Code-Example-015.2--Gradient-Descents-Vectorized.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import time\n",
    "import psutil\n",
    "import matplotlib.pyplot as plt \n",
    "import numpy as np\n",
    "\n",
    "# We create a very simple data set with 5 data items in it. \n",
    "size= 5\n",
    "\n",
    "# mu, sigma = 100, 5000 # mean and standard deviation\n",
    "# error=np.random.normal(mu, sigma, size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([0, 5]), array([1, 6]), array([2, 7]), array([3, 8]), array([4, 9])]\n",
      "[-5.  -3.5 -2.  -0.5  1. ]\n"
     ]
    }
   ],
   "source": [
    "x1 = np.arange(0, size)\n",
    "# x2 = np.arange(1, size)\n",
    "x2 = np.arange(5, 5+size)\n",
    "# y = 2.5*x1 + error\n",
    "y1=2.5 * x1\n",
    "y2 =-1 *x2\n",
    "\n",
    "# y = 2*x1 + 10* x2\n",
    "x = []\n",
    "for i in range(size):\n",
    "    x.append(np.array([x1[i],x2[i]]))\n",
    "\n",
    "y = y1 + y2\n",
    "\n",
    "\n",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/dd/wjnc44wn6t3g77ly4h81s60c0000gp/T/ipykernel_20930/2064018942.py:13: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
      "  ax = fig.gca(projection='3d')\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "\n",
    "import matplotlib as mpl\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "mpl.rcParams['legend.fontsize'] = 10\n",
    " \n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "\n",
    "x1 = np.arange(0, size)\n",
    "# x2 = np.arange(1, size)\n",
    "x2 = np.arange(5, 5+size)\n",
    "ax.scatter3D(x1, x2, y, label='parametric curve')\n",
    "ax.legend()\n",
    " \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta=np.zeros(2)\n",
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 beta =  [0. 0.]  Cost= 42.5\n",
      "1 beta =  [-0.01 -0.11]  Cost= 33.5645\n",
      "2 beta =  [-0.0018 -0.1623]  Cost= 31.392868550000003\n",
      "3 beta =  [ 0.014276 -0.189239]  Cost= 30.532238746894997\n",
      "4 beta =  [ 0.03369768 -0.20501127]  Cost= 29.932011752353187\n",
      "5 beta =  [ 0.05447762 -0.21584715]  Cost= 29.38965773095855\n",
      "6 beta =  [ 0.07574451 -0.22448152]  Cost= 28.86602394426417\n",
      "7 beta =  [ 0.09711688 -0.23211507]  Cost= 28.353433547975342\n",
      "8 beta =  [ 0.11842828 -0.23927508]  Cost= 27.850275694662844\n",
      "9 beta =  [ 0.1396066  -0.24619332]  Cost= 27.35611045054374\n",
      "10 beta =  [ 0.16062113 -0.25297178]  Cost= 26.87072575002126\n",
      "11 beta =  [ 0.18145935 -0.25965555]  Cost= 26.39395568369584\n",
      "12 beta =  [ 0.20211668 -0.26626472]  Cost= 25.925645452726474\n",
      "13 beta =  [ 0.22259203 -0.27280838]  Cost= 25.465644578160983\n",
      "14 beta =  [ 0.24288585 -0.27929083]  Cost= 25.013805554089178\n",
      "15 beta =  [ 0.26299923 -0.28571424]  Cost= 24.56998355019686\n",
      "16 beta =  [ 0.28293356 -0.29207986]  Cost= 24.134036317153765\n",
      "17 beta =  [ 0.30269032 -0.2983885 ]  Cost= 23.70582413173796\n",
      "18 beta =  [ 0.32227106 -0.30464082]  Cost= 23.28520975026551\n",
      "19 beta =  [ 0.34167733 -0.31083737]  Cost= 22.872058364258823\n",
      "20 beta =  [ 0.36091067 -0.31697868]  Cost= 22.466237557173706\n",
      "21 beta =  [ 0.37997262 -0.32306526]  Cost= 22.06761726194651\n",
      "22 beta =  [ 0.3988647 -0.3290976]  Cost= 21.67606971930476\n",
      "23 beta =  [ 0.41758843 -0.33507617]  Cost= 21.291469436819334\n",
      "24 beta =  [ 0.43614532 -0.34100148]  Cost= 20.913693148683592\n",
      "25 beta =  [ 0.45453683 -0.34687397]  Cost= 20.542619776206212\n",
      "26 beta =  [ 0.47276446 -0.35269414]  Cost= 20.178130389005027\n",
      "27 beta =  [ 0.49082965 -0.35846244]  Cost= 19.820108166889383\n",
      "28 beta =  [ 0.50873387 -0.36417934]  Cost= 19.468438362418862\n",
      "29 beta =  [ 0.52647853 -0.3698453 ]  Cost= 19.12300826412628\n",
      "30 beta =  [ 0.54406506 -0.37546076]  Cost= 18.783707160393252\n",
      "31 beta =  [ 0.56149488 -0.38102618]  Cost= 18.45042630396674\n",
      "32 beta =  [ 0.57876938 -0.38654201]  Cost= 18.12305887710511\n",
      "33 beta =  [ 0.59588994 -0.39200869]  Cost= 17.80149995734269\n",
      "34 beta =  [ 0.61285793 -0.39742665]  Cost= 17.485646483861707\n",
      "35 beta =  [ 0.62967472 -0.40279633]  Cost= 17.17539722446095\n",
      "36 beta =  [ 0.64634165 -0.40811815]  Cost= 16.870652743110437\n",
