finding roots of transcendental equations.ipynb

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  "metadata": {
    "colab": {
      "name": "Untitled15.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNg7UZdoMBNDak7dApPsmxd",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/k00sharath/hello-world/blob/master/finding%20roots%20of%20transcendental%20equations.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tCY-VGCqv7sN",
        "outputId": "c04be812-d0eb-41c2-f2b6-8e79b0b49d7e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "\n",
        "import sympy as sp\n",
        "def newton_raphson(x1,x2,func,error_tolerance=10^-2):\n",
        "    root=(x1+x2)/2.0\n",
        "    func_root=func.evalf(subs={x:root})\n",
        "    derivative=sp.diff(func)\n",
        "    der_value=derivative.evalf(subs={x:root})\n",
        "    error=1000\n",
        "    while abs(error)>error_tolerance:\n",
        "        old_root=root\n",
        "        root=root-(func_root/der_value)\n",
        "        func_root=func.evalf(subs={x:root})\n",
        "        der_value=derivative.evalf(subs={x:root})\n",
        "        error=((root-old_root)/(root))*100\n",
        "        print('old_root',old_root,'root',root,'error',error)\n",
        "\n",
        "x=sp.Symbol('x')\n",
        "func=-0.875*x*x+1.75*x+2.625\n",
        "newton_raphson(-1.2,-0.9,func,10^-1)\n",
        "\n",
        "    \n",
        "\n",
        "    \n",
        "\n",
        "\n",
        "\n"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
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            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n",
            "old_root -1.00000000000000 root -1.00000000000000 error 0\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "error",
          "ename": "KeyboardInterrupt",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-10-54ebdcbac28a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     17\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSymbol\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'x'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.875\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1.75\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m2.625\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 19\u001b[0;31m \u001b[0mnewton_raphson\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1.2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.9\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m^\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     20\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-10-54ebdcbac28a>\u001b[0m in \u001b[0;36mnewton_raphson\u001b[0;34m(x1, x2, func, error_tolerance)\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0mold_root\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mroot\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m         \u001b[0mroot\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mroot\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc_root\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mder_value\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m         \u001b[0mfunc_root\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mroot\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m         \u001b[0mder_value\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mderivative\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mroot\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m         \u001b[0merror\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mroot\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mold_root\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mroot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sympy/core/evalf.py\u001b[0m in \u001b[0;36mevalf\u001b[0;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[1;32m   1392\u001b[0m             \u001b[0moptions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'quad'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquad\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1393\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1394\u001b[0;31m             \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1395\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1396\u001b[0m             \u001b[0;31m# Fall back to the ordinary evalf\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sympy/core/evalf.py\u001b[0m in \u001b[0;36mevalf\u001b[0;34m(x, prec, options)\u001b[0m\n\u001b[1;32m   1284\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1285\u001b[0m         \u001b[0mrf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1286\u001b[0;31m         \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1287\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1288\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sympy/core/evalf.py\u001b[0m in \u001b[0;36mevalf_add\u001b[0;34m(v, prec, options)\u001b[0m\n\u001b[1;32m    496\u001b[0m         \u001b[0moptions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'maxprec'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moldmaxprec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mprec\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    497\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 498\u001b[0;31m         \u001b[0mterms\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    499\u001b[0m         re, re_acc = add_terms(\n\u001b[1;32m    500\u001b[0m             [a[0::2] for a in terms if a[0]], prec, target_prec)\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sympy/core/evalf.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m    496\u001b[0m         \u001b[0moptions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'maxprec'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moldmaxprec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mprec\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    497\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 498\u001b[0;31m         \u001b[0mterms\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    499\u001b[0m         re, re_acc = add_terms(\n\u001b[1;32m    500\u001b[0m             [a[0::2] for a in terms if a[0]], prec, target_prec)\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sympy/core/evalf.py\u001b[0m in \u001b[0;36mevalf\u001b[0;34m(x, prec, options)\u001b[0m\n\u001b[1;32m   1284\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1285\u001b[0m         \u001b[0mrf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1286\u001b[0;31m         \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1287\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1288\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sympy/core/evalf.py\u001b[0m in \u001b[0;36mevalf_mul\u001b[0;34m(v, prec, options)\u001b[0m\n\u001b[1;32m    536\u001b[0m     \u001b[0;32mfrom\u001b[0m \u001b[0msympy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumbers\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mFloat\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    537\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 538\u001b[0;31m         \u001b[0marg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    539\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0marg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    540\u001b[0m             \u001b[0;32mcontinue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sympy/core/evalf.py\u001b[0m in \u001b[0;36mevalf\u001b[0;34m(x, prec, options)\u001b[0m\n\u001b[1;32m   1284\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1285\u001b[0m         \u001b[0mrf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1286\u001b[0;31m         \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1287\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1288\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sympy/core/evalf.py\u001b[0m in \u001b[0;36mevalf_symbol\u001b[0;34m(x, prec, options)\u001b[0m\n\u001b[1;32m   1214\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mcached_prec\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0mprec\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1215\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mcached\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1216\u001b[0;31m         \u001b[0mv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msympify\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1217\u001b[0m         \u001b[0mcache\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1218\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sympy/core/evalf.py\u001b[0m in \u001b[0;36mevalf\u001b[0;34m(x, prec, options)\u001b[0m\n\u001b[1;32m   1281\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1282\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1283\u001b[0;31m     \u001b[0;32mfrom\u001b[0m \u001b[0msympy\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mre\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mre_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mim\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mim_\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1284\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1285\u001b[0m         \u001b[0mrf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/lib/python3.6/importlib/_bootstrap.py\u001b[0m in \u001b[0;36m_handle_fromlist\u001b[0;34m(module, fromlist, import_, recursive)\u001b[0m\n",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "36RzskDex_84",
