Book4_Power-of-Matrix/Book4_Ch14_Python_Codes/Bk4_Ch14_02.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 14\n",
    "\n",
    "# 稳态向量\n",
    "Book_4《矩阵力量》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b60e1cce-b633-4a2e-a18f-79469897d1e1",
   "metadata": {},
   "source": [
    "该代码模拟了一个两种状态（鸡和兔）之间的状态转移过程，主要利用转移矩阵$T$的迭代作用来观察状态变化，直到系统趋于稳态。具体步骤如下：\n",
    "\n",
    "1. **定义转移矩阵$T$**：  \n",
    "   代码首先定义了一个$2 \\times 2$的转移矩阵：\n",
    "   $$\n",
    "   T = \\begin{bmatrix} 0.7 & 0.2 \\\\ 0.3 & 0.8 \\end{bmatrix}\n",
    "   $$\n",
    "   该矩阵表示在每个时间步长中，鸡和兔从一种状态转移到另一种状态的概率。\n",
    "\n",
    "2. **计算稳态向量**：  \n",
    "   程序接着通过求解转移矩阵$T$的特征向量来得到其稳态。稳态向量$sstate$可以表示为：\n",
    "   $$\n",
    "   T \\cdot sstate = sstate\n",
    "   $$\n",
    "   使用NumPy的`eig`函数得到特征向量，并将其归一化，以确保元素和为1。\n",
    "\n",
    "3. **定义初始状态矩阵并进行多次迭代**：  \n",
    "   程序为鸡和兔定义了多个初始状态，分别是：\n",
    "   $$\n",
    "   initial\\_x\\_array = \\begin{bmatrix} 1 & 0 & 0.5 & 0.4 \\\\ 0 & 1 & 0.5 & 0.6 \\end{bmatrix}\n",
    "   $$\n",
    "   其中每列代表不同的初始概率配置。在每次迭代中，从这些初始状态开始，逐步计算下一状态，迭代的数量设置为$num\\_iterations = 10$。\n",
    "\n",
    "4. **状态转移迭代过程**：  \n",
    "   对于每个初始状态，程序通过以下公式逐步计算转移：\n",
    "   $$\n",
    "   x_{i+1} = T \\cdot x_i\n",
    "   $$\n",
    "   每次迭代后，$x_i$代表的状态会向稳态收敛，将每步的结果存储在$X$中，以便后续绘图。\n",
    "\n",
    "5. **绘制状态变化图**：  \n",
    "   程序为每个初始状态绘制迭代次数$k$与状态（鸡和兔的概率）的关系图。横轴为迭代步数，纵轴为状态概率。鸡的状态用红色线表示，兔的状态用蓝色线表示。通过观察这些曲线，可以直观地看到系统从初始状态向稳态的收敛过程。\n",
    "\n",
    "总结来说，此代码演示了马尔可夫链在状态转移矩阵的作用下，通过迭代逐步趋于稳态的过程。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dde41df-cb67-464f-9474-acbbe46db77a",
   "metadata": {},
   "source": [
    "## 导入所需的库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3c268b7d-d25f-45d1-9359-5021616911ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入NumPy库\n",
    "import matplotlib.pyplot as plt  # 导入Matplotlib库用于绘图"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e88433bd-5277-4f2b-856d-20db126e7c5d",
   "metadata": {},
   "source": [
    "## 定义转移矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4f3e8d59-3124-41c6-a730-17d171bb05d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "T = np.matrix([[0.7, 0.2],  # 定义转移矩阵T的元素\n",
    "               [0.3, 0.8]])  # 转移概率的矩阵"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8dc6e11-b939-4246-af1b-fe741cc3b9c4",
   "metadata": {},
   "source": [
    "## 计算稳态向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0960ac9d-9335-48b4-87db-d9db97863e24",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.4]\n",
      " [0.6]]\n"
     ]
    }
   ],
   "source": [
    "sstate = np.linalg.eig(T)[1][:,1]  # 获取转移矩阵T的稳态特征向量\n",
    "sstate = sstate/sstate.sum()  # 归一化稳态向量\n",
    "print(sstate)  # 输出稳态向量"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cc44864-0986-4377-83ea-ec81cbda0312",
   "metadata": {},
   "source": [
    "## 定义初始状态"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dce53935-17b3-4a97-b07a-7ce90b55220e",
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_x_array = np.array([[1, 0, 0.5, 0.4],  # 鸡的初始状态\n",
    "                            [0, 1, 0.5, 0.6]])  # 兔的初始状态\n",
    "\n",
    "num_iterations = 10  # 设置迭代次数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "519c12b5-2717-4ff6-84a8-eabc98a97b27",
   "metadata": {},
   "source": [
    "## 遍历每个初始状态进行状态转移"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bfa24eb6-9c37-43ef-b7a8-cd2fb8309e7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in np.arange(0,4):\n",
    "    \n",
    "    initial_x = initial_x_array[:,i][:, None]  # 提取第i个初始状态\n",
    "    \n",
    "    x_i = np.zeros_like(initial_x)  # 初始化当前状态变量\n",
    "    x_i = initial_x  # 将当前状态设置为初始状态\n",
    "    X = initial_x.T  # 记录初始状态的转置形式\n",
    "    \n",
    "    ## 通过迭代计算状态转移\n",
    "    for x in np.arange(0,num_iterations):\n",
    "        x_i = T @ x_i  # 应用转移矩阵T进行状态转移\n",
    "        X = np.concatenate([X, x_i.T], axis=0)  # 将转移后的状态添加到X中\n",
    "    \n",
    "    fig, ax = plt.subplots()  # 创建绘图对象\n",
    "    \n",
    "    itr = np.arange(0, num_iterations + 1)  # 定义迭代次数范围\n",
    "    plt.plot(itr, X[:,0], marker='x', color=(1, 0, 0))  # 绘制鸡的状态变化曲线\n",
    "    plt.plot(itr, X[:,1], marker='x', color=(0, 0.6, 1))  # 绘制兔的状态变化曲线\n",
    "    \n",
    "    ax.grid(linestyle='--', linewidth=0.25, color=[0.5, 0.5, 0.5])  # 设置网格线样式\n",
    "    ax.set_xlim(0, num_iterations)  # 设置x轴范围\n",
    "    ax.set_ylim(0, 1)  # 设置y轴范围\n",
    "    ax.set_xlabel('Iteration, k')  # 设置x轴标签\n",
    "    ax.set_ylabel('State')  # 设置y轴标签"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}