      "37 beta =  [ 0.66286005 -0.41339256]  Cost= 16.57131536808183\n",
      "38 beta =  [ 0.67923126 -0.41861996]  Cost= 16.277289160644273\n",
      "39 beta =  [ 0.69545658 -0.42380078]  Cost= 15.98847988431567\n",
      "40 beta =  [ 0.71153731 -0.42893544]  Cost= 15.704794974659567\n",
      "41 beta =  [ 0.72747474 -0.43402433]  Cost= 15.426143509617896\n",
      "42 beta =  [ 0.74327015 -0.43906788]  Cost= 15.152436180370108\n",
      "43 beta =  [ 0.7589248  -0.44406649]  Cost= 14.883585262709392\n",
      "44 beta =  [ 0.77443995 -0.44902055]  Cost= 14.619504588926734\n",
      "45 beta =  [ 0.78981684 -0.45393046]  Cost= 14.360109520193832\n",
      "46 beta =  [ 0.8050567  -0.45879662]  Cost= 14.105316919436074\n",
      "47 beta =  [ 0.82016076 -0.46361942]  Cost= 13.855045124686765\n",
      "48 beta =  [ 0.83513022 -0.46839924]  Cost= 13.609213922914188\n",
      "49 beta =  [ 0.84996629 -0.47313646]  Cost= 13.367744524313029\n",
      "50 beta =  [ 0.86467014 -0.47783147]  Cost= 13.130559537051939\n",
      "51 beta =  [ 0.87924297 -0.48248464]  Cost= 12.897582942469187\n",
      "52 beta =  [ 0.89368593 -0.48709635]  Cost= 12.668740070708397\n",
      "53 beta =  [ 0.90800019 -0.49166696]  Cost= 12.443957576786563\n",
      "54 beta =  [ 0.9221869  -0.49619684]  Cost= 12.223163417086738\n",
      "55 beta =  [ 0.93624718 -0.50068636]  Cost= 12.006286826267772\n",
      "56 beta =  [ 0.95018216 -0.50513586]  Cost= 11.793258294583762\n",
      "57 beta =  [ 0.96399297 -0.50954572]  Cost= 11.584009545605948\n",
      "58 beta =  [ 0.97768071 -0.51391628]  Cost= 11.378473514339813\n",
      "59 beta =  [ 0.99124647 -0.51824789]  Cost= 11.17658432573056\n",
      "60 beta =  [ 1.00469134 -0.5225409 ]  Cost= 10.978277273549885\n",
      "61 beta =  [ 1.01801641 -0.52679566]  Cost= 10.783488799657393\n",
      "62 beta =  [ 1.03122273 -0.5310125 ]  Cost= 10.592156473629993\n",
      "63 beta =  [ 1.04431136 -0.53519176]  Cost= 10.404218972752712\n",
      "64 beta =  [ 1.05728336 -0.53933378]  Cost= 10.219616062364526\n",
      "65 beta =  [ 1.07013977 -0.54343889]  Cost= 10.03828857655295\n",
      "66 beta =  [ 1.0828816  -0.54750742]  Cost= 9.860178399191135\n",
      "67 beta =  [ 1.09550989 -0.55153969]  Cost= 9.68522844531143\n",
      "68 beta =  [ 1.10802565 -0.55553603]  Cost= 9.513382642809459\n",
      "69 beta =  [ 1.12042988 -0.55949676]  Cost= 9.344585914472777\n",
      "70 beta =  [ 1.13272357 -0.56342219]  Cost= 9.178784160328448\n",
      "71 beta =  [ 1.1449077  -0.56731265]  Cost= 9.015924240303782\n",
      "72 beta =  [ 1.15698326 -0.57116843]  Cost= 8.855953957194762\n",
      "73 beta =  [ 1.16895122 -0.57498985]  Cost= 8.698822039936644\n",
      "74 beta =  [ 1.18081252 -0.57877722]  Cost= 8.544478127171383\n",
      "75 beta =  [ 1.19256813 -0.58253084]  Cost= 8.392872751106648\n",
      "76 beta =  [ 1.20421897 -0.58625101]  Cost= 8.243957321661192\n",
      "77 beta =  [ 1.215766   -0.58993803]  Cost= 8.097684110891583\n",
      "78 beta =  [ 1.22721012 -0.59359219]  Cost= 7.954006237695181\n",
      "79 beta =  [ 1.23855227 -0.59721379]  Cost= 7.812877652784607\n",
      "80 beta =  [ 1.24979334 -0.60080312]  Cost= 7.674253123928768\n",
      "81 beta =  [ 1.26093424 -0.60436046]  Cost= 7.538088221455737\n",
      "82 beta =  [ 1.27197586 -0.6078861 ]  Cost= 7.404339304012927\n",
      "83 beta =  [ 1.28291908 -0.61138033]  Cost= 7.272963504579826\n",
      "84 beta =  [ 1.29376479 -0.61484341]  Cost= 7.143918716728992\n",
      "85 beta =  [ 1.30451385 -0.61827564]  Cost= 7.017163581130775\n",
      "86 beta =  [ 1.31516712 -0.62167728]  Cost= 6.892657472297501\n",
      "87 beta =  [ 1.32572546 -0.62504861]  Cost= 6.770360485562864\n",
      "88 beta =  [ 1.33618971 -0.62838989]  Cost= 6.650233424292315\n",
      "89 beta =  [ 1.34656071 -0.6317014 ]  Cost= 6.532237787320409\n",
      "90 beta =  [ 1.35683929 -0.6349834 ]  Cost= 6.4163357566110335\n",
      "91 beta =  [ 1.36702627 -0.63823615]  Cost= 6.302490185136601\n",
      "92 beta =  [ 1.37712248 -0.64145992]  Cost= 6.190664584972269\n",
      "93 beta =  [ 1.38712872 -0.64465496]  Cost= 6.0808231156014445\n",
      "94 beta =  [ 1.39704579 -0.64782152]  Cost= 5.97293057242876\n",
      "95 beta =  [ 1.40687449 -0.65095987]  Cost= 5.866952375496865\n",
      "96 beta =  [ 1.4166156  -0.65407026]  Cost= 5.762854558403437\n",
      "97 beta =  [ 1.4262699  -0.65715292]  Cost= 5.660603757414804\n",
