Gradient Descent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient Descent Implementation\n",
    "\n",
    "### Step 1: Generate Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X=2*np.random.rand(100,1)\n",
    "y=4+3*X+np.random.randn(100,1)\n",
    "# y= 4+3*X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ndPfbJR13H8imKvOSPktSqDIJx3L5nyd5xtJoDTuHrt59essoP5X13WvSgjYUx7bMJSizh5klsVaZhGO5/M+z7XQMW1VLg8/hsrLKT7Fc3aBZSPwlKLOHOShZTKwyTay2Y45VnYRjufzP0wDF0mj1n8NBykjQsVzdoFnYq6cEZW/zKx0/g2fQsaqTcAyX/3k2VItpE7blc7hh7gYNmpNcNEHHUpJDs5h7/FPkZ2ZmfGFhoe4whlpZZ5V6PUwGyLBs8/zugQl6empSe+a25P69fPcwipntdffjxlMp9ZQglrII4lVV+YnvHvKgx49SxLBgKnacI4Q2rMdPjR+FNWWFat1iGDMBJEo9KAFTCoFmocePwtJMKaTMAcSDHj8KG7dgKpa9cwD0kPhbpqw9g7IYN2OFUhAQF0o9kSlSEqlrkHXcgilWlwJxIfEHkiahF03co3rWda7yZXUpEBdKPQGkrXEXLYnE2rOOZe8cAD0k/gDSJvSiiTuWXSlXYnUpEBdKPQGkTehFSyJl3C6xqmmXLF4C4kGPP4C0PfGiJZGit0vMO+2yjplEAPLrVI+/rkVEs1s3DtxBcWVCH7Ul8+b53WPjLloqyjM4zHYNR7FIDU3RmcRfZ4LKsj/8ypJIlriHlYpOnpxIFWeehqPOmUQxoQFEk3Sm1FP3IqJtm6a1Z26L7pk/X3vmtqROBlnint26UROr7Ljj//uzR1OVX/IMDsc6kyi0ur9fQBadSfxNTVBZ4t62aVpPOun4i7ilI54qAeUZY4h1JlFoTf1+oZs6UerZtW9Rq8x0ZMC9B8YlqF37FvWu67+qQ4eXJElr10xo+wVnBbt8zzrT59DDSwOPp0lAeW5ZmHb8ou1YpIYmaX3iX669Dkr64xLUrn2Lmr1mv5YeO/reBx9e0uzO/ZLC1G6zJtaiCSjrtMuY7m9bJxpANEnrE/+g2qskrTYbu4joyhsPHJP0ly2XTkIkt6yJtY4EFNMc/bpm1tAAoklan/iHlTgecx/7H+Wo8kjI2m2WxNrlBFT3zJqYGkBglNYn/iKlj2HvTfv+LMrsqXY1ATG1FEin9bN6iqyGHTY9cmK1lVo64UYl5WBmDZBOa3v8/T3oqTUTOvGEVXro8FKm3vTya6qe1UNPtRzMrAHSaWXiX1nrffDhJU1OrNZ7X3125kQaomxCT7UczKwB0mllqadpqyhZBFUOtn8G0mllj79pPejzzjxVH731PvVPHKWnmk9XB7aBLFrZ429SD3rXvkVdu3fxmKRvki4+lwQGoBqtTPxNutXfoLKUK/0e+gCQVStLPU1axDSqLMX+7gCq0MrEL+Wv9YZOtsOmIE6tmWB/dwCVaGWpJ686FlINK0u5q1EzkwA0B4m/T13TQE+aOPpnmJqc0BUXPUcPHc6/vTIAjELi7xN6GujyFcaDfXvoP/LoY5KaNTMJQLPUlvjNbLWZ7TOzT9UVw0qhk+2oK4wmzUwC0Cx19vjfKunrNX7+cUIn22FXEouHDuvKGw/o4nOnWYUKoHS1zOoxs6dJOl/S30h6ex0xDBJ6GuiobZ8XDx3WtXsXSfYASmc+4JaElX+o2U5JV0h6sqQ/cfdXDnjN5ZIul6RnPOMZ5957772FPjPGOfErN5MbZHpqUnvmtgSMCkBbmNled59ZeTx4j9/MXinpAXffa2YvGvY6d98haYckzczMFGqd6roz07jGpv8KY1jPn1k8AMpWR41/s6RXmdm3JX1c0hYz+0iVH1jHNM20awK2bZrWnrktmmYWD4BAgid+d3+Huz/N3ddLukTSbnd/bZWfWdY0zV37FrV5frc2zN2gzfO7Ry7sytrYMIsHQCit3bKhXxl3ZspaLsra2FQ9sBzjGAeAetSa+N39Fkm3VP05ZdyZKevtEfM0NlXtJV/XGAeAOHVi5W4Zd2bK2oOPqXTTtDuSAahWJ0o9UvHedNYefExbQzftjmQAqtWZxF9UnnJRLLcBLGOMA0B7dKLUU4Ym38g7prITgPrR488glh58VjGVnQDUj8TfEU1ttACUj1IPAHQMiR8AOobEDwAdQ+IHgI4h8QNAx5D4AaBjOjudk90qAXRVJxM/u1UC6LJOlnrYrRJAl3Wyx1/FbpWUjgA0RSd7/MN2pcy7W2Xa++sCQAw6mfjL3q2S0hGAJulkqafs3Sq50QmAJulk4pfK3a2SG50AaJJOlnrKxo1OADRJZ3v8ZeJGJwCahMRfEm50AqApKPUAQMeQ+AGgY0j8ANAxJH4A6BgSPwB0jLl73TGMZWYHJd2b8W3rJP2wgnDKEGtsscYlxRsbcWUXa2yxxiXlj+2Z7n7qyoONSPx5mNmCu8/UHccgscYWa