        "outputId": "b5095f0b-6fba-4509-9de4-be187c04739d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "u=sp.Symbol('u')\n",
        "o=5*(u**3)\n",
        "o.subs(u,2)\n",
        "h=sp.diff(o)\n",
        "print(h.subs(u,2))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "60\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qXvoy6nq01n2",
        "outputId": "cb1913e6-4ecb-4e22-ea75-00684fd7d954",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "import sympy as sp\n",
        "x=sp.Symbol('x')\n",
        "y=sp.exp(-x)-x\n",
        "\n",
        "sp.diff(y).subs(x,0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wtyBfwItIV_E",
        "outputId": "87f102f6-600a-414f-a77b-9e4c1cfa5eea",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 493
        }
      },
      "source": [
        "import sympy as sp\n",
        "def bisection_method(xinitial_1,xinitial_2,func,error_tolerance):\n",
        "    x1=xinitial_1\n",
        "    x2=xinitial_2\n",
        "    x_r=(x1+x2)/2\n",
        "    func_x1=func.evalf(subs={x:x1})\n",
        "    func_x2=func.evalf(subs={x:x2})\n",
        "    func_root=func.evalf(subs={x:x_r})\n",
        "    error=1000\n",
        "    while abs(error)>=error_tolerance:\n",
        "        \n",
        "        \n",
        "        \n",
        "        if (func_x1)*(func_root)<0:\n",
        "            old_root=x_r\n",
        "            x1=x1\n",
        "         \n",
        "           \n",
        "            x2=x_r\n",
        "            x_r=(x1+x2)/2\n",
        "            func_x1=func.evalf(subs={x:x1})\n",
        "            func_x2=func.evalf(subs={x:x2})\n",
        "            func_root=func.evalf(subs={x:x_r})\n",
        "            error=((x_r-old_root)/(x_r))*100\n",
        "            print('x1=',x1   , 'x2=' , x2, 'x_r=',x_r  , abs(error),'\\n')\n",
        "        if abs(error)>=error_tolerance:\n",
        "            if (func_x2)*(func_root)<0:\n",
        "                old_root=x_r\n",
        "                x2=x2\n",
        "                x1=x_r\n",
        "                x_r=(x1+x2)/2\n",
        "                func_x1=func.evalf(subs={x:x1})\n",
        "                func_x2=func.evalf(subs={x:x2})\n",
        "                func_root=func.evalf(subs={x:x_r})\n",
        "                error=((x_r-old_root)/(x_r))*100\n",
        "                print('x1=',x1, 'x2=',    x2,'x_r=', x_r,   abs(error),'\\n')\n",
        "    return\n",
        "x=sp.Symbol('x')\n",
        "func=sp.exp(-x)-x\n",
        "bisection_method(0,1,func,0.01)\n",
        "       \n",
        "\n"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "x1= 0.5 x2= 1 x_r= 0.75 33.33333333333333 \n",
            "\n",
            "x1= 0.5 x2= 0.75 x_r= 0.625 20.0 \n",
            "\n",
            "x1= 0.5 x2= 0.625 x_r= 0.5625 11.11111111111111 \n",
            "\n",
            "x1= 0.5625 x2= 0.625 x_r= 0.59375 5.263157894736842 \n",
            "\n",
            "x1= 0.5625 x2= 0.59375 x_r= 0.578125 2.7027027027027026 \n",
            "\n",
            "x1= 0.5625 x2= 0.578125 x_r= 0.5703125 1.36986301369863 \n",
            "\n",
            "x1= 0.5625 x2= 0.5703125 x_r= 0.56640625 0.6896551724137931 \n",
            "\n",
            "x1= 0.56640625 x2= 0.5703125 x_r= 0.568359375 0.3436426116838488 \n",
            "\n",
            "x1= 0.56640625 x2= 0.568359375 x_r= 0.5673828125 0.17211703958691912 \n",
            "\n",
            "x1= 0.56640625 x2= 0.5673828125 x_r= 0.56689453125 0.08613264427217916 \n",
            "\n",
            "x1= 0.56689453125 x2= 0.5673828125 x_r= 0.567138671875 0.04304778303917348 \n",
            "\n",
            "x1= 0.567138671875 x2= 0.5673828125 x_r= 0.5672607421875 0.021519259737465032 \n",
            "\n",
            "x1= 0.567138671875 x2= 0.5672607421875 x_r= 0.56719970703125 0.010760787689658883 \n",
            "\n",
            "x1= 0.567138671875 x2= 0.56719970703125 x_r= 0.567169189453125 0.005380683346785042 \n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MsO0z-XoOBBr",
        "outputId": "b887e0f5-d784-43b2-d8a1-d5ee71023880",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "x=5\n",
        "y=x\n",
        "x=4\n",
        "print(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "4 5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8KfDNL4qpahL",
        "outputId": "3d0c3bc4-f914-484b-c893-8a583e3367b1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        }
      },
      "source": [
        "import sympy as sp\n",
        "def regular_falsi_method(xinitial_1,xinitial_2,func,error_tolerance):\n",