      "98 beta =  [ 1.43583818 -0.66020812]  Cost= 5.560167200772762\n",
      "99 beta =  [ 1.44532118 -0.66323608]  Cost= 5.461512698191104\n",
      "100 beta =  [ 1.45471969 -0.66623707]  Cost= 5.364608630538501\n",
      "101 beta =  [ 1.46403444 -0.66921131]  Cost= 5.269423939704475\n",
      "102 beta =  [ 1.47326618 -0.67215905]  Cost= 5.175928118645138\n",
      "103 beta =  [ 1.48241566 -0.67508053]  Cost= 5.084091201605595\n",
      "104 beta =  [ 1.4914836  -0.67797596]  Cost= 4.993883754515789\n",
      "105 beta =  [ 1.50047074 -0.6808456 ]  Cost= 4.905276865556782\n",
      "106 beta =  [ 1.50937779 -0.68368966]  Cost= 4.818242135894412\n",
      "107 beta =  [ 1.51820547 -0.68650838]  Cost= 4.732751670577363\n",
      "108 beta =  [ 1.52695448 -0.68930198]  Cost= 4.648778069596722\n",
      "109 beta =  [ 1.53562553 -0.69207069]  Cost= 4.566294419104188\n",
      "110 beta =  [ 1.54421931 -0.69481472]  Cost= 4.485274282786073\n",
      "111 beta =  [ 1.55273651 -0.6975343 ]  Cost= 4.4056916933903665\n",
      "112 beta =  [ 1.5611778  -0.70022965]  Cost= 4.327521144404146\n",
      "113 beta =  [ 1.56954388 -0.70290098]  Cost= 4.250737581878639\n",
      "114 beta =  [ 1.5778354 -0.7055485]  Cost= 4.175316396399339\n",
      "115 beta =  [ 1.58605304 -0.70817243]  Cost= 4.101233415198597\n",
      "116 beta =  [ 1.59419745 -0.71077298]  Cost= 4.028464894408167\n",
      "117 beta =  [ 1.60226927 -0.71335035]  Cost= 3.9569875114492\n",
      "118 beta =  [ 1.61026917 -0.71590476]  Cost= 3.8867783575572807\n",
      "119 beta =  [ 1.61819778 -0.7184364 ]  Cost= 3.817814930440073\n",
      "120 beta =  [ 1.62605574 -0.72094548]  Cost= 3.750075127065266\n",
      "121 beta =  [ 1.63384367 -0.7234322 ]  Cost= 3.683537236576457\n",
      "122 beta =  [ 1.64156221 -0.72589677]  Cost= 3.6181799333347553\n",
      "123 beta =  [ 1.64921196 -0.72833937]  Cost= 3.5539822700838233\n",
      "124 beta =  [ 1.65679354 -0.7307602 ]  Cost= 3.4909236712362146\n",
      "125 beta =  [ 1.66430756 -0.73315947]  Cost= 3.4289839262788173\n",
      "126 beta =  [ 1.67175462 -0.73553735]  Cost= 3.3681431832953095\n",
      "127 beta =  [ 1.67913532 -0.73789404]  Cost= 3.30838194260355\n",
      "128 beta =  [ 1.68645025 -0.74022973]  Cost= 3.249681050505857\n",
      "129 beta =  [ 1.69369999 -0.74254461]  Cost= 3.1920216931501724\n",
      "130 beta =  [ 1.70088513 -0.74483886]  Cost= 3.1353853905001667\n",
      "131 beta =  [ 1.70800623 -0.74711266]  Cost= 3.0797539904123057\n",
      "132 beta =  [ 1.71506389 -0.7493662 ]  Cost= 3.025109662818023\n",
      "133 beta =  [ 1.72205864 -0.75159966]  Cost= 2.9714348940091257\n",
      "134 beta =  [ 1.72899107 -0.75381322]  Cost= 2.918712481024584\n",
      "135 beta =  [ 1.73586172 -0.75600705]  Cost= 2.8669255261369058\n",
      "136 beta =  [ 1.74267115 -0.75818133]  Cost= 2.8160574314363735\n",
      "137 beta =  [ 1.74941989 -0.76033623]  Cost= 2.7660918935113408\n",
      "138 beta =  [ 1.75610849 -0.76247194]  Cost= 2.717012898222926\n",
      "139 beta =  [ 1.76273749 -0.76458861]  Cost= 2.668804715572433\n",
      "140 beta =  [ 1.76930742 -0.76668642]  Cost= 2.6214518946598173\n",
      "141 beta =  [ 1.7758188  -0.76876553]  Cost= 2.574939258731625\n",
      "142 beta =  [ 1.78227216 -0.77082612]  Cost= 2.529251900316782\n",
      "143 beta =  [ 1.78866801 -0.77286834]  Cost= 2.484375176448696\n",
      "144 beta =  [ 1.79500686 -0.77489237]  Cost= 2.440294703972129\n",
      "145 beta =  [ 1.80128923 -0.77689836]  Cost= 2.3969963549333504\n",
      "146 beta =  [ 1.80751562 -0.77888647]  Cost= 2.3544662520520676\n",
      "147 beta =  [ 1.81368651 -0.78085687]  Cost= 2.3126907642737122\n",
      "148 beta =  [ 1.81980242 -0.78280971]  Cost= 2.2716565024006323\n",
      "149 beta =  [ 1.82586383 -0.78474515]  Cost= 2.231350314800808\n",
      "150 beta =  [ 1.83187122 -0.78666333]  Cost= 2.1917592831927113\n",
      "151 beta =  [ 1.83782508 -0.78856443]  Cost= 2.1528707185049334\n",
      "152 beta =  [ 1.84372589 -0.79044858]  Cost= 2.1146721568093043\n",
      "153 beta =  [ 1.84957411 -0.79231595]  Cost= 2.077151355326156\n",
      "154 beta =  [ 1.85537021 -0.79416667]  Cost= 2.0402962885004614\n",
      "155 beta =  [ 1.86111467 -0.7960009 ]  Cost= 2.0040951441475996\n",
      "156 beta =  [ 1.86680793 -0.79781879]  Cost= 1.9685363196675154\n",