1xSvLERV3axxhZrXFL5sVHqAYCOIfEDQMe0OfHvqDuAEWKNLda4pHhjI67sYo0t1rikkmNrbY0fADBYm3v8AIABSPwA0DGNTPxm9jIzO2Bmd5nZ3IDnTzSzTyTP32Zm6/uee0dy/ICZbQ0c19vN7Gtm9mUz+5yZPbPvuSNmdnvy7/oy40oZ22VmdrAvhjf2PXepmd2Z/Ls0cFzv7Yvpm2Z2qO+5ys6ZmV1tZg+Y2VeGPG9m9ndJ3F82s3P6nqvyfI2L67eTeO4wsy+Y2a/0Pfft5PjtZrZQZlwpY3uRmT3U9zf7y77nRn4PKo5rti+mryTfq1OS5yo7Z2b2dDO7OckJXzWztw54TTXfM3dv1D9JqyV9S9Lpkp4gab+kZ614ze9L+qfk8SWSPpE8flby+hMlbUh+z+qAcZ0naU3y+PeW40p+/mnN5+wySX8/4L2nSLo7+d+1yeO1oeJa8fq3SLo60Dl7gaRzJH1lyPOvkPRpSSbpuZJuq/p8pYzrecufJ+nly3ElP39b0roaz9mLJH2q6Peg7LhWvPYCSbtDnDNJp0k6J3n8ZEnfHPDfZSXfsyb2+H9V0l3ufre7/0zSxyVduOI1F0r6UPJ4p6QXm5klxz/u7o+4+z2S7kp+X5C43P1md384+fFWSU8r6bMLxzbCVkk3ufuP3f1BSTdJellNcb1G0sdK+uyR3P3zkn484iUXSvqw99wqacrMTlO152tsXO7+heRzpbDfsTTnbJgi38+y4wr5Hbvf3b+UPP4fSV+XtPKmHpV8z5qY+Kclfafv5+/q+JP1+Gvc/VFJD0n6uZTvrTKufm9QryVfdpKZLZjZrWa2raSYssZ2cXI5udPMnp7xvVXGpaQstkHS7r7DVZ6zcYbFXuX5ymrld8wlfdbM9prZ5TXF9Gtmtt/MPm1mZyXHojhnZrZGveR5bd/hIOfMeuXoTZJuW/FUJd8z7sBVAzN7raQZSS/sO/xMd180s9Ml7TazO9z9WwHD+ndJH3P3R8zsd9W7YtoS8PPHuUTSTnc/0nes7nMWLTM7T73E//y+w89PztfPS7rJzL6R9IZD+ZJ6f7OfmtkrJO2SdEbAzx/nAkl73L3/6qDyc2ZmT1Kvsfljd/9Jmb97mCb2+BclPb3v56clxwa+xsxOkHSypB+lfG+VccnMXiLpnZJe5e6PLB9398Xkf++WdIt6rX9Zxsbm7j/qi+cqSeemfW+VcfW5RCsuwSs+Z+MMi73K85WKmf2yen/DC939R8vH+87XA5L+VeWVOVNx95+4+0+Tx/8hacLM1imCc5YY9R2r5JyZ2YR6Sf+j7n7dgJdU8z2rYtCiyn/qXaXcrd5l//JA0FkrXvMHOnZw95PJ47N07ODu3SpvcDdNXJvUG8Q6Y8XxtZJOTB6vk3Snyh3cShPbaX2Pf0PSrX50EOmeJMa1yeNTQsWVvO5M9QbZLNQ5S37veg0fqDxfxw66fbHq85UyrmeoN3b1vBXHnyjpyX2PvyDpZWXGlSK2X1j+G6qXQO9Lzl+q70FVcSXPn6zeOMATQ52z5P/7hyW9b8RrKvmelfpHD/VPvZHub6qXRN+ZHPtr9XrRknSSpGuS/wC+KOn0vve+M3nfAUkvDxzXf0r6gaTbk3/XJ8efJ+mO5At/h6Q31HDOrpD01SSGmyWd2ffe1yfn8i5JrwsZV/LzuyTNr3hfpedMvZ7f/ZKW1KufvkHSmyW9OXneJP1DEvcdkmYCna9xcV0l6cG+79hCcvz05FztT/7O76zgOzYutj/s+47dqr7GadD3IFRcyWsuU2/iR//7Kj1n6pXhXNKX+/5erwjxPWPLBgDomCbW+AEABZD4AaBjSPwA0DEkfgDoGBI/AHQMiR/IKNlV8Z6+HRzXJj+vrzk0IBUSP5CRu39H0gckzSeH5iXtcPdv1xYUkAHz+IEckqX2eyVdLelNks5296V6owLSYZM2IAd3XzKzWUmfkfRSkj6ahFIPkN/L1dsK4Nl1BwJkQeIHcjCzsyX9unobZ70tuTkG0AgkfiCj5G5uH1Bv//T7JF0p6T31RgWkR+IHsnuTpPvc/abk53+U9Etm9sIR7wGiwaweAOgYevwA0DEkfgDoGBI/AHQMiR8AOobEDwAdQ+IHgI4h8QNAx/w/cVMmcp5u71wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"y\")\n",
    "# plt.plot(X,y,'ro')\n",
    "plt.scatter(X,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Training Set --> Learning Algorithm --> Hypothesis\n",
    "# Hypothesis maps from xs to ys\n",
    "# How we represent h Ex: Linear Regression with 1 variable (Univariate)\n",
    "# h_theta(x)=theta0 + theta1*X\n",
    "\n",
    "#Cost Function\n",
    "# In our case we have defined: Xs and Ys\n",
    "# Hypothesis: h_theta(x)=theta0 + theta1*X\n",
