Newton__Raphson_method.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Newton _Raphson method.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "9qeqJ9jTZM3V",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 546
        },
        "outputId": "0468599c-af7c-4dca-9e35-8e81744994dd"
      },
      "source": [
        "import math\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "def func(x):\n",
        "    return (math.exp(x) - 3 * x - math.sin(x))\n",
        "\n",
        "def derivFunc(x):\n",
        "    return (math.exp(x) - 3 -math.cos(x))\n",
        "\n",
        "def newtonRaphson(x):\n",
        "    cnt = 0\n",
        "    z = 0\n",
        "\n",
        "    print(\"----------------------------------------------------------------------------------------------------------\")\n",
        "    print(\"N   \", \"\\t Xn \", \"\\t  f(Xn)  \", \"\\t  f'(Xn)    \", \"\\t f(Xn)/f'(Xn)\\t\", \"\\tXn-f(Xn)/f'(Xn)\")\n",
        "    print(\"----------------------------------------------------------------------------------------------------------\")\n",
        "    print()\n",
        "    h = func(x) / derivFunc(x)\n",
        "\n",
        "    while abs(h) >= 0.0001:\n",
        "        if cnt == 0:\n",
        "            h = func(x) / derivFunc(x)\n",
        "            x = x - h\n",
        "            print(cnt, \"\\t|\", \"%.6f\" % x0, \"\\t|\", \"%.6f\" % func(x), \"\\t|\", \"%.6f\" % derivFunc(x), \"\\t|\", \"%.6f\" % h,\n",
        "                  \"\\t|\", \"%.6f\" % x)\n",
        "            print()\n",
        "        z = x\n",
        "        cnt = cnt + 1\n",
        "        h = func(x) / derivFunc(x)\n",
        "        x = z - h\n",
        "        if (cnt != 0):\n",
        "            print(cnt, \"\\t|\", \"%.6f\" % z, \"\\t|\", \"%.6f\" % func(x), \"\\t|\", \"%.6f\" % derivFunc(x), \"\\t|\", \"%.6f\" % h,\n",
        "                  \"\\t|\", \"%.6f\" % x)\n",
        "            print()\n",
        "\n",
        "    print(\"-----------------------------------------------------------------------------------------------------\")\n",
        "    print()\n",
        "    print(\"-----------------------------------------------------------------------------------------------------\")\n",
        "    print(\"The value of the root is : \", \"%.4f\" % x)\n",
        "    a=np.linspace(-2,7,1000)\n",
        "    f2 = np.vectorize(func)\n",
        "    \n",
        "    plt.plot(a,f2(a))\n",
        "    plt.plot(x,f2(x),\"d\")\n",
        "    plt.grid()\n",
        "    plt.show()\n",
        "\n",
        "\n",
        "\n",
        "x0 = 0\n",
        "newtonRaphson(x0)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "----------------------------------------------------------------------------------------------------------\n",
            "N    \t Xn  \t  f(Xn)   \t  f'(Xn)     \t f(Xn)/f'(Xn)\t \tXn-f(Xn)/f'(Xn)\n",
            "----------------------------------------------------------------------------------------------------------\n",
            "\n",
            "0 \t| 0.000000 \t| 0.068418 \t| -2.549345 \t| -0.333333 \t| 0.333333\n",
            "\n",
            "1 \t| 0.333333 \t| 0.000628 \t| -2.502263 \t| -0.026837 \t| 0.360171\n",
            "\n",
            "2 \t| 0.360171 \t| 0.000000 \t| -2.501814 \t| -0.000251 \t| 0.360422\n",
            "\n",
            "3 \t| 0.360422 \t| 0.000000 \t| -2.501814 \t| -0.000000 \t| 0.360422\n",
            "\n",
            "-----------------------------------------------------------------------------------------------------\n",
            "\n",
            "-----------------------------------------------------------------------------------------------------\n",
            "The value of the root is :  0.3604\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}