      "157 beta =  [ 1.87245046 -0.79962048]  Cost= 1.9336084183260347\n",
      "158 beta =  [ 1.87804271 -0.80140611]  Cost= 1.899300245602172\n",
      "159 beta =  [ 1.88358513 -0.80317583]  Cost= 1.8656008056002487\n",
      "160 beta =  [ 1.88907815 -0.80492978]  Cost= 1.8324992975256613\n",
      "161 beta =  [ 1.89452223 -0.80666809]  Cost= 1.7999851122231922\n",
      "162 beta =  [ 1.89991779 -0.80839092]  Cost= 1.7680478287767347\n",
      "163 beta =  [ 1.90526527 -0.8100984 ]  Cost= 1.7366772111693527\n",
      "164 beta =  [ 1.91056509 -0.81179066]  Cost= 1.7058632050025946\n",
      "165 beta =  [ 1.91581769 -0.81346784]  Cost= 1.6755959342740279\n",
      "166 beta =  [ 1.92102349 -0.81513007]  Cost= 1.6458656982119384\n",
      "167 beta =  [ 1.92618289 -0.81677749]  Cost= 1.616662968166204\n",
      "168 beta =  [ 1.93129631 -0.81841023]  Cost= 1.587978384554318\n",
      "169 beta =  [ 1.93636417 -0.82002842]  Cost= 1.55980275386162\n",
      "170 beta =  [ 1.94138687 -0.8216322 ]  Cost= 1.5321270456947265\n",
      "171 beta =  [ 1.94636481 -0.82322168]  Cost= 1.504942389887268\n",
      "172 beta =  [ 1.95129839 -0.82479699]  Cost= 1.478240073656968\n",
      "173 beta =  [ 1.956188   -0.82635827]  Cost= 1.4520115388131516\n",
      "174 beta =  [ 1.96103405 -0.82790563]  Cost= 1.426248379013833\n",
      "175 beta =  [ 1.96583691 -0.82943921]  Cost= 1.4009423370714345\n",
      "176 beta =  [ 1.97059696 -0.83095912]  Cost= 1.3760853023063362\n",
      "177 beta =  [ 1.9753146  -0.83246548]  Cost= 1.35166930794737\n",
      "178 beta =  [ 1.97999021 -0.83395842]  Cost= 1.3276865285784503\n",
      "179 beta =  [ 1.98462414 -0.83543806]  Cost= 1.304129277630478\n",
      "180 beta =  [ 1.98921678 -0.83690451]  Cost= 1.2809900049177925\n",
      "181 beta =  [ 1.9937685 -0.8383579]  Cost= 1.2582612942182874\n",
      "182 beta =  [ 1.99827965 -0.83979833]  Cost= 1.2359358608964965\n",
      "183 beta =  [ 2.0027506  -0.84122593]  Cost= 1.2140065495688377\n",
      "184 beta =  [ 2.00718172 -0.8426408 ]  Cost= 1.1924663318102886\n",
      "185 beta =  [ 2.01157334 -0.84404307]  Cost= 1.171308303901744\n",
      "186 beta =  [ 2.01592583 -0.84543284]  Cost= 1.1505256846173566\n",
      "187 beta =  [ 2.02023953 -0.84681022]  Cost= 1.1301118130511267\n",
      "188 beta =  [ 2.0245148  -0.84817533]  Cost= 1.1100601464820474\n",
      "189 beta =  [ 2.02875196 -0.84952828]  Cost= 1.0903642582771584\n",
      "190 beta =  [ 2.03295137 -0.85086917]  Cost= 1.0710178358317672\n",
      "191 beta =  [ 2.03711336 -0.85219811]  Cost= 1.0520146785462487\n",
      "192 beta =  [ 2.04123825 -0.85351521]  Cost= 1.0333486958387215\n",
      "193 beta =  [ 2.04532639 -0.85482057]  Cost= 1.0150139051929994\n",
      "194 beta =  [ 2.0493781 -0.8561143]  Cost= 0.9970044302411729\n",
      "195 beta =  [ 2.0533937  -0.85739651]  Cost= 0.9793144988802087\n",
      "196 beta =  [ 2.05737352 -0.85866728]  Cost= 0.9619384414219714\n",
      "197 beta =  [ 2.06131788 -0.85992673]  Cost= 0.9448706887760667\n",
      "198 beta =  [ 2.06522708 -0.86117496]  Cost= 0.9281057706649283\n",
      "199 beta =  [ 2.06910145 -0.86241206]  Cost= 0.9116383138705729\n",
      "200 beta =  [ 2.07294129 -0.86363814]  Cost= 0.8954630405124657\n",
      "201 beta =  [ 2.07674692 -0.8648533 ]  Cost= 0.8795747663559357\n",
      "202 beta =  [ 2.08051863 -0.86605762]  Cost= 0.8639683991506172\n",
      "203 beta =  [ 2.08425673 -0.86725122]  Cost= 0.8486389369983587\n",
      "204 beta =  [ 2.08796152 -0.86843417]  Cost= 0.8335814667500958\n",
      "205 beta =  [ 2.0916333  -0.86960659]  Cost= 0.8187911624311728\n",
      "206 beta =  [ 2.09527235 -0.87076856]  Cost= 0.8042632836945989\n",
      "207 beta =  [ 2.09887898 -0.87192017]  Cost= 0.7899931743017461\n",
      "208 beta =  [ 2.10245347 -0.87306152]  Cost= 0.7759762606300115\n",
      "209 beta =  [ 2.1059961 -0.8741927]  Cost= 0.7622080502069521\n",
      "210 beta =  [ 2.10950717 -0.8753138 ]  Cost= 0.7486841302704352\n",
      "211 beta =  [ 2.11298695 -0.87642491]  Cost= 0.7354001663543238\n",
      "212 beta =  [ 2.11643572 -0.87752612]  Cost= 0.7223519008992727\n",
      "213 beta =  [ 2.11985375 -0.87861751]  Cost= 0.7095351518881574\n",
      "214 beta =  [ 2.12324133 -0.87969918]  Cost= 0.6969458115057321\n",
      "215 beta =  [ 2.12659872 -0.88077121]  Cost= 0.684579844822049\n",
