{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 马尔可夫链的模拟\n", "\n", "## 简单的马尔可夫链\n", "\n", "假设有3个状态,使用如下转移概率矩阵描述的马尔可夫链:$$Q=\\left[\\begin{array}{ccc}\n", "0.3 & 0.4 & 0.3\\\\\n", "0.3 & 0.1 & 0.6\\\\\n", "0.3 & 0.2 & 0.5\n", "\\end{array}\\right]$$的模拟如下:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "转移矩阵:\n", " [[0.3 0.4 0.3]\n", " [0.3 0.1 0.6]\n", " [0.3 0.2 0.5]]\n", "路径: [0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 0, 1, 1, 2, 2, 2, 1, 2, 2, 2, 0, 1, 2, 2, 2, 2, 1, 0, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 1, 2, 1, 2, 0, 0, 0, 2, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2, 2, 1, 1, 2, 0, 1, 2, 2, 2, 1, 2, 2, 2, 2, 0, 0, 1, 0, 1]\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numpy.random as nprd\n", "\n", "states=[0,1,2] # 状态空间,讲义中为1、2、3,这里方便起见记为0、1、2,最后画图的时候+1即可。\n", "current_state=0 # 从0出发\n", "Path=[0] # 初始化路径\n", "Q=np.array([[0.3,0.4,0.3],[0.3,0.1,0.6],[0.3,0.2,0.5]])\n", "print(\"转移矩阵:\\n\",Q)\n", "## 定义转移函数\n", "def trans(x,Q):\n", " prob=Q[x] #提取出Q矩阵的第x行,比如第0行为[0.3,0.4,0.3]\n", " cum_prob=np.add.accumulate(prob) #将prob累加,比如第0行累加后得到[0.3,0.7,1.0]\n", " u=nprd.random() #产生一个(0,1)上的均匀分布随机数\n", " s=0\n", " while u>=cum_prob[s]:\n", " s+=1\n", " return s\n", "\n", "N=99 # 时间长度\n", "for i in range(N):\n", " current_state=trans(current_state, Q)\n", " Path.append(current_state)\n", "print(\"路径:\",Path)\n", "\n", "## 画图\n", "## 导入matplotlib\n", "import matplotlib.pyplot as plt \n", "## 使图形直接插入到jupyter中\n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (10.0, 6.0)\n", "fig=plt.figure()\n", "plt.scatter(np.linspace(0,N,N+1),np.array(Path)+1) ##画出路径点,\n", "plt.plot(np.linspace(0,N,N+1),np.array(Path)+1) ##画出路径线\n", "plt.xlabel('n')\n", "plt.ylabel(\"State\")\n", "plt.title('A simple Markov chain')\n", "plt.show() ## 画图\n", "fig.savefig(\"simple_markov.pdf\") ## 保存文件" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 随机游走的模拟\n", "\n", "接下来我们模拟随机游走,即转移概率为:$$P\\left(X_{n}=i+1|X_{n-1}=i\\right)=0.5$$ $$P\\left(X_{n}=i-1|X_{n-1}=i\\right)=0.5$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numpy.random as nprd\n", "\n", "def random_walk(N):\n", " current_state=0 # 从0出发\n", " Path=[0] # 初始化路径\n", " ## 定义转移函数\n", " def trans(x):\n", " u=nprd.random() #产生一个(0,1)上的均匀分布随机数\n", " if u<0.5:\n", " return x+1\n", " else:\n", " return x-1\n", "\n", " for i in range(N):\n", " current_state=trans(current_state)\n", " Path.append(current_state)\n", " return Path\n", "\n", "N=299\n", "Path1=random_walk(N)\n", "Path2=random_walk(N)\n", "Path3=random_walk(N)\n", "Path4=random_walk(N)\n", "Path5=random_walk(N)\n", "## 画图\n", "## 