enakai00/solution-7-3.ipynb

## solution-7-3.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPsv5q2YVYki19B5Aw8xu3A",
      "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/gist/enakai00/6c80a7a2ed1bfdf6a10a922214fb628a/solution-7-3.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np \n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "iqsmtDtTT64b"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "IA5lVn2XTStE"
      },
      "outputs": [],
      "source": [
        "def S(t):\n",
        "    d = 1 - 4 * beta * beta * np.exp(-gamma*t) * (1-np.exp(-gamma * t))\n",
        "    lambda1 = (1 + np.sqrt(d))/2\n",
        "    lambda2 = (1 - np.sqrt(d))/2\n",
        "    S = 0\n",
        "    if lambda1 != 0:\n",
        "        S += -lambda1 * np.log(lambda1)\n",
        "    if lambda2 != 0:\n",
        "        S += -lambda2 * np.log(lambda2)\n",
        "        \n",
        "    return S"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "xs = np.linspace(0, 100, 100)\n",
        "beta = 0.5\n",
        "gamma = 0.1\n",
        "plt.plot(xs, [S(x) for x in xs])\n",
        "print('Max S = {}'.format(np.max([S(x) for x in xs])))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "WstfG-t2T4p2",
        "outputId": "b6d1e208-b5ce-4923-cc57-8a91a23edfbf"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Max S = 0.24573902363689326\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "beta = 0.5\n",
        "gamma = 0.1\n",
        "lambda1 = (1+np.sqrt(1 - beta**2))/2\n",
        "lambda2 = (1-np.sqrt(1 - beta**2))/2\n",
        "-lambda1 * np.log(lambda1) - lambda2 * np.log(lambda2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6P4KKQr-bhHL",
        "outputId": "3a1f4c84-99d3-4ce7-b798-252d3b7b31f7"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.24577536666847116"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    }
  ]
}
	{
	"nbformat": 4,
	"nbformat_minor": 0,
	"metadata": {
	"colab": {
	"provenance": [],
	"authorship_tag": "ABX9TyPsv5q2YVYki19B5Aw8xu3A",
	"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/gist/enakai00/6c80a7a2ed1bfdf6a10a922214fb628a/solution-7-3.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
	]
	},
	{
	"cell_type": "code",
	"source": [
	"import numpy as np \n",
	"import matplotlib.pyplot as plt"
	],
	"metadata": {
	"id": "iqsmtDtTT64b"
	},
	"execution_count": 1,
	"outputs": []
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {
	"id": "IA5lVn2XTStE"
	},
	"outputs": [],
	"source": [
	"def S(t):\n",
	" d = 1 - 4 * beta * beta * np.exp(-gammat) (1-np.exp(-gamma * t))\n",
	" lambda1 = (1 + np.sqrt(d))/2\n",
	" lambda2 = (1 - np.sqrt(d))/2\n",
	" S = 0\n",
	" if lambda1 != 0:\n",
	" S += -lambda1 * np.log(lambda1)\n",
	" if lambda2 != 0:\n",
	" S += -lambda2 * np.log(lambda2)\n",
	" \n",
	" return S"
	]
	},
	{
	"cell_type": "code",
	"source": [
	"xs = np.linspace(0, 100, 100)\n",
	"beta = 0.5\n",
	"gamma = 0.1\n",
	"plt.plot(xs, [S(x) for x in xs])\n",
	"print('Max S = {}'.format(np.max([S(x) for x in xs])))"
	],
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 283
	},
	"id": "WstfG-t2T4p2",
	"outputId": "b6d1e208-b5ce-4923-cc57-8a91a23edfbf"
	},
	"execution_count": 3,
	"outputs": [
	{
	"output_type": "stream",
	"name": "stdout",
	"text": [
	"Max S = 0.24573902363689326\n"
	]
	},
	{
	"output_type": "display_data",
	"data": {
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	],
	"image/png": 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\n"
	},
	"metadata": {
	"needs_background": "light"
	}
	}
	]
	},
	{
	"cell_type": "code",
	"source": [
	"beta = 0.5\n",
	"gamma = 0.1\n",
	"lambda1 = (1+np.sqrt(1 - beta**2))/2\n",
	"lambda2 = (1-np.sqrt(1 - beta**2))/2\n",
	"-lambda1 * np.log(lambda1) - lambda2 * np.log(lambda2)"
	],
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/"
	},
	"id": "6P4KKQr-bhHL",
	"outputId": "3a1f4c84-99d3-4ce7-b798-252d3b7b31f7"
	},
	"execution_count": 4,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"0.24577536666847116"
	]
	},
	"metadata": {},
	"execution_count": 4
	}
	]
	}
	]
	}