    "# Thetas: learnable parameters\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# Vary values of w0 and w1 to manually see the blue line getting closer to red.\n",
    "H=w0+w1*X\n",
    "\n",
    "w0=0\n",
    "w1=5\n",
    "plt.plot(X,y,'ro',X,H,'bo')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Idea: Chose w0 and w1 so that H is sclose to y for our training examples(X,y)\n",
    "# minimize (1/2m)*Sum((H-y)^2) from 1 to m (Number of training examples)\n",
    "# minimize average of square of difference of hypothesis and y\n",
    "# Why square difference , we can take mod as well but differentiation of mod is noit defined at 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def linear_model(X,w0,w1):\n",
    "    return (w0+w1*X)\n",
    "\n",
    "def cost_function(X,w0,w1,y,m):\n",
    "    return (1/(2*m))*sum((linear_model(X,w0,w1)-y)**2)\n",
    "\n",
    "def gradient_w0(X,w0,w1,y,m):\n",
    "    return (1/m)*sum(linear_model(X,w0,w1)-y)\n",
    "\n",
    "def gradient_w1(X,w0,w1,y,m):\n",
    "    return (1/m)*sum((linear_model(X,w0,w1)-y)*X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0, Cost: [18.2871499]\n",
      "Epoch: 1, Cost: [17.66966594]\n",
      "Epoch: 2, Cost: [17.07385673]\n",
      "Epoch: 3, Cost: [16.49896065]\n",
      "Epoch: 4, Cost: [15.94424286]\n",
      "Epoch: 5, Cost: [15.40899432]\n",
      "Epoch: 6, Cost: [14.89253094]\n",
      "Epoch: 7, Cost: [14.39419265]\n",
      "Epoch: 8, Cost: [13.91334256]\n",
      "Epoch: 9, Cost: [13.44936619]\n",
      "Epoch: 10, Cost: [13.00167064]\n",
      "Epoch: 11, Cost: [12.56968384]\n",
      "Epoch: 12, Cost: [12.15285383]\n",
      "Epoch: 13, Cost: [11.75064805]\n",
      "Epoch: 14, Cost: [11.36255265]\n",
      "Epoch: 15, Cost: [10.98807183]\n",
      "Epoch: 16, Cost: [10.62672722]\n",
      "Epoch: 17, Cost: [10.27805727]\n",
      "Epoch: 18, Cost: [9.94161663]\n",
      "Epoch: 19, Cost: [9.61697561]\n",
      "Epoch: 20, Cost: [9.30371963]\n",
      "Epoch: 21, Cost: [9.00144865]\n",
      "Epoch: 22, Cost: [8.70977671]\n",
      "Epoch: 23, Cost: [8.42833142]\n",
      "Epoch: 24, Cost: [8.15675345]\n",
      "Epoch: 25, Cost: [7.89469612]\n",
      "Epoch: 26, Cost: [7.64182492]\n",
      "Epoch: 27, Cost: [7.3978171]\n",
      "Epoch: 28, Cost: [7.16236125]\n",
      "Epoch: 29, Cost: [6.9351569]\n",
      "Epoch: 30, Cost: [6.71591415]\n",
      "Epoch: 31, Cost: [6.50435328]\n",
      "Epoch: 32, Cost: [6.30020439]\n",
      "Epoch: 33, Cost: [6.10320708]\n",
      "Epoch: 34, Cost: [5.9131101]\n",
      "Epoch: 35, Cost: [5.72967101]\n",
      "Epoch: 36, Cost: [5.55265591]\n",
      "Epoch: 37, Cost: [5.38183911]\n",