导入matplotlib\n", "import matplotlib.pyplot as plt \n", "## 使图形直接插入到jupyter中\n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (10.0, 6.0)\n", "fig=plt.figure()\n", "plt.scatter(np.linspace(0,N,N+1),np.array(Path1)) ##画出路径点\n", "plt.plot(np.linspace(0,N,N+1),np.array(Path1)) ##画出路径线\n", "plt.scatter(np.linspace(0,N,N+1),np.array(Path2)) ##画出路径点\n", "plt.plot(np.linspace(0,N,N+1),np.array(Path2)) ##画出路径线\n", "plt.scatter(np.linspace(0,N,N+1),np.array(Path3)) ##画出路径点\n", "plt.plot(np.linspace(0,N,N+1),np.array(Path3)) ##画出路径线\n", "plt.scatter(np.linspace(0,N,N+1),np.array(Path4)) ##画出路径点\n", "plt.plot(np.linspace(0,N,N+1),np.array(Path4)) ##画出路径线\n", "plt.scatter(np.linspace(0,N,N+1),np.array(Path5)) ##画出路径点\n", "plt.plot(np.linspace(0,N,N+1),np.array(Path5)) ##画出路径线\n", "plt.xlabel('n')\n", "plt.ylabel(\"State\")\n", "plt.title('Random Walks')\n", "plt.show() ## 画图\n", "fig.savefig(\"markov_random_walk.pdf\") ## 保存文件" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "而对于一个二维的随机游走:$$q_{\\left(i,j\\right),\\left(i,j+1\\right)}=q_{\\left(i,j\\right),\\left(i,j-1\\right)}=q_{\\left(i,j\\right),\\left(i+1,j\\right)}=q_{\\left(i,j\\right),\\left(i-1,j\\right)}=\\frac{1}{4}$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numpy.random as nprd\n", "\n", "def random_walk(N):\n", " current_state_x,current_state_y=0,0 # 从(0,0)出发\n", " Path_x=[0] # 初始化路径\n", " Path_y=[0] # 初始化路径\n", " ## 定义转移函数\n", " def trans(x,y):\n", " u=nprd.random() #产生一个(0,1)上的均匀分布随机数\n", " if u<0.25:\n", " return x+1,y\n", " elif u<0.5:\n", " return x-1,y\n", " elif u<0.75:\n", " return x,y+1\n", " else:\n", " return x,y-1\n", "\n", " for i in range(N):\n", " current_state_x,current_state_y=trans(current_state_x,current_state_y)\n", " Path_x.append(current_state_x)\n", " Path_y.append(current_state_y)\n", " return Path_x,Path_y\n", "\n", "N=299\n", "Path_x1,Path_y1=random_walk(N)\n", "Path_x2,Path_y2=random_walk(N)\n", "Path_x3,Path_y3=random_walk(N)\n", "## 画图\n", "## 导入matplotlib\n", "import matplotlib.pyplot as plt \n", "## 使图形直接插入到jupyter中\n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (10.0, 10.0)\n", "fig=plt.figure()\n", "plt.scatter(np.array(Path_x1),np.array(Path_y1)) ##画出路径点\n", "plt.plot(np.array(Path_x1),np.array(Path_y1)) ##画出路径线\n", "plt.scatter(np.array(Path_x2),np.array(Path_y2)) ##画出路径点\n", "plt.plot(np.array(Path_x2),np.array(Path_y2)) ##画出路径线\n", "plt.scatter(np.array(Path_x3),np.array(Path_y3)) ##画出路径点\n", "plt.plot(np.array(Path_x3),np.array(Path_y3)) ##画出路径线\n", "plt.xlabel('x')\n", "plt.ylabel(\"y\")\n", "plt.title('2D Random Walks')\n", "plt.show() ## 画图\n", "fig.savefig(\"markov_random_walk2d.pdf\") ## 保存文件" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 马尔可夫链的大数定律\n", "\n", "在马尔可夫链的大数定律中,有两个重要结论,其中第一个结论是:$$L_{n}\\left(j\\right)\\overset{\\textrm{a.s.