Mystery_function.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPeW3fdpu945p5+XRkuZ2GC",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/tsourolampis/bu-cs630-fall23/blob/main/Mystery_function.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "-81DJPaGsLsk"
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def mystery_function(a, b, T=100):\n",
        "    if b >= a or a <= 0 or b <= 0:\n",
        "        raise ValueError(\"Ensure 0 < b < a\")\n",
        "\n",
        "    x, y = a, b\n",
        "    sequence = [(x, y)]\n",
        "\n",
        "    for _ in range(T):\n",
        "        x_next = (x + y) / 2\n",
        "        y_next = 2 * x * y / (x + y)\n",
        "        sequence.append((x_next, y_next))\n",
        "        x, y = x_next, y_next\n",
        "\n",
        "    return sequence\n",
        "\n",
        "\n",
        "def visualize_sequence(sequence):\n",
        "    x_vals, y_vals = zip(*sequence)\n",
        "\n",
        "    plt.scatter(x_vals, y_vals, color='blue')\n",
        "    for i in range(len(sequence)-1):\n",
        "        x1, y1 = sequence[i]\n",
        "        x2, y2 = sequence[i+1]\n",
        "        t = np.linspace(0, 1, 100)\n",
        "        plt.plot((1-t)*x1 + t*x2, (1-t)*y1 + t*y2, color='red')\n",
        "\n",
        "    plt.xlabel('x')\n",
        "    plt.ylabel('y')\n",
        "    plt.title('Visualization of Sequence')\n",
        "    plt.grid(True)\n",
        "    plt.show()\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "# Example usage:\n",
        "a = 100000\n",
        "b = 1\n",
        "T = 100\n",
        "sequence = mystery_function(a, b, T)\n",
        "visualize_sequence(sequence)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "lDDVaCywul2t",
        "outputId": "fbf11efe-9637-4420-bdc2-8835f071d674"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sequence[0:20]"
      ],
      "metadata": {
        "id": "jDts_scMsbot",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1730761c-47f1-4dd8-e6c0-3a9cb7a271c1"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(100000, 1),\n",
              " (50000.5, 1.999980000199998),\n",
              " (25001.2499900001, 3.999800011599324),\n",
              " (12502.624895005849, 7.998320419893972),\n",
              " (6255.311607712872, 15.986413830559432),\n",
              " (3135.6490107717154, 31.891324461531163),\n",
              " (1583.7701676166232, 63.14047457434278),\n",
              " (823.455321095483, 121.43949700508959),\n",
              " (472.4474090502863, 211.66377057929049),\n",
              " (342.0555898147884, 292.3501412567081),\n",
              " (317.2028655357483, 315.25566400890585),\n",
              " (316.22926477232704, 316.2262672684521),\n",
              " (316.2277660203896, 316.2277660132862),\n",
              " (316.2277660168379, 316.2277660168379),\n",
              " (316.2277660168379, 316.2277660168379),\n",
              " (316.2277660168379, 316.2277660168379),\n",
              " (316.2277660168379, 316.2277660168379),\n",
              " (316.2277660168379, 316.2277660168379),\n",
              " (316.2277660168379, 316.2277660168379),\n",
              " (316.2277660168379, 316.2277660168379)]"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "math.sqrt(a*b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "p7MjCkYPUClX",
        "outputId": "7d9f86e3-6d0f-428b-f60b-6b2d45cef931"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "316.22776601683796"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "oOSAQeCxUG4G"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}