Polynomial_Root_Finding_Using_Bisection_Method.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8pEm4kxLqhN7"
      },
      "source": [
        "Make sure you remove `raise NotImplementedError()` and fill in any place that says `# YOUR CODE HERE`, as well as your `NAME`, `ID`, and `SECTION` below:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "N6FXZz_eqhN9"
      },
      "outputs": [],
      "source": [
        "NAME = \"ARNOB MAJUMDER\"\n",
        "ID = \"20301089\"\n",
        "SECTION = \"07\""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D1WB3NXNqhN-"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "4323c48f5d5276b38804080cab43e0d5",
          "grade": false,
          "grade_id": "title",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "8BwuBD__qhN-"
      },
      "source": [
        "Polynomial Root Finding Using Bisection Method\n",
        "---\n",
        "\n",
        "### `pandas` Dataframe:\n",
        "Before we start we will know a little about `pandas` dataframe. `pandas` is a python library. Dataframes are classes that are used to store complex data. You can initialize one as a python dictionary. Let's take a look. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "adc6b91c35993f4ecedcfd53d807a206",
          "grade": false,
          "grade_id": "pd",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "F1iPegcMqhN-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "2a3778e9-c692-4ede-f179-0b79439b9270"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>5.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>3.9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>8.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>14.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>5</td>\n",
              "      <td>12.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>6</td>\n",
              "      <td>8.9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>7</td>\n",
              "      <td>10.2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   x     y\n",
              "0  0   1.0\n",
              "1  1   5.2\n",
              "2  2   3.9\n",
              "3  3   8.4\n",
              "4  4  14.6\n",
              "5  5  12.3\n",
              "6  6   8.9\n",
              "7  7  10.2"
            ]
          },
          "metadata": {},
          "execution_count": 1
        }
      ],
      "source": [
        "import pandas as pd\n",
        "\n",
        "x = [0, 1, 2, 3, 4, 5, 6, 7]\n",
        "y = [1.0, 5.2, 3.9, 8.4, 14.6, 12.3, 8.9, 10.2]\n",
        "\n",
        "dictionary = {\n",
        "    \"x\": x,\n",
        "    \"y\": y,\n",
        "}\n",
        "df = pd.DataFrame(dictionary)\n",
        "df.head(8)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "e8de09a00f2f32f8cfbb6b7823ebb992",
          "grade": false,
          "grade_id": "np_into",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "o1qgr3HYqhN_"
      },
      "source": [
        "We can use it to print data in a tabular format. We can even use more numpy arrays with it."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "b7b72bb172e2e46389ca4f41fd18628d",
          "grade": false,
          "grade_id": "np",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "gT5eXzSxqhN_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 520
        },
        "outputId": "99633c3f-44dd-4056-850e-de7061ed017c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>sin(x)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.112200</td>\n",
              "      <td>0.111964</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.224399</td>\n",
              "      <td>0.222521</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.336599</td>\n",
              "      <td>0.330279</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.448799</td>\n",
              "      <td>0.433884</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>0.560999</td>\n",
              "      <td>0.532032</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>0.673198</td>\n",
              "      <td>0.623490</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>0.785398</td>\n",
              "      <td>0.707107</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>0.897598</td>\n",
              "      <td>0.781831</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>1.009798</td>\n",
              "      <td>0.846724</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>1.121997</td>\n",
              "      <td>0.900969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>1.234197</td>\n",
              "      <td>0.943883</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>1.346397</td>\n",
              "      <td>0.974928</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>1.458597</td>\n",
              "      <td>0.993712</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>1.570796</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "           x    sin(x)\n",