}}{\\rightarrow}\\frac{V_{ij}}{\\mathbb{E}\\left(T_{i}|X_{0}=i\\right)}$$ 其中$L_{n}\\left(j\\right)$即马尔可夫链经过$n$步之后经过状态$j$的比例;$\\mathbb{E}\\left(T_{i}|X_{0}=i\\right)$为从状态$i$出发第一次回到状态$i$的平均时间长度;$V_{ij}$为从状态$i$出发第一次回到状态$i$这段时间经过状态$i$的平均次数。\n", "\n", "而第二个结论是,对于常返的状态$i$,有:$$L_{n}\\left(i\\right)\\overset{\\textrm{a.s.}}{\\rightarrow}\\frac{1}{\\mathbb{E}\\left(T_{i}|X_{0}=i\\right)}$$\n", "\n", "我们使用3个食堂的例子,验证以上结论。实际上,我们在讲义中已经计算出,$\\mathbb{E}\\left(T_{1}|X_{0}=1\\right)=\\frac{10}{3}$,我们下面将使用以下结论。" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5000步以内共有1438个状态1,占比0.2876\n", "---------切割的eta-------------\n", "[1, 2]\n", "[1, 2]\n", "[1, 2, 3, 3, 3, 2, 3]\n", "[1, 2, 3, 3, 3, 2]\n", "[1, 2, 3, 2, 3, 3]\n", "[1, 2]\n", "[1, 3, 3, 2, 3, 3, 3, 2]\n", "[1, 2, 3, 3, 3, 3, 3]\n", "[1, 2]\n", "[1, 3]\n", "[1]\n", "[1, 3]\n", "[1, 3, 2, 3, 3, 3, 2, 3, 2, 3, 2, 3, 3]\n", "[1]\n", "[1, 2, 3]\n", "[1, 3]\n", "[1, 2, 3]\n", "[1, 3, 2]\n", "[1, 3, 2]\n", "......\n", "从状态1返回状态1的平均时间长度为3.477383437717467,倒数为0.28757254352611566\n" ] } ], "source": [ "import numpy as np\n", "import numpy.random as nprd\n", "\n", "Q=np.array([[0.3,0.4,0.3],[0.3,0.1,0.6],[0.3,0.2,0.5]])\n", "\n", "def get_path(N):\n", " states=[0,1,2] # 状态空间,讲义中为1、2、3,这里方便起见记为0、1、2,最后画图的时候+1即可。\n", " current_state=0 # 从0出发\n", " Path=[0] # 初始化路径\n", " ## 定义转移函数\n", " def trans(x,Q):\n", " prob=Q[x] #提取出Q矩阵的第x行,比如第0行为[0.3,0.4,0.3]\n", " cum_prob=np.add.accumulate(prob) #将prob累加,比如第0行累加后得到[0.3,0.7,1.0]\n", " u=nprd.random() #产生一个(0,1)上的均匀分布随机数\n", " s=0\n", " while u>=cum_prob[s]:\n", " s+=1\n", " return s\n", "\n", " for i in range(N-1):\n", " current_state=trans(current_state, Q)\n", " Path.append(current_state)\n", " return [i+1 for i in Path]\n", "\n", "N=5000\n", "Path=get_path(N) ## 产生路径\n", "## 计算L_n(1),即5000步以内在状态1的比率\n", "Nn1=sum([i==1 for i in Path])\n", "Ln1=Nn1/len(Path)\n", "print(\"%s步以内共有%s个状态1,占比%s\" % (N,Nn1,Ln1))\n", "## 将马尔可夫链按照状态1进行分割\n", "Eta=[]\n", "eta=None #初始化\n", "# 切割:\n", "for s in Path:\n", " if s==1:\n", " Eta.append(eta)\n", " eta=[1]\n", " else:\n", " eta.append(s)\n", "del Eta[0]\n", "lines=1 #仅仅是计数\n", "print(\"---------切割的eta-------------\")\n", "for eta in Eta:\n", " lines+=1\n", " if lines<=20: ## 只打印前20个。\n", " print(eta)\n", " else:\n", " print(\"......\")\n", " break\n", " \n", "## 计算每个eta的长度\n", "ET1=sum([len(eta) for eta in Eta])/len(Eta)\n", "print(\"从状态1返回状态1的平均时间长度为%s,倒数为%s\"%(ET1,1/ET1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 马尔可夫链的平稳分布\n", "\n", "### 平稳分布的含义\n", "\n", "平稳分布即当马尔可夫链运行了足够长的时间后,$X_n$的分布是否会达到一个不变的分布。