      "216 beta =  [ 2.12992619 -0.88183369]  Cost= 0.6724332884992525\n",
      "217 beta =  [ 2.13322401 -0.8828867 ]  Cost= 0.6605022495213204\n",
      "218 beta =  [ 2.13649244 -0.88393032]  Cost= 0.6487829039463275\n",
      "219 beta =  [ 2.13973174 -0.88496465]  Cost= 0.6372714956808678\n",
      "220 beta =  [ 2.14294218 -0.88598976]  Cost= 0.6259643352762077\n",
      "221 beta =  [ 2.14612401 -0.88700573]  Cost= 0.6148577987458042\n",
      "222 beta =  [ 2.14927749 -0.88801265]  Cost= 0.603948326403805\n",
      "223 beta =  [ 2.15240286 -0.8890106 ]  Cost= 0.5932324217241561\n",
      "224 beta =  [ 2.15550039 -0.88999965]  Cost= 0.5827066502199505\n",
      "225 beta =  [ 2.15857031 -0.89097989]  Cost= 0.5723676383426669\n",
      "226 beta =  [ 2.16161287 -0.8919514 ]  Cost= 0.5622120724009299\n",
      "227 beta =  [ 2.16462832 -0.89291424]  Cost= 0.5522366974984604\n",
      "228 beta =  [ 2.1676169  -0.89386851]  Cost= 0.5424383164908746\n",
      "229 beta =  [ 2.17057885 -0.89481428]  Cost= 0.5328137889609833\n",
      "230 beta =  [ 2.1735144  -0.89575161]  Cost= 0.5233600302122736\n",
      "231 beta =  [ 2.1764238  -0.89668059]  Cost= 0.514074010280259\n",
      "232 beta =  [ 2.17930726 -0.8976013 ]  Cost= 0.5049527529613582\n",
      "233 beta =  [ 2.18216504 -0.8985138 ]  Cost= 0.4959933348590186\n",
      "234 beta =  [ 2.18499734 -0.89941817]  Cost= 0.4871928844467466\n",
      "235 beta =  [ 2.18780441 -0.90031448]  Cost= 0.4785485811477848\n",
      "236 beta =  [ 2.19058646 -0.9012028 ]  Cost= 0.47005765443109576\n",
      "237 beta =  [ 2.19334372 -0.90208321]  Cost= 0.4617173829234049\n",
      "238 beta =  [ 2.19607641 -0.90295577]  Cost= 0.4535250935369845\n",
      "239 beta =  [ 2.19878475 -0.90382055]  Cost= 0.44547816061292206\n",
      "240 beta =  [ 2.20146895 -0.90467763]  Cost= 0.4375740050795852\n",
      "241 beta =  [ 2.20412924 -0.90552707]  Cost= 0.4298100936260252\n",
      "242 beta =  [ 2.20676581 -0.90636894]  Cost= 0.42218393789003184\n",
      "243 beta =  [ 2.20937889 -0.90720331]  Cost= 0.4146930936606137\n",
      "244 beta =  [ 2.21196869 -0.90803025]  Cost= 0.4073351600946139\n",
      "245 beta =  [ 2.21453541 -0.90884981]  Cost= 0.4001077789472326\n",
      "246 beta =  [ 2.21707925 -0.90966207]  Cost= 0.3930086338162002\n",
      "247 beta =  [ 2.21960043 -0.9104671 ]  Cost= 0.386035449399363\n",
      "248 beta =  [ 2.22209914 -0.91126495]  Cost= 0.37918599076544157\n",
      "249 beta =  [ 2.22457558 -0.91205569]  Cost= 0.3724580626377243\n",
      "250 beta =  [ 2.22702996 -0.91283938]  Cost= 0.3658495086904709\n",
      "251 beta =  [ 2.22946246 -0.91361609]  Cost= 0.35935821085781167\n",
      "252 beta =  [ 2.23187329 -0.91438588]  Cost= 0.3529820886548876\n",
      "253 beta =  [ 2.23426263 -0.91514881]  Cost= 0.3467190985110592\n",
      "254 beta =  [ 2.23663068 -0.91590494]  Cost= 0.34056723311492215\n",
      "255 beta =  [ 2.23897763 -0.91665433]  Cost= 0.3345245207709666\n",
      "256 beta =  [ 2.24130366 -0.91739704]  Cost= 0.3285890247676372\n",
      "257 beta =  [ 2.24360897 -0.91813314]  Cost= 0.3227588427566106\n",
      "258 beta =  [ 2.24589374 -0.91886267]  Cost= 0.3170321061430849\n",
      "259 beta =  [ 2.24815814 -0.91958571]  Cost= 0.3114069794868918\n",
      "260 beta =  [ 2.25040236 -0.9203023 ]  Cost= 0.30588165991422345\n",
      "261 beta =  [ 2.25262659 -0.9210125 ]  Cost= 0.3004543765398131\n",
      "262 beta =  [ 2.25483099 -0.92171638]  Cost= 0.29512338989935766\n",
      "263 beta =  [ 2.25701576 -0.92241399]  Cost= 0.28988699139200913\n",
      "264 beta =  [ 2.25918105 -0.92310537]  Cost= 0.2847435027327655\n",
      "265 beta =  [ 2.26132705 -0.9237906 ]  Cost= 0.27969127541457317\n",
      "266 beta =  [ 2.26345392 -0.92446972]  Cost= 0.2747286901799751\n",
      "267 beta =  [ 2.26556184 -0.92514279]  Cost= 0.26985415650212957\n",
      "268 beta =  [ 2.26765098 -0.92580986]  Cost= 0.26506611207504654\n",
      "269 beta =  [ 2.26972149 -0.92647099]  Cost= 0.26036302231285585\n",
      "270 beta =  [ 2.27177356 -0.92712622]  Cost= 0.255743379857974\n",
      "271 beta =  [ 2.27380735 -0.92777562]  Cost= 0.2512057040979833\n",
      "272 beta =  [ 2.275823   -0.92841923]  Cost= 0.2467485406910953\n",
      "273 beta =  [ 2.2778207 -0.9290571]  Cost= 0.24237046110002625\n",
      "274 beta =  [ 2.27980059 -0.92968929]  Cost= 0.2380700621341486\n",
