Gradient Descent from Scratch in Python.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the required Libraries\n",
    "import pandas as pd\n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gradient of y with respect to x\n",
    "gradient_of_y = lambda x: 2(x-5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Initial value of x close to zero\n",
    "current_x_value = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# maximum number of iterations that can be done\n",
    "maximum_iterations = 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# current interation\n",
    "current_iteration = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Learning Rate\n",
    "learning_rate = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "previous_step_size = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration count  1 The current value of x is 0.198\n",
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      "Iteration count  282 The current value of x is 4.983558197568708\n",
      "Iteration count  283 The current value of x is 4.983887033617334\n",
      "Iteration count  284 The current value of x is 4.984209292944987\n",
      "Iteration count  285 The current value of x is 4.984525107086087\n",
      "Iteration count  286 The current value of x is 4.984834604944365\n",
      "Iteration count  287 The current value of x is 4.985137912845477\n",
      "Iteration count  288 The current value of x is 4.985435154588568\n",
      "Iteration count  289 The current value of x is 4.985726451496796\n",
      "Iteration count  290 The current value of x is 4.98601192246686\n",
      "Iteration count  291 The current value of x is 4.986291684017522\n",
      "Iteration count  292 The current value of x is 4.986565850337172\n",
      "Iteration count  293 The current value of x is 4.986834533330429\n",
      "Iteration count  294 The current value of x is 4.98709784266382\n",
      "Iteration count  295 The current value of x is 4.987355885810543\n",
      "Iteration count  296 The current value of x is 4.987608768094332\n",
      "Iteration count  297 The current value of x is 4.987856592732445\n",
      "Iteration count  298 The current value of x is 4.988099460877796\n",
      "Iteration count  299 The current value of x is 4.98833747166024\n",
      "Iteration count  300 The current value of x is 4.988570722227036\n",
      "Iteration count  301 The current value of x is 4.988799307782495\n",
      "Iteration count  302 The current value of x is 4.989023321626845\n",
      "Iteration count  303 The current value of x is 4.989242855194308\n",
      "Iteration count  304 The current value of x is 4.989457998090422\n",
      "Iteration count  305 The current value of x is 4.989668838128614\n",
      "Iteration count  306 The current value of x is 4.989875461366041\n",
      "Iteration count  307 The current value of x is 4.99007795213872\n",
      "Iteration count  308 The current value of x is 4.990276393095946\n",
      "Iteration count  309 The current value of x is 4.990470865234027\n",
      "Iteration count  310 The current value of x is 4.990661447929346\n",
      "Iteration count  311 The current value of x is 4.9908482189707595\n",
      "Iteration count  312 The current value of x is 4.991031254591344\n",
      "Iteration count  313 The current value of x is 4.991210629499517\n",
      "Iteration count  314 The current value of x is 4.991386416909527\n",
      "Iteration count  315 The current value of x is 4.991558688571336\n",
      "Iteration count  316 The current value of x is 4.991727514799909\n",
      "Iteration count  317 The current value of x is 4.991892964503911\n",
      "Iteration count  318 The current value of x is 4.992055105213833\n",
      "Iteration count  319 The current value of x is 4.992214003109556\n",
      "Iteration count  320 The current value of x is 4.992369723047365\n",
      "Iteration count  321 The current value of x is 4.992522328586418\n",
      "Iteration count  322 The current value of x is 4.992671882014689\n",
      "Iteration count  323 The current value of x is 4.992818444374396\n",
      "Iteration count  324 The current value of x is 4.992962075486908\n",
      "Iteration count  325 The current value of x is 4.9931028339771695\n",
      "Iteration count  326 The current value of x is 4.993240777297626\n",
      "Iteration count  327 The current value of x is 4.993375961751674\n",
      "Iteration count  328 The current value of x is 4.9935084425166405\n",
      "Iteration count  329 The current value of x is 4.993638273666308\n",
      "Iteration count  330 The current value of x is 4.993765508192982\n",
      "Iteration count  331 The current value of x is 4.993890198029122\n",
      "Iteration count  332 The current value of x is 4.99401239406854\n",
      "Iteration count  333 The current value of x is 4.9941321461871695\n",
      "Iteration count  334 The current value of x is 4.994249503263426\n",
      "Iteration count  335 The current value of x is 4.994364513198158\n",
      "Iteration count  336 The current value of x is 4.9944772229341945\n",
      "Iteration count  337 The current value of x is 4.9945876784755106\n",
      "Iteration count  338 The current value of x is 4.994695924906001\n",
      "Iteration count  339 The current value of x is 4.99480200640788\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration count  340 The current value of x is 4.994905966279723\n",
      "Iteration count  341 The current value of x is 4.995007846954128\n",
      "Iteration count  342 The current value of x is 4.995107690015046\n",
      "The local minima found at  4.995107690015046\n"
     ]
    }
   ],
   "source": [
    "while previous_step_size > precision_value and current_iteration < maximum_iterations:\n",
    "    previous_x_value = current_x_value \n",
    "    current_x_value = current_x_value - learning_rate * gradient_of_y * (previous_x_value)\n",
    "    previous_step_size = abs(current_x_value - previous_x_value)\n",
    "    current_iteration = current_iteration + 1 \n",
    "    print(\"Iteration count \",current_iteration ,\"The current value of x is\",current_x_value) \n",
    "    \n",
    "print(\"The local minima found at \", current_x_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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