Bisection Method.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "78f91780",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e22fb1f",
   "metadata": {},
   "source": [
    "## Bisection Method\n",
    "- Implement the <b>bisection method</b> as a function and solve the following equations:\n",
    "    - 𝒇(𝒙)=𝒙^𝟑−𝒙−𝟐,          𝒙∈[𝟏,𝟐]\n",
    "    - 𝒇(𝒙)=𝒙^2−𝟐,          𝒙∈[0,𝟐]\n",
    "- Draw both functions and check out the roots.\n",
    "- Try your function in another intervals and check out the results.\n",
    "- [Bisection method](https://www.youtube.com/watch?v=mzQFGOvH-mk&t=10s&ab_channel=JeffreyChasnov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d975dfa4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bisection(f,a,b,epsilon = 0.1,iterations=100):\n",
    "    for i in range(iterations):\n",
    "        #set midpoint\n",
    "        m = (a+b) / 2.0\n",
    "    \n",
    "        #check if a and b are in the root bound\n",
    "        if(np.sign(f(a)) == np.sign(f(b))):\n",
    "            raise Exception(\"The scalars a and b do not bound a root\")\n",
    "        \n",
    "        if np.sign(f(m)) == np.sign(f(a)):\n",
    "            a = m\n",
    "        else:\n",
    "            b = m\n",
    "        #set stop condition for convergence\n",
    "        if np.abs(f(m)) < epsilon:\n",
    "            break\n",
    "            \n",
    "    return m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2c26b8fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r1 = 1.53125\n",
      "\n",
      "r01 = 1.521484375\n",
      "\n",
      "f(r1) = 0.059112548828125\n",
      "\n",
      "f(r01) = 0.0006221756339073181\n",
      "\n"
     ]
    }
   ],
   "source": [
    "f1 = lambda x: x**3 - x - 2\n",
    "r1 = bisection(f1,1,2,0.1)\n",
    "r01 = bisection(f1,1,2,0.01)\n",
    "print(\"r1 = {}\\n\".format(r1))\n",
    "print(\"r01 = {}\\n\".format(r01))\n",
    "print(\"f(r1) = {}\\n\".format(f1(r1)))\n",
    "print(\"f(r01) = {}\\n\".format(f1(r01)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6d3ea6d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-5,5,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a3aa7bc7",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (5,5))\n",
    "plt.plot(x, f1(x))\n",
    "plt.scatter(r1, 0)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "10b3351e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r2 = 1.4375\n",
      "\n",
      "r02 = 1.4140625\n",
      "\n",
      "f(r2) = 0.06640625\n",
      "\n",
      "f(r02) = -0.00042724609375\n",
      "\n"
     ]
    }
   ],
   "source": [
    "f2 = lambda x: x**2 - 2\n",
    "r2 = bisection(f2,0,2,0.1)\n",
    "r02 = bisection(f2,0,2,0.01)\n",
    "print(\"r2 = {}\\n\".format(r2))\n",
    "print(\"r02 = {}\\n\".format(r02))\n",
    "print(\"f(r2) = {}\\n\".format(f2(r2)))\n",
    "print(\"f(r02) = {}\\n\".format(f2(r02)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "97abbe2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (5,5))\n",
    "plt.plot(x, f2(x))\n",
    "plt.scatter(r2, 0)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d6379ca5",
   "metadata": {},
   "outputs": [
    {
     "ename": "Exception",
     "evalue": "The scalars a and b do not bound a root",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mException\u001b[0m                                 Traceback (most recent call last)",
      "Input \u001b[1;32mIn [9]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[0m r3 \u001b[38;5;241m=\u001b[39m \u001b[43mbisection\u001b[49m\u001b[43m(\u001b[49m\u001b[43mf1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0.1\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "Input \u001b[1;32mIn [2]\u001b[0m, in \u001b[0;36mbisection\u001b[1;34m(f, a, b, epsilon, iterations)\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[38;5;66;03m#check if a and b are in the root bound\u001b[39;00m\n\u001b[0;32m      7\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m(np\u001b[38;5;241m.\u001b[39msign(f(a)) \u001b[38;5;241m==\u001b[39m np\u001b[38;5;241m.\u001b[39msign(f(b))):\n\u001b[1;32m----> 8\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mThe scalars a and b do not bound a root\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m     10\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m np\u001b[38;5;241m.\u001b[39msign(f(m)) \u001b[38;5;241m==\u001b[39m np\u001b[38;5;241m.\u001b[39msign(f(a)):\n\u001b[0;32m     11\u001b[0m     a \u001b[38;5;241m=\u001b[39m m\n",
      "\u001b[1;31mException\u001b[0m: The scalars a and b do not bound a root"
     ]
    }
   ],
   "source": [
    "r3 = bisection(f1, -2, 1, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "71fc3b09",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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