      "275 beta =  [ 2.28176285 -0.93031585]  Cost= 0.23384596549975856\n",
      "276 beta =  [ 2.28370761 -0.93093682]  Cost= 0.22969681735833253\n",
      "277 beta =  [ 2.28563505 -0.93155226]  Cost= 0.22562128789261227\n",
      "278 beta =  [ 2.2875453  -0.93216221]  Cost= 0.22161807088039975\n",
      "279 beta =  [ 2.28943854 -0.93276673]  Cost= 0.21768588327590216\n",
      "280 beta =  [ 2.29131491 -0.93336587]  Cost= 0.21382346479851444\n",
      "281 beta =  [ 2.29317455 -0.93395966]  Cost= 0.21002957752889162\n",
      "282 beta =  [ 2.29501762 -0.93454816]  Cost= 0.20630300551219663\n",
      "283 beta =  [ 2.29684427 -0.93513142]  Cost= 0.2026425543683751\n",
      "284 beta =  [ 2.29865464 -0.93570948]  Cost= 0.19904705090935892\n",
      "285 beta =  [ 2.30044888 -0.93628239]  Cost= 0.1955153427630504\n",
      "286 beta =  [ 2.30222713 -0.93685019]  Cost= 0.19204629800398393\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "287 beta =  [ 2.30398953 -0.93741293]  Cost= 0.18863880479054318\n",
      "288 beta =  [ 2.30573623 -0.93797066]  Cost= 0.18529177100860567\n",
      "289 beta =  [ 2.30746736 -0.93852342]  Cost= 0.18200412392151988\n",
      "290 beta =  [ 2.30918307 -0.93907125]  Cost= 0.17877480982629063\n",
      "291 beta =  [ 2.31088348 -0.93961421]  Cost= 0.17560279371585935\n",
      "292 beta =  [ 2.31256875 -0.94015232]  Cost= 0.1724870589473827\n",
      "293 beta =  [ 2.31423899 -0.94068564]  Cost= 0.16942660691639702\n",
      "294 beta =  [ 2.31589436 -0.9412142 ]  Cost= 0.1664204567367557\n",
      "295 beta =  [ 2.31753497 -0.94173805]  Cost= 0.1634676449262591\n",
      "296 beta =  [ 2.31916096 -0.94225724]  Cost= 0.16056722509784907\n",
      "297 beta =  [ 2.32077246 -0.9427718 ]  Cost= 0.15771826765629213\n",
      "298 beta =  [ 2.3223696  -0.94328178]  Cost= 0.15491985950023673\n",
      "299 beta =  [ 2.32395251 -0.94378721]  Cost= 0.15217110372956633\n"
     ]
    }
   ],
   "source": [
    "learningRate = 0.01\n",
    "num_iteration = 300 \n",
    "\n",
    "# This is our regression coefficients. \n",
    "beta=np.zeros(2)\n",
    "\n",
    "n = float(size)\n",
    "# print(\"Sample size\", n)\n",
    "\n",
    "# Let's start with main iterative part of gradient descent algorithm \n",
    "for i in range(num_iteration):\n",
    "    \n",
    "    # Calculate the prediction with current regression coefficients. \n",
    "    cost = 0\n",
    "    gradient = 0\n",
    "    \n",
    "    for j in range(size):\n",
    "        \n",
    "        y_prediction = np.dot(beta , x[j])\n",
    "    \n",
    "        # We compute costs just for monitoring \n",
    "        cost += ( y[j] - y_prediction)**2\n",
    "\n",
    "        # calculate gradients. sum the gradients for all rows\n",
    "        gradient += x[j] * (y[j] - y_prediction)\n",
    "    \n",
    "    gradient = (-1.0/n)* gradient\n",
    "    \n",
    "    print(i , \"beta = \", beta, \" Cost=\", cost)\n",
    "        \n",
    "    # update the weights - Regression Coefficients \n",
    "    beta = beta - learningRate * gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([0, 5, 2]), array([1, 6, 3]), array([2, 7, 4]), array([3, 8, 5]), array([4, 9, 6])]\n",
      "[-3.  -0.5  2.   4.5  7. ]\n",
      "0 beta= [0. 0. 0.]  Cost= 82.5\n",
      "1 beta= [0.09 0.19 0.13]  Cost= 43.685500000000005\n",
      "2 beta= [0.1312 0.2297 0.1706]  Cost= 40.27730895\n",
      "3 beta= [0.159516 0.230381 0.187862]  Cost= 39.283553738855\n",
      "4 beta= [0.18429788 0.22100553 0.19898094]  Cost= 38.46895382995289\n",
      "5 beta= [0.20798103 0.20911077 0.20843292]  Cost= 37.68176671515962\n",
      "6 beta= [0.23120115 0.19665743 0.21738366]  Cost= 36.91140067508757\n",
      "7 beta= [0.25412553 0.18415486 0.22613726]  Cost= 36.15683229495866\n",
      "8 beta= [0.27679949 0.17173462 0.23477354]  Cost= 35.41769259524891\n",
      "9 beta= [0.29923663 0.15942998 0.24331397]  Cost= 34.69366305521507\n",
      "10 beta= [0.32144224 0.14724864 0.2517648 ]  Cost= 33.98443457273744\n",
      "11 beta= [0.34341944 0.13519164 0.26012832]  Cost= 33.28970456148909\n",
      "12 beta= [0.36517078 0.1232583  0.26840579]  Cost= 32.60917663413411\n",
      "13 beta= [0.38669863 0.1114475  0.27659818]  Cost= 31.942560463166455\n",
      "14 beta= [0.40800529 0.09975804 0.28470639]  Cost= 31.28957165618875\n",
      "15 beta= [0.42909305 0.08818868 0.2927313 ]  Cost= 30.649931634526183\n",