      "Epoch: 38, Cost: [5.21700285]\n",
      "Epoch: 39, Cost: [5.05793704]\n",
      "Epoch: 40, Cost: [4.90443894]\n",
      "Epoch: 41, Cost: [4.75631296]\n",
      "Epoch: 42, Cost: [4.61337038]\n",
      "Epoch: 43, Cost: [4.47542909]\n",
      "Epoch: 44, Cost: [4.34231342]\n",
      "Epoch: 45, Cost: [4.21385383]\n",
      "Epoch: 46, Cost: [4.08988677]\n",
      "Epoch: 47, Cost: [3.97025442]\n",
      "Epoch: 48, Cost: [3.8548045]\n",
      "Epoch: 49, Cost: [3.74339011]\n",
      "Epoch: 50, Cost: [3.63586948]\n",
      "Epoch: 51, Cost: [3.53210584]\n",
      "Epoch: 52, Cost: [3.43196722]\n",
      "Epoch: 53, Cost: [3.33532629]\n",
      "Epoch: 54, Cost: [3.24206019]\n",
      "Epoch: 55, Cost: [3.15205039]\n",
      "Epoch: 56, Cost: [3.0651825]\n",
      "Epoch: 57, Cost: [2.98134618]\n",
      "Epoch: 58, Cost: [2.90043495]\n",
      "Epoch: 59, Cost: [2.82234606]\n",
      "Epoch: 60, Cost: [2.7469804]\n",
      "Epoch: 61, Cost: [2.67424233]\n",
      "Epoch: 62, Cost: [2.60403956]\n",
      "Epoch: 63, Cost: [2.53628305]\n",
      "Epoch: 64, Cost: [2.47088689]\n",
      "Epoch: 65, Cost: [2.40776819]\n",
      "Epoch: 66, Cost: [2.34684698]\n",
      "Epoch: 67, Cost: [2.28804609]\n",
      "Epoch: 68, Cost: [2.23129105]\n",
      "Epoch: 69, Cost: [2.17651003]\n",
      "Epoch: 70, Cost: [2.12363372]\n",
      "Epoch: 71, Cost: [2.07259523]\n",
      "Epoch: 72, Cost: [2.02333004]\n",
      "Epoch: 73, Cost: [1.97577588]\n",
      "Epoch: 74, Cost: [1.92987267]\n",
      "Epoch: 75, Cost: [1.88556246]\n",
      "Epoch: 76, Cost: [1.84278932]\n",
      "Epoch: 77, Cost: [1.80149928]\n",
      "Epoch: 78, Cost: [1.76164028]\n",
      "Epoch: 79, Cost: [1.72316209]\n",
      "Epoch: 80, Cost: [1.68601623]\n",
      "Epoch: 81, Cost: [1.65015594]\n",
      "Epoch: 82, Cost: [1.61553608]\n",
      "Epoch: 83, Cost: [1.58211314]\n",
      "Epoch: 84, Cost: [1.54984508]\n",
      "Epoch: 85, Cost: [1.51869139]\n",
      "Epoch: 86, Cost: [1.48861295]\n",
      "Epoch: 87, Cost: [1.45957203]\n",
      "Epoch: 88, Cost: [1.43153223]\n",
      "Epoch: 89, Cost: [1.4044584]\n",
      "Epoch: 90, Cost: [1.37831666]\n",
      "Epoch: 91, Cost: [1.35307431]\n",
      "Epoch: 92, Cost: [1.32869978]\n",
      "Epoch: 93, Cost: [1.30516264]\n",
      "Epoch: 94, Cost: [1.2824335]\n",
      "Epoch: 95, Cost: [1.26048403]\n",
      "Epoch: 96, Cost: [1.23928687]\n",
      "Epoch: 97, Cost: [1.21881564]\n",
      "Epoch: 98, Cost: [1.19904487]\n",
      "Epoch: 99, Cost: [1.17995001]\n",
      "Epoch: 100, Cost: [1.16150735]\n",
      "Epoch: 101, Cost: [1.14369402]\n",
      "Epoch: 102, Cost: [1.12648795]\n",