        "    x1=xinitial_1\n",
        "    x2=xinitial_2\n",
        "    func_x1=func.evalf(subs={x:x1})\n",
        "    func_x2=func.evalf(subs={x:x2})\n",
        "    x_r=x2-func_x2*((x1-x2)/(func_x1-func_x2))\n",
        "    func_xr=func.evalf(subs={x:x_r})\n",
        "    error=1000\n",
        "    while abs(error)>=error_tolerance:\n",
        "        if (func_xr)*(func_x1)<0:\n",
        "            old_root=x_r\n",
        "            x1=x1\n",
        "            x2=x_r\n",
        "            func_x1=func.evalf(subs={x:x1})\n",
        "            func_x2=func.evalf(subs={x:x2})\n",
        "            x_r=x2-func_x2*((x1-x2)/(func_x1-func_x2))\n",
        "            func_xr=func.evalf(subs={x:x_r})\n",
        "            error=((x_r-old_root)/(x_r))*100\n",
        "            print('x1=',x1,'x2=',x2,'x_r=',x_r,'error=',abs(error),'\\n')\n",
        "        if abs(error)>=error_tolerance:\n",
        "            if (func_xr)*(func_x2)<0:\n",
        "                old_root=x_r\n",
        "                x1=x_r\n",
        "                x2=x2\n",
        "                func_x1=func.evalf(subs={x:x1})\n",
        "                func_x2=func.evalf(subs={x:x2})\n",
        "                x_r=x2-func_x2*((x1-x2)/(func_x1-func_x2))\n",
        "                func_xr=func.evalf(subs={x:x_r})\n",
        "                error=((x_r-old_root)/(x_r))*100\n",
        "                print('x1=',x1,'x2=',x2,'x_r=',x_r,'error',abs(error),'\\n')\n",
        "    return\n",
        "\n",
        "x=sp.Symbol('x')\n",
        "func=x*sp.exp(x)-1\n",
        "regular_falsi_method(0,1,func,0.001)    "
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "x1= 0.367879441171442 x2= 1 x_r= 0.503314332132986 error 26.9086100504205 \n",
            "\n",
            "x1= 0.503314332132986 x2= 1 x_r= 0.547412050944398 error 8.05567190845268 \n",
            "\n",
            "x1= 0.547412050944398 x2= 1 x_r= 0.561115043794732 error 2.44210042162883 \n",
            "\n",
            "x1= 0.561115043794732 x2= 1 x_r= 0.565308289103787 error 0.741762572719953 \n",
            "\n",
            "x1= 0.565308289103787 x2= 1 x_r= 0.566585341808409 error 0.225394589373896 \n",
            "\n",
            "x1= 0.566585341808409 x2= 1 x_r= 0.566973699148894 error 0.0684965353891316 \n",
            "\n",
            "x1= 0.566973699148894 x2= 1 x_r= 0.567091747661905 error 0.0208164751995583 \n",
            "\n",
            "x1= 0.567091747661905 x2= 1 x_r= 0.567127625859380 error 0.00632630043733156 \n",
            "\n",
            "x1= 0.567127625859380 x2= 1 x_r= 0.567138529783095 error 0.00192262086654611 \n",
            "\n",
            "x1= 0.567138529783095 x2= 1 x_r= 0.567141843607949 error 0.000584302655614373 \n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bsJwR5D14GOr",
        "outputId": "ecb882f9-ac41-4af5-ef52-65e7819af638",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "import sympy as sp\n",
        "x=sp.Symbol('x')\n",
        "func1=x**3+sp.exp(-5)\n",
        "func1.evalf(subs={x:2})"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "8.00673794699908"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7vNedSAODQOV",
        "outputId": "2c5c8372-edbb-4e32-8bcb-4f652fecd82c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        }
      },
      "source": [
        "import sympy as sp\n",
        "def successive_approximation(func,initial_x,error_tolerance):\n",
        "    error=10000\n",
        "    y=initial_x\n",
        "    while abs(error)>error_tolerance:                                               # express the x in the form of function of x for this method\n",
        "        old_root=y\n",
        "        y=func.subs(x,old_root)\n",
        "        error=old_root-y\n",
        "        print('root',y,'error',error)\n",
        "    return\n",
        "x=sp.Symbol('x')\n",
        "func=sp.exp(-x)\n",
        "successive_approximation(func,0.5,0.001)\n"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "root 0.606530659712633 error -0.106530659712633\n",
            "root 0.545239211892605 error 0.0612914478200284\n",
            "root 0.579703094878068 error -0.0344638829854632\n",
            "root 0.560064627938902 error 0.0196384669391664\n",
            "root 0.571172148977215 error -0.0111075210383133\n",
            "root 0.564862946980323 error 0.00630920199689167\n",
            "root 0.568438047570066 error -0.00357510058974275\n",
            "root 0.566409452746921 error 0.00202859482314544\n",
            "root 0.567559634262242 error -0.00115018151532165\n",
            "root 0.566907212935471 error 0.000652421326771013\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}