              "0   0.000000  0.000000\n",
              "1   0.112200  0.111964\n",
              "2   0.224399  0.222521\n",
              "3   0.336599  0.330279\n",
              "4   0.448799  0.433884\n",
              "5   0.560999  0.532032\n",
              "6   0.673198  0.623490\n",
              "7   0.785398  0.707107\n",
              "8   0.897598  0.781831\n",
              "9   1.009798  0.846724\n",
              "10  1.121997  0.900969\n",
              "11  1.234197  0.943883\n",
              "12  1.346397  0.974928\n",
              "13  1.458597  0.993712\n",
              "14  1.570796  1.000000"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "import numpy as np\n",
        "\n",
        "x = np.linspace(0, np.pi/2, 15)\n",
        "y = np.sin(x)\n",
        "\n",
        "dictionary = {\n",
        "    \"x\": x,\n",
        "    \"sin(x)\": y,\n",
        "}\n",
        "df = pd.DataFrame(dictionary)\n",
        "df.head(15)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "2e1c412437306d2e9b0078176867e80c",
          "grade": false,
          "grade_id": "root_intro",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "2LJFoJfEqhN_"
      },
      "source": [
        "### Root Finding:\n",
        "Let $f(x)$ be a function of $x$. if for some $x=\\alpha, f(x) = f(\\alpha) = 0$, we say $\\alpha$ is a root of function $x$.\n",
        "\n",
        "Let, \n",
        "$$f(x) = x^5 + 2.5x^4 - 2x^3 -6x^2 + x + 2\\tag{6.1}$$\n",
        "\n",
        "The graph of $f(x)$ looks like this."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "023d32066c1625932a80604228bac0d6",
          "grade": false,
          "grade_id": "example",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "iiIEjH97qhN_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "ab8bd187-8f7d-414b-fad4-69fe6bdb96f9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[-2.22027583 -1.61803399 -0.65499178  0.61803399  1.37526761]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "from numpy.polynomial import Polynomial\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "f = Polynomial([2.0, 0.5, -6.0, -2.0, 2.5, 1.0])\n",
        "x = np.linspace(-2.5, 1.5, 100)\n",
        "y = f(x)\n",
        "dictionary = {\n",
        "    'x': x,\n",
        "    'y': y\n",
        "}\n",
        "plt.axhline(y=0, color='k')\n",
        "plt.plot(x, y)\n",
        "plt.plot(f.roots(), [0.0]*5, 'ro')\n",
        "print(f.roots())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "a77a2920b884f394a02829392b097131",
          "grade": false,
          "grade_id": "bisection_intro",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "ZDBo-CT3qhOA"
      },
      "source": [
        "Roots are the points where the graph intersects with the $X$-axis.\n",
        "\n",
        "### Bisection\n",
        "\n",
        "One way to find out root's are to use bisection method. Here is the strategy, if $\\alpha$ is a root between and interval $[a, b]$ then graph will cross the $X$-axis at $\\alpha$. So, $sign( f(\\alpha-h) ) = - sign( f(\\alpha+h) )$, for small value of $h$. \n",
        "\n",
        "So, we can work our way up towards the root by taking average of $a$ and $b$, as long as the signs are different.\n",
        "\n",
        "we will start with $a_0$ and $b_0$, such that, $f(a_0) f(b_0) < 0$.\n",
        "Then we iterate as this,\n",
        "\\begin{align}\n",
        "m_k &= \\frac{a_k + b_k}{2} \\\\\n",
        "\\text{if, } f(a_k) f(m_k) < 0, \\text{ then, } a_{k+1} &= a_k \\text{ and } b_{k+1} = m_k\\\\\n",
        "\\text{else, } a_{k+1} &= m_k \\text{ and, } b_{k+1} = b_k\n",
        "\\end{align}\n",
        "\n",
        "We keep iterating until we find the root with sufficient precision. We usually use a formula like this,\n",
        "$$\n",
        "\\frac{|m_{k+1} - m_k|}{|m_{k+1}|} \\leq \\epsilon \\\\  \n",
        "$$\n",
        "Where, $\\epsilon$ is a very small value, like $\\epsilon < 10^{-6}$\n",
        "\n",
        "### Complete the code below\n",
        "Complete the code below to iterate and solve for a root of the following equation, between the interval, $[-0.5, 1.3]$:\n",
        "\\begin{aligned}\n",
        "    f(x) = 2 + x - 6x^2 - 2x^3 + 2.5x^4 + x^5.\n",
        "\\end{aligned}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "250514194ec182b83282f90c837cb559",
          "grade": false,
          "grade_id": "ans",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "vcMvvqN4qhOA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b3eb6f95-6d05-4454-f4cc-e94c396b3f5d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "20.0\n",
            "20.0\n",
            "0.18000000000000008\n",
            "0.10975609756097567\n",
            "0.049450549450549566\n",
            "0.023560209424083732\n",