      "Epoch: 103, Cost: [1.10986785]\n",
      "Epoch: 104, Cost: [1.09381319]\n",
      "Epoch: 105, Cost: [1.07830414]\n",
      "Epoch: 106, Cost: [1.06332157]\n",
      "Epoch: 107, Cost: [1.04884704]\n",
      "Epoch: 108, Cost: [1.03486274]\n",
      "Epoch: 109, Cost: [1.02135148]\n",
      "Epoch: 110, Cost: [1.0082967]\n",
      "Epoch: 111, Cost: [0.99568241]\n",
      "Epoch: 112, Cost: [0.98349316]\n",
      "Epoch: 113, Cost: [0.97171408]\n",
      "Epoch: 114, Cost: [0.96033079]\n",
      "Epoch: 115, Cost: [0.94932944]\n",
      "Epoch: 116, Cost: [0.93869666]\n",
      "Epoch: 117, Cost: [0.92841953]\n",
      "Epoch: 118, Cost: [0.9184856]\n",
      "Epoch: 119, Cost: [0.90888287]\n",
      "Epoch: 120, Cost: [0.89959975]\n",
      "Epoch: 121, Cost: [0.89062504]\n",
      "Epoch: 122, Cost: [0.88194795]\n",
      "Epoch: 123, Cost: [0.87355809]\n",
      "Epoch: 124, Cost: [0.86544539]\n",
      "Epoch: 125, Cost: [0.85760016]\n",
      "Epoch: 126, Cost: [0.85001305]\n",
      "Epoch: 127, Cost: [0.84267505]\n",
      "Epoch: 128, Cost: [0.83557743]\n",
      "Epoch: 129, Cost: [0.8287118]\n",
      "Epoch: 130, Cost: [0.82207005]\n",
      "Epoch: 131, Cost: [0.81564437]\n",
      "Epoch: 132, Cost: [0.80942719]\n",
      "Epoch: 133, Cost: [0.80341125]\n",
      "Epoch: 134, Cost: [0.79758951]\n",
      "Epoch: 135, Cost: [0.7919552]\n",
      "Epoch: 136, Cost: [0.78650177]\n",
      "Epoch: 137, Cost: [0.78122292]\n",
      "Epoch: 138, Cost: [0.77611255]\n",
      "Epoch: 139, Cost: [0.77116479]\n",
      "Epoch: 140, Cost: [0.76637396]\n",
      "Epoch: 141, Cost: [0.76173461]\n",
      "Epoch: 142, Cost: [0.75724144]\n",
      "Epoch: 143, Cost: [0.75288937]\n",
      "Epoch: 144, Cost: [0.74867348]\n",
      "Epoch: 145, Cost: [0.74458904]\n",
      "Epoch: 146, Cost: [0.74063146]\n",
      "Epoch: 147, Cost: [0.73679633]\n",
      "Epoch: 148, Cost: [0.73307939]\n",
      "Epoch: 149, Cost: [0.72947654]\n",
      "Epoch: 150, Cost: [0.7259838]\n",
      "Epoch: 151, Cost: [0.72259736]\n",
      "Epoch: 152, Cost: [0.71931351]\n",
      "Epoch: 153, Cost: [0.71612871]\n",
      "Epoch: 154, Cost: [0.7130395]\n",
      "Epoch: 155, Cost: [0.71004257]\n",
      "Epoch: 156, Cost: [0.70713473]\n",
      "Epoch: 157, Cost: [0.70431288]\n",
      "Epoch: 158, Cost: [0.70157405]\n",
      "Epoch: 159, Cost: [0.69891536]\n",
      "Epoch: 160, Cost: [0.69633404]\n",
      "Epoch: 161, Cost: [0.69382741]\n",
      "Epoch: 162, Cost: [0.69139289]\n",
      "Epoch: 163, Cost: [0.68902798]\n",
      "Epoch: 164, Cost: [0.68673029]\n",
      "Epoch: 165, Cost: [0.68449749]\n",
      "Epoch: 166, Cost: [0.68232734]\n",