      "16 beta= [0.44996415 0.07673817 0.30067376]  Cost= 30.023367514375096\n",
      "17 beta= [0.47062081 0.06540531 0.30853461]  Cost= 29.409611990384747\n",
      "18 beta= [0.49106525 0.05418889 0.31631471]  Cost= 28.80840322161925\n",
      "19 beta= [0.51129965 0.0430877  0.32401487]  Cost= 28.21948471985076\n",
      "20 beta= [0.53132615 0.03210057 0.33163592]  Cost= 27.64260524013627\n",
      "21 beta= [0.5511469  0.02122632 0.33917867]  Cost= 27.07751867363119\n",
      "22 beta= [0.570764   0.01046379 0.34664392]  Cost= 26.523983942594235\n",
      "23 beta= [ 5.90179565e-01 -1.88157527e-04  3.54032476e-01]  Cost= 25.98176489753861\n",
      "24 beta= [ 0.60939565 -0.01073067  0.36134512]  Cost= 25.450630216485656\n",
      "25 beta= [ 0.6284143  -0.02116487  0.36858264]  Cost= 24.930353306278143\n",
      "26 beta= [ 0.64723756 -0.03149186  0.37574579]  Cost= 24.420712205910796\n",
      "27 beta= [ 0.66586743 -0.04171276  0.38283535]  Cost= 23.921489491837164\n",
      "28 beta= [ 0.68430589 -0.05182865  0.38985207]  Cost= 23.43247218521216\n",
      "29 beta= [ 0.70255491 -0.0618406   0.39679671]  Cost= 22.95345166103085\n",
      "30 beta= [ 0.72061644 -0.07174969  0.40366999]  Cost= 22.484223559124622\n",
      "31 beta= [ 0.73849241 -0.08155698  0.41047265]  Cost= 22.02458769697693\n",
      "32 beta= [ 0.75618471 -0.0912635   0.41720543]  Cost= 21.5743479843212\n",
      "33 beta= [ 0.77369525 -0.1008703   0.42386903]  Cost= 21.133312339484647\n",
      "34 beta= [ 0.79102588 -0.11037839  0.43046417]  Cost= 20.701292607442202\n",
      "35 beta= [ 0.80817845 -0.1197888   0.43699155]  Cost= 20.278104479545657\n",
      "36 beta= [ 0.8251548  -0.12910253  0.44345187]  Cost= 19.863567414893744\n",
      "37 beta= [ 0.84195673 -0.13832057  0.44984581]  Cost= 19.4575045633096\n",
      "38 beta= [ 0.85858603 -0.1474439   0.45617406]  Cost= 19.0597426898928\n",
      "39 beta= [ 0.87504449 -0.15647349  0.4624373 ]  Cost= 18.67011210111373\n",
      "40 beta= [ 0.89133385 -0.16541032  0.46863618]  Cost= 18.288446572418753\n",
      "41 beta= [ 0.90745585 -0.17425533  0.47477138]  Cost= 17.91458327731536\n",
      "42 beta= [ 0.92341222 -0.18300946  0.48084354]  Cost= 17.54836271790699\n",
      "43 beta= [ 0.93920464 -0.19167365  0.48685332]  Cost= 17.189628656847884\n",
      "44 beta= [ 0.95483482 -0.20024883  0.49280136]  Cost= 16.83822805068897\n",
      "45 beta= [ 0.9703044  -0.2087359   0.49868828]  Cost= 16.49401098458632\n",
      "46 beta= [ 0.98561506 -0.21713578  0.50451472]  Cost= 16.156830608344368\n",
      "47 beta= [ 1.00076841 -0.22544936  0.5102813 ]  Cost= 15.826543073766514\n",
      "48 beta= [ 1.01576607 -0.23367752  0.51598863]  Cost= 15.503007473286502\n",
      "49 beta= [ 1.03060964 -0.24182115  0.52163733]  Cost= 15.186085779854288\n",
      "50 beta= [ 1.04530072 -0.2498811   0.52722799]  Cost= 14.875642788050842\n",
      "51 beta= [ 1.05984085 -0.25785825  0.53276121]  Cost= 14.571546056406664\n",
      "52 beta= [ 1.0742316  -0.26575344  0.53823758]  Cost= 14.273665850899492\n",
      "53 beta= [ 1.0884745  -0.27356752  0.54365769]  Cost= 13.981875089607055\n",
      "54 beta= [ 1.10257106 -0.28130131  0.54902211]  Cost= 13.696049288491285\n",
      "55 beta= [ 1.11652279 -0.28895565  0.55433142]  Cost= 13.4160665082908\n",
      "56 beta= [ 1.13033119 -0.29653134  0.55958618]  Cost= 13.141807302499078\n",
      "57 beta= [ 1.14399771 -0.3040292   0.56478695]  Cost= 12.873154666406087\n",
      "58 beta= [ 1.15752383 -0.31145003  0.56993429]  Cost= 12.609993987181614\n",
      "59 beta= [ 1.17091097 -0.31879461  0.57502874]  Cost= 12.352212994979048\n",
      "60 beta= [ 1.18416058 -0.32606374  0.58007085]  Cost= 12.099701715038718\n",
      "61 beta= [ 1.19727406 -0.33325818  0.58506116]  Cost= 11.852352420770346\n",
      "62 beta= [ 1.21025281 -0.34037871  0.5900002 ]  Cost= 11.610059587794655\n",
      "63 beta= [ 1.22309821 -0.34742608  0.5948885 ]  Cost= 11.372719848924449\n",
      "64 beta= [ 1.23581164 -0.35440104  0.59972657]  Cost= 11.140231950065994\n",
      "65 beta= [ 1.24839445 -0.36130434  0.60451493]  Cost= 10.912496707021955\n",
      "66 beta= [ 1.26084799 -0.36813672  0.6092541 ]  Cost= 10.689416963177276\n",
      "67 beta= [ 1.27317357 -0.3748989   0.61394458]  Cost= 10.470897548050216\n",
      "68 beta= [ 1.28537252 -0.38159161  0.61858687]  Cost= 10.256845236690541\n",
