxKIJ42pWaee5wUVQ/+Ql873tithHs5cDxNv5U18zKjU3sPdbGsOJ8vjjDw4KZZYzoX2i3eJ8gDm7BFEKVDQ/OurWqjEM0x264cuBtbdFlFgSrGVpcwD1zxrLhO1fxm/81nfEjivnVqx9w6UOv8pU/1PP6+166u90zWZeVRRqQCvNEtHNYYVNPdGXhb9QEzjLbiBlJaDp0muqNTTxZ38yhU2fwDOrDwkoPt0wrZXBRvi0yycoiQwgXNmo2JSXGIBeuEdGCBWc7wDU2muN8jbaqKSmBBx7ovV9e3tlKpn4zWLiwXytCgkMdM9bfycoQZcF+PIP7cN+nz+eN+2fzy/mTGd6/gIdefI+Lf/wq31i1hbqGwzh2Ah9LHXM3PDKxn4XZDYoikcqmNcFEkvHAAa0LCsLfg0hyW3FNoY4Z6+9k5z0W7GPnx8f1957dpid+b60uv3eNvubnr+s/vLFbH289k5Lz45bmR2Y9MlFZJNqgyE8qu+ZZSbhmQ5HktuKaInXJi/Y7Of0eC9Zzqr1Dr6xt1J/5fxt0+b1r9Ph/e1Hf99Tbevueo5aeN1Zl4d4cdSEpx3K4xj1z5/a2p9vVtCZWwpVSjyQ3mH9N4c4H0X8np99jwXr65OUwf6aH+TM9bG0+yoraRp7Z0sLKjU1MLjOS/a6/0L5kP/FZuJhYIpXCEU8JCSc0rYmG3z8Ra5SWFdcU7phTplgXUeYmH4ebZLWbi8oG8J9fuIja++fy/c9ewIm2Dr715FYqf7SeB9e8w4fek6kXKpblhxsemWiG8hOr3yF4H6t6XCdCItcQC5HktuKakunvHa88bvJxuElWJ9Ld3a3f2HVQf3XFJn3uA8/r8nvX6AWPvamff3uvPtPZldSxidEMJaGzGUy84a5WhX5aXX47ktxWNYJK9Jix7uumelFuktUNeE+080R9M9W1Tew52kpJv3z+ac5Y/mFWeULHkwxuISbsjv2XgSQxwmXNP/kkDBzorFwOqzL8M52ubs3r7x9gRU0TV44r4R8urkjoOLEqC3FwZzglJfYOKpno2DVDQYfycbS2wo03Oq9Bkht8Xm4kO0sx+/xhzD5/WErOZ5uDWyl1i1Jqh1KqWyk1PWB7hVKqVSn1lu+x1C4ZM5lUOSMzbSAxK4kyOLihoACUMhTGsWPG8+LFznAmJxOIITgHO6OhtgM3AxtCfPah1nqy73F3iM8FC0lVVji4cyBJVJEGhivHO6CHOmdg1vzq1Wdb0PpxUoMkKzL8hdRim7LQWr+rtd5p1/kFg+BBKJkBLVHcNJAko0gT7XgX6Zz+kOEpU2JfodkVwhoqvFlwD07NsxitlNqilHpdKXW53cKkK6EGIbtaeLphIElWkSZicov1nLGu0FK5ahTSC0uVhVJqnVJqe4jHDRF22wd4tNZTgH8GqpVSxWGOf6dSql4pVe91gnE2xSQzQww3CBUVZZYPIR6SVaSJmNziOWe0FZodq0YhfbA0GkprPTeBfdqBdt/rTUqpD4HzgF5xsVrrx4DHwAidTU5ad5FsbkK4KKSTJ41jBedfOHXGn8rQXzOc8eFKk5h1zkjRbZkYeSaYh+PMUEqpEqVUtu/1GGAs8JG9UjkLM2aIkQYht/gQUm1SMcsZH2xyi7RCNDMAINMizwSTiSXN24oHcBPQgrGK2A+85Nv+eWAHsBXYDHw2luNlUrmPZKvN+rG6hIeV2Fml1czSJPFU/jXjnG7+zQVrQMp9pC9mZj3bncGdKOmQFWxX9rpbf3PBGqRTXhpjpmnCDVFIoUgHk4pEngluQpSFS3GLX8Eq3JjMF0w6KDwhc5DaUC7G7rpOdhNvZJHT8Cs8t0SeCZmNKAvB1bhdYbpd4QmZgygLQbAZtys8ITMQn4WQlkgLT0EwF1EWQtoh9Y8EwXxEWQhphdQ/EgRrEGXhYsTU0hu7chcEId0RZeFSxNQSGsldEARrEGXhQsTUEp50SNYTBCciobMuREpNR8ZpuQtSi0lIB2Rl4ULE1BIdp9Q/EnOhkC6IsnAhYmpxB2IuFNIJMUO5FKeZWqKRiaYYMRcK6YSsLFyMU0wt0chUU4yYC4V0QpSFYCmZbIrJFHOh5PtkBrYpC6XUT5RS7yml3lZKPaOUGhDw2f1KqV1KqZ1KqXl2ySgkT6YnyaV735FMXTVmInauLF4BJmqtLwTeB+4HUEpdAMwHJgDXAr9WSmXbJqWQFGKKcY+5MF4yedWYidimLLTWL2utO31va4BS3+sbgFVa63at9W5gFzDTDhmF5MkUU0wmkumrxkzDKdFQdwB/8r0ehaE8/LT4tgkuxW2RW0JsyKoxs7BUWSil1gHDQ3z0Xa31at93vgt0Aiv8u4X4vg5z/DuBOwE8Hk/S8grWIQ1+0g9pC5tZWKostNZzI32ulLoNuB6Yo7X2K4QWoCzga6XA3jDHfwx4DGD69OkhFYogCNYhq8bMwTYzlFLqWuBe4FNa69MBHz0HVCulfg6MBMYCG20QURCEGJBVY2Zgp8/iYSAfeEUpBVCjtb5ba71DKfUE8A6GeeqrWusuG+UUBEHIeGxTFlrrcyN89kPghykURxAEQYiAZHALgiAIURFlIQiCIERFlIUgCIIQFVEWgiAIQlREWQiCIAhREWUhCIIgREWUhSAIghAVURaC45BmOoLgPERZCI5CmukIgjMRZSE4BmmmIwjORZSF4BikmY4gOBdRFoJjkGY6guBcRFkIjkFasAqCc3FKW1VBAKSZjiA4FVEWguOQZjqC4DzEDCUIgiBERZSFIAiCEBVRFoIgCEJURFkIgiAIURFlIQiCIERFaa3tlsEUlFJeoDHB3YcAB00UJxWIzKnBbTK7TV4QmVNFOJnLtdZR4w/TRlkkg1KqXms93W454kFkTg1uk9lt8oLInCqSlVnMUIIgCEJURFkIgiAIURFlYfCY3QIkgMicGtwms9vkBZE5VSQls/gsBEEQhKjIykIQBEGISkYrC6XUT5RS7yml3lZKPaOUGhDw2f1KqV1KqZ1KqXl2yhmIUuoWpdQOpVS3Ump6wPYKpVSrUuot32OpnXIGEk5m32eOvM9+lFI/UErtCbiv19ktUziUUtf67uMupdR9dssTC0qpBqXUNt+9rbdbnlAopR5XSh1QSm0P2DZIKfWKUuoD3/NAO2UMJozMSf0tZ7SyAF4BJmqtLwTeB+4HUEpdAMwHJgDXAr9WSmXbJmVPtgM3AxtCfPah1nqy73F3iuWKREiZHX6fA1kScF9fsFuYUPju238BnwYuABb47q8buMp3b50aivo7jL/PQO4D1mutxwLrfe+dxO/oLTMk8bec0cpCa/2y1rrT97YGKPW9vgFYpbVu11rvBnYBM+2QMRit9bta6512yxEPEWR27H12ITOBXVrrj7TWZ4BVGPdXSBKt9QbgcNDmG4Df+17/HrgxpUJFIYzMSZHRyiKIO4AXfa9HAc0Bn7X4tjmd0UqpLUqp15VSl9stTAy45T5/zWeqfNxp5oYA3HIvg9HAy0qpTUqpO+0WJg6Gaa33Afieh9osT6wk/Lec9s2PlFLrgOEhPvqu1nq17zvfBTqBFf7dQnw/ZWFjscgcgn2AR2t9SCk1DXhWKTVBa33cMkEDSFBmW+/zJ0JEkB14BHgQQ64HgZ9hTCychiPuZQJcqrXeq5QaCryilHrPNysWzCepv+W0VxZa67mRPldK3QZcD8zRZ+OIW4CygK+VAnutkbA30WQOs0870O57vUkp9SFwHpASp2EiMmPzffYTq+xKqd8AaywWJ1EccS/jRWu91/d8QCn1DIY5zQ3KYr9SaoTWep9SagRwwG6BoqG13u9/ncjfckaboZRS1wL3Ap/TWp8O+Og5YL5SKl8pNRoYC2y0Q8ZYUUqV+J3DSqkxGDJ/ZK9UUXH8ffYNBH5uwnDWO5E6YKxSarRSKg8jcOA5m2WKiFKqr1Kqn/81cA3Ovb/BPAfc5nt9GxBu9ewYkv1bTvuVRRQeBvIxlr8ANVrru7XWO5RSTwDvYJinvqq17rJRzk9QSt0E/AooAZ5XSr2ltZ4HXAH8u1KqE+gC7tZam+rgSpRwMjv5Pgfwn0qpyRhL9wbgLnvFCY3WulMp9TXgJSAbeFxrvcNmsaIxDHjG97+XA1RrrdfaK1JvlFIrgSuBIUqpFuD7wEPAE0qpxUATcIt9EvYmjMxXJvO3LBncgiAIQlQy2gwlCIIgxIYoC0EQBCEqoiwEQRCEqIiyEARBEKIiykIQBEGIiigLQRAEISqiLAQhSZRSZUqp3UqpQb73A33vy8N8/zZfaesPfBUEBMHxSJ6FIJiAUuo7wLla6zuVUo8CDVrrH4f43iCMEizTMZKjNgHTtNZHUiqwIMSJrCwEwRyWALOUUt8ALsMo0haKecArWuvDPgXxCqH7DgiCo8j0ch+CYApa6w6l1LeBtcA1vp4SoXBrKXEhw5GVhSCYx6cxSsVPjPAdt5YSFzIcURaCYAK+Am1XA7OAbwZV+AzElaXEBUEc3IKQJMoom/oG8D2t9StKqXuAWVrrqhDfHYTh1J7q27QZw8HtiArBghAOWVkIQvJ8BWjSWr/ie/9r4Hyl1KeCv+hTCg9i9J+oA/5dFIXgBmRlIQiCIERFVhaCIAhCVCR0VhAsQCk1Cfhj0OZ2rXWlHfIIQrKIGUoQBEGIipihBEEQhKiIshAEQRCiIspCEARBiIooC0EQBCEqoiwEQRCEqPx/fxWWoJ4UOvQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def graph(formula, x_range):  \n",
    "    x = np.array(x_range)  \n",
    "    y = formula(x)  \n",
    "    plt.plot(x, y)  \n",
    "    \n",
    "def my_formula(x):\n",
    "    return (-w[0]-w[1]*x)/w[2]\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from pandas import DataFrame \n",
    "df = DataFrame(dict(x=X[:,0], y=X[:,1], label=Y))\n",
    "colors = {0:'blue', 1:'orange'}\n",
    "fig, ax = plt.subplots()\n",
    "grouped = df.groupby('label')\n",
    "for key, group in grouped:\n",
    "    group.plot(ax=ax, kind='scatter', x='x', y='y', label=key, color=colors[key])\n",
    "graph(my_formula, range(-20,15))\n",
    "plt.xlabel('X_0')\n",
    "plt.ylabel('X_1')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}