      "Epoch: 167, Cost: [0.68021769]\n",
      "Epoch: 168, Cost: [0.67816645]\n",
      "Epoch: 169, Cost: [0.6761716]\n",
      "Epoch: 170, Cost: [0.67423121]\n",
      "Epoch: 171, Cost: [0.67234341]\n",
      "Epoch: 172, Cost: [0.67050638]\n",
      "Epoch: 173, Cost: [0.66871839]\n",
      "Epoch: 174, Cost: [0.66697775]\n",
      "Epoch: 175, Cost: [0.66528284]\n",
      "Epoch: 176, Cost: [0.66363209]\n",
      "Epoch: 177, Cost: [0.662024]\n",
      "Epoch: 178, Cost: [0.6604571]\n",
      "Epoch: 179, Cost: [0.65892998]\n",
      "Epoch: 180, Cost: [0.65744129]\n",
      "Epoch: 181, Cost: [0.65598972]\n",
      "Epoch: 182, Cost: [0.65457401]\n",
      "Epoch: 183, Cost: [0.65319292]\n",
      "Epoch: 184, Cost: [0.6518453]\n",
      "Epoch: 185, Cost: [0.65052999]\n",
      "Epoch: 186, Cost: [0.64924591]\n",
      "Epoch: 187, Cost: [0.64799199]\n",
      "Epoch: 188, Cost: [0.64676722]\n",
      "Epoch: 189, Cost: [0.64557061]\n",
      "Epoch: 190, Cost: [0.64440121]\n",
      "Epoch: 191, Cost: [0.64325811]\n",
      "Epoch: 192, Cost: [0.64214041]\n",
      "Epoch: 193, Cost: [0.64104727]\n",
      "Epoch: 194, Cost: [0.63997785]\n",
      "Epoch: 195, Cost: [0.63893137]\n",
      "Epoch: 196, Cost: [0.63790706]\n",
      "Epoch: 197, Cost: [0.63690418]\n",
      "Epoch: 198, Cost: [0.63592201]\n",
      "Epoch: 199, Cost: [0.63495986]\n",
      "Weight w0: [2.80046876], w1: [3.70365928]\n"
     ]
    }
   ],
   "source": [
    "epoch=200\n",
    "w0=0\n",
    "w1=1\n",
    "alpha=0.008\n",
    "m=100\n",
    "cost=[]\n",
    "weight0=[]\n",
    "weight1=[]\n",
    "for i in range(epoch):\n",
    "    #Step 1 Calculate Cost\n",
    "    J=cost_function(X,w0,w1,y,m)\n",
    "    cost.append(J)\n",
    "    print(\"Epoch: {0}, Cost: {1}\".format(i,J))\n",
    "    # Step 2 Calculate and Update the weights\n",
    "    temp0=w0-alpha*gradient_w0(X,w0,w1,y,m)\n",
    "    temp1=w1-alpha*gradient_w1(X,w0,w1,y,m)\n",
    "    w0=temp0\n",
    "    w1=temp1\n",
    "    weight0.append(w0)\n",
    "    weight1.append(w1)\n",
    "\n",
    "print(\"Weight w0: {0}, w1: {1}\".format(w0,w1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seeing above we see: w0: 2.80046876 and w1: 3.70365928, which reduces the cost to minimum of 0.63495986 with Epochs: 200, Learning rate alpha: 0.008.\n",
    "\n",
    "Vary different values of alpha, wo,w1 initial values and epochs and see the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(X,y,'ro',X,linear_model(X,w0,w1),'bo')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(weight0,cost,'r',weight1,cost,'b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}