            "0.011508951406649507\n",
            "0.00568900126422254\n",
            "0.0028284098051540984\n",
            "0.0014182161991805507\n",
            "0.0007101151964650968\n",
            "0.00035530990919861467\n",
            "0.00017771809960122936\n",
            "8.887484446898626e-05\n",
            "4.444137195442376e-05\n",
            "2.2219698503236163e-05\n",
            "1.111009611460409e-05\n",
            "5.555109775105573e-06\n",
            "2.7775394579263736e-06\n",
            "1.388765871521362e-06\n",
            "6.943839000973432e-07\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from numpy.polynomial import Polynomial\n",
        "\n",
        "# The polynomial and the range is defined for you\n",
        "f = Polynomial([2.0, 0.5, -6.0, -2.0, 2.5, 1.0])\n",
        "a = -0.5\n",
        "b = 1.3\n",
        "m = (a + b) / 2\n",
        "e = 1e-6\n",
        "\n",
        "root = m    # You need to update this value\n",
        "\n",
        "# Populate the following lists in each iteration\n",
        "list_a = [-0.5]\n",
        "list_b = [1.3]\n",
        "list_m = [m]\n",
        "list_f = [f(m)]\n",
        "\n",
        "# YOUR CODE HERE\n",
        "x = 0\n",
        "y = 0\n",
        "val = 2e1\n",
        "while(val >= e):\n",
        "    if(f(list_a[x]) * f(list_m[x]) < 0):\n",
        "        list_a.append(list_a[x])\n",
        "        list_b.append(list_m[x])\n",
        "    elif(f(list_b[x]) * f(list_m[x]) < 0):\n",
        "        list_a.append(list_m[x])\n",
        "        list_b.append(list_b[x])\n",
        "    m = (list_a[x + 1] + list_b[x + 1]) / 2\n",
        "    root = m\n",
        "    list_f.append(f(m))\n",
        "    list_m.append(m)\n",
        "        \n",
        "    if x > 1:\n",
        "        val = (abs(list_m[y + 1] - list_m[y]) / abs(list_m[y]))\n",
        "    print(val)\n",
        "    x = x + 1\n",
        "    y = y + 1\n",
        "#raise NotImplementedError()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "62d14c64cdf4fb8a8d96afa669625d11",
          "grade": true,
          "grade_id": "test_0",
          "locked": true,
          "points": 10,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "n80r3n_4qhOB"
      },
      "outputs": [],
      "source": [
        "xs = np.linspace(-2.5, 1.5, 100)\n",
        "ys = f(xs)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "d605d35c8e5cb989a20d59e7bf1dca54",
          "grade": true,
          "grade_id": "test",
          "locked": true,
          "points": 10,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "trVJZs-dqhOB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 664
        },
        "outputId": "7d758bde-1d8f-4306-f864-f6f9120eb1b3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "           a         b         m          f(m)\n",
            "0  -0.500000  1.300000  0.400000  1.186240e+00\n",
            "1   0.400000  1.300000  0.850000 -1.389529e+00\n",
            "2   0.400000  0.850000  0.625000 -4.269409e-02\n",
            "3   0.400000  0.625000  0.512500  6.189171e-01\n",
            "4   0.512500  0.625000  0.568750  2.966661e-01\n",
            "5   0.568750  0.625000  0.596875  1.286523e-01\n",
            "6   0.596875  0.625000  0.610938  4.333223e-02\n",
            "7   0.610938  0.625000  0.617969  3.991260e-04\n",
            "8   0.617969  0.625000  0.621484 -2.112851e-02\n",
            "9   0.617969  0.621484  0.619727 -1.035982e-02\n",
            "10  0.617969  0.619727  0.618848 -4.979112e-03\n",
            "11  0.617969  0.618848  0.618408 -2.289682e-03\n",
            "12  0.617969  0.618408  0.618188 -9.452003e-04\n",
            "13  0.617969  0.618188  0.618079 -2.730176e-04\n",
            "14  0.617969  0.618079  0.618024  6.305907e-05\n",
            "15  0.618024  0.618079  0.618051 -1.049781e-04\n",
            "16  0.618024  0.618051  0.618037 -2.095919e-05\n",
            "17  0.618024  0.618037  0.618031  2.105002e-05\n",
            "18  0.618031  0.618037  0.618034  4.543651e-08\n",
            "19  0.618034  0.618037  0.618036 -1.045687e-05\n",
            "20  0.618034  0.618036  0.618035 -5.205715e-06\n",
            "21  0.618034  0.618035  0.618034 -2.580139e-06\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.axhline(y=0, color='k')\n",
        "plt.plot(xs, ys)\n",
        "plt.plot(root, f(root), 'ro')\n",
        "\n",
        "print(pd.DataFrame({'a':list_a, 'b':list_b, 'm':list_m, 'f(m)':list_f}))\n",
        "\n",
        "assert \"{:.3f}\".format(root) == \"0.618\""
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "M5kTaH-6qhOC"
      },
      "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": "3.7.4"
    },
    "colab": {
      "name": "Polynomial_Root_Finding_Using_Bisection_Method_20301089_07.ipynb",
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}