III_CS230_Assgn4_2103322 (1).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5e6bb548",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The following steady state probabilities turn out to be a good approximation to the ones that are computed theoretically, i.e., 0.2. \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''\n",
    "Name: Karan Sutariya\n",
    "Roll No: 2103322\n",
    "CS230 Assignment[4]: Part III - Q1 Simulating Markov Chain and estimating the steady state probabilities of various states\n",
    "\n",
    "'''\n",
    "\n",
    "\n",
    "#Importing the following libraries to fabricate a markov chain\n",
    "\n",
    "import numpy as np\n",
    "import random \n",
    "import matplotlib.pyplot as plot \n",
    "\n",
    "\n",
    "p = q = 1/4 #probabilities \n",
    "\n",
    "iterations = 1000 #running the experiment for 1000 times for getting an accurate ans\n",
    "\n",
    "initial_state = 0 #initial state \n",
    "\n",
    "markov_run = 100 #steps in MARKOV CHAIN\n",
    "\n",
    "estimate = {} #creating a dictionary to store the state along with its count in 1000\n",
    "\n",
    "\n",
    "for i in range(iterations): #iterating the experiment for 1000 times\n",
    "    \n",
    "    present_state = initial_state #initialization\n",
    "    \n",
    "    for x in range(markov_run): #running the markov chain for over 100 steps\n",
    "        \n",
    "        prob = random.uniform(0,1) #throws a random number in between 0 and 1\n",
    "        \n",
    "        if ( prob < p): \n",
    "            if (present_state != 4): present_state += 1  #moving to the next step\n",
    "        \n",
    "        elif ( prob < (p+q) ): \n",
    "            if (present_state != 0): present_state -= 1 #moving to the back step\n",
    "                \n",
    "    \n",
    "    \n",
    "    #inserting the states and their counts \n",
    "    if present_state in estimate: estimate[present_state] += 1\n",
    "    \n",
    "    else: estimate[present_state] = 1\n",
    "        \n",
    " \n",
    " #for plotting the probabilities\n",
    "for k in estimate.keys(): estimate[k] /= 1000\n",
    "    \n",
    "#Plotting the distribution\n",
    "    \n",
    "plot.bar(estimate.keys(), estimate.values(), color = 'pink', ec='black')\n",
    "\n",
    "plot.xlabel(\"State  ------------->\")\n",
    "\n",
    "plot.ylabel(\"Steady State Probability  ------------->\")\n",
    "\n",
    "plot.title(\"ESTIMATION OF STEADY STATE PROBABILITY\")\n",
    "\n",
    "print(\"\\nThe following steady state probabilities turn out to be a good approximation to the ones that are computed theoretically, i.e., 0.2. \")       \n",
    "                \n",
    "            \n",
    "        \n",
    "        \n",
    "    \n",
    "    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "107fc01f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "132bcd45",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}