      "69 beta= [ 1.29744614 -0.38821555  0.62318146]  Cost= 10.047168709907897\n",
      "70 beta= [ 1.30939572 -0.39477144  0.62772885]  Cost= 9.841778515313088\n",
      "71 beta= [ 1.32122252 -0.40125998  0.63222952]  Cost= 9.64058702915582\n",
      "72 beta= [ 1.33292781 -0.40768185  0.63668395]  Cost= 9.443508418942587\n",
      "73 beta= [ 1.34451284 -0.41403774  0.64109261]  Cost= 9.25045860681874\n",
      "74 beta= [ 1.35597885 -0.42032833  0.64545598]  Cost= 9.06135523369909\n",
      "75 beta= [ 1.36732705 -0.42655429  0.64977452]  Cost= 8.876117624131846\n",
      "76 beta= [ 1.37855867 -0.43271629  0.65404869]  Cost= 8.694666751880733\n",
      "77 beta= [ 1.38967488 -0.43881497  0.65827894]  Cost= 8.516925206210782\n",
      "78 beta= [ 1.40067689 -0.444851    0.66246574]  Cost= 8.342817158863273\n",
      "79 beta= [ 1.41156586 -0.45082501  0.66660951]  Cost= 8.172268331705817\n",
      "80 beta= [ 1.42234296 -0.45673765  0.67071072]  Cost= 8.005205965043773\n",
      "81 beta= [ 1.43300934 -0.46258954  0.67476979]  Cost= 7.841558786579408\n",
      "82 beta= [ 1.44356612 -0.4683813   0.67878715]  Cost= 7.681256981005671\n",
      "83 beta= [ 1.45401445 -0.47411356  0.68276324]  Cost= 7.524232160221513\n",
      "84 beta= [ 1.46435543 -0.47978693  0.68669848]  Cost= 7.370417334156093\n",
      "85 beta= [ 1.47459016 -0.48540201  0.69059329]  Cost= 7.219746882189414\n",
      "86 beta= [ 1.48471975 -0.4909594   0.69444809]  Cost= 7.072156525157201\n",
      "87 beta= [ 1.49474526 -0.49645969  0.69826328]  Cost= 6.927583297928065\n",
      "88 beta= [ 1.50466776 -0.50190347  0.70203927]  Cost= 6.7859655225412485\n",
      "89 beta= [ 1.51448833 -0.50729133  0.70577647]  Cost= 6.647242781893533\n",
      "90 beta= [ 1.52420799 -0.51262382  0.70947527]  Cost= 6.511355893964031\n",
      "91 beta= [ 1.5338278  -0.51790153  0.71313607]  Cost= 6.378246886565903\n",
      "92 beta= [ 1.54334877 -0.52312502  0.71675925]  Cost= 6.247858972614219\n",
      "93 beta= [ 1.55277192 -0.52829484  0.72034522]  Cost= 6.120136525899386\n",
      "94 beta= [ 1.56209826 -0.53341154  0.72389434]  Cost= 5.995025057355844\n",
      "95 beta= [ 1.57132878 -0.53847568  0.72740699]  Cost= 5.872471191815913\n",
      "96 beta= [ 1.58046446 -0.54348778  0.73088356]  Cost= 5.7524226452387985\n",
      "97 beta= [ 1.58950628 -0.5484484   0.73432441]  Cost= 5.63482820240516\n",
      "98 beta= [ 1.59845521 -0.55335804  0.73772991]  Cost= 5.519637695067601\n",
      "99 beta= [ 1.60731219 -0.55821725  0.74110042]  Cost= 5.406801980547865\n"
     ]
    }
   ],
   "source": [
    "x1 = np.arange(0, size)\n",
    "# x2 = np.arange(1, size)\n",
    "x2 = np.arange(5, 5+size)\n",
    "x3 = np.arange(2, 2+size)\n",
    "\n",
    "# y = 2.5*x1 + error\n",
    "y1=2.5 * x1\n",
    "y2 =-1 *x2\n",
    "y3 = 1*x3\n",
    "# y = 2*x1 + 10* x2\n",
    "x = []\n",
    "for i in range(size):\n",
    "    x.append(np.array([x1[i],x2[i],x3[i]]))\n",
    "\n",
    "y = y1+y2+y3\n",
    "# plt.plot(x1, y, 'o', markersize=2)\n",
    "# plt.show()\n",
    "\n",
    "print(x)\n",
    "# print(x2)\n",
    "# print(error)\n",
    "print(y)\n",
    "\n",
    "\n",
    "learningRate = 0.01\n",
    "num_iteration = 100 \n",
    "\n",
    "\n",
    "# Now we have 3 variables. \n",
    "beta = np.zeros(3)\n",
    "\n",
    "n = float(size)\n",
    "# print(\"Sample size\", n)\n",
    "\n",
    "# Let's start with main iterative part of gradient descent algorithm \n",
    "for i in range(num_iteration):\n",
    "    \n",
    "    # Calculate the prediction with current regression coefficients. \n",
    "    cost = 0\n",
    "    m_gradient = 0\n",
    "    \n",
    "    for j in range(size):\n",
    "        \n",
    "        y_prediction = np.dot(beta, x[j])\n",
    "    \n",
    "    \n",
    "        # We compute costs just for monitoring \n",
    "        cost += ( y[j] - y_prediction)**2\n",
    "\n",
    "        # calculate gradients.\n",
    "        gradient += x[j] * (y[j] - y_prediction)\n",
    "    \n",
    "    gradient = (-1.0/n)* gradient\n",
    "    \n",
    "    print(i , \"beta=\", beta, \" Cost=\", cost)\n",
    "        \n",
    "    # update the weights - Regression Coefficients \n",
    "    beta = beta - learningRate * gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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