在此我们用以下模拟来说明这个定义:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1000条马尔可夫链路径的第300个状态:\n", "[2, 1, 3, 3, 1, 2, 3, 2, 3, 3, 3, 3, 1, 2, 3, 2, 3, 1, 3, 3, 3, 3, 1, 2, 3, 1, 3, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 2, 3, 3, 1, 2, 1, 3, 2, 3, 1, 1, 1, 1, 3, 3, 1, 3, 1, 3, 1, 1, 3, 1, 2, 1, 2, 3, 2, 1, 1, 1, 2, 1, 3, 3, 1, 3, 2, 3, 1, 2, 3, 1, 1, 3, 3, 3, 3, 1, 3, 1, 3, 1, 2, 3, 2, 1, 1, 3, 3, 1, 3, 1, 1, 3, 2, 1, 1, 2, 3, 1, 3, 2, 1, 3, 3, 1, 3, 1, 2, 3, 3, 2, 1, 2, 3, 3, 3, 1, 3, 3, 3, 3, 2, 1, 3, 3, 3, 1, 3, 1, 2, 3, 3, 3, 3, 1, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 1, 2, 3, 2, 2, 3, 3, 2, 1, 3, 3, 2, 1, 2, 3, 2, 3, 3, 2, 3, 1, 1, 3, 2, 3, 2, 3, 3, 2, 3, 1, 1, 3, 1, 3, 1, 1, 3, 1, 3, 2, 1, 3, 1, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 3, 3, 1, 3, 1, 2, 2, 3, 3, 2, 3, 3, 1, 3, 3, 1, 1, 2, 1, 3, 3, 3, 3, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 1, 2, 3, 3, 3, 3, 3, 2, 3, 1, 1, 1, 3, 1, 2, 3, 1, 1, 3, 3, 1, 3, 3, 1, 1, 3, 3, 3, 2, 2, 3, 3, 1, 1, 3, 2, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 1, 2, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 1, 3, 2, 2, 2, 2, 2, 1, 1, 1, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 1, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 1, 3, 3, 3, 3, 2, 3, 1, 1, 3, 3, 1, 3, 2, 2, 1, 3, 1, 3, 2, 2, 1, 2, 2, 3, 3, 3, 3, 1, 3, 1, 1, 2, 1, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 1, 3, 3, 3, 1, 3, 1, 3, 1, 3, 1, 2, 1, 3, 2, 1, 1, 3, 1, 1, 3, 3, 3, 3, 3, 2, 3, 1, 1, 1, 3, 1, 1, 1, 2, 3, 2, 3, 1, 1, 1, 1, 3, 3, 3, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 3, 2, 3, 2, 1, 2, 1, 2, 3, 1, 2, 2, 3, 2, 1, 3, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 3, 3, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 2, 2, 1, 3, 2, 1, 1, 3, 2, 1, 2, 1, 1, 3, 1, 1, 2, 3, 3, 3, 1, 1, 1, 3, 2, 3, 3, 2, 2, 2, 3, 2, 2, 3, 2, 3, 3, 3, 1, 3, 2, 3, 2, 1, 1, 3, 3, 1, 3, 1, 3, 2, 1, 2, 1, 1, 2, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 1, 3, 3, 2, 1, 3, 3, 3, 3, 1, 3, 1, 3, 3, 3, 3, 3, 1, 2, 2, 3, 2, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 3, 1, 1, 3, 1, 1, 2, 3, 3, 3, 1, 3, 3, 1, 1, 3, 3, 3, 3, 3, 1, 1, 3, 1, 2, 3, 3, 1, 3, 1, 1, 3, 3, 3, 3, 3, 1, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 1, 3, 1, 3, 1, 3, 3, 3, 3, 1, 3, 1, 3, 3, 1, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 1, 1, 1, 1, 1, 1, 3, 1, 2, 2, 1, 3, 3, 1, 1, 3, 1, 3, 3, 2, 1, 3, 2, 2, 2, 3, 2, 3, 2, 1, 1, 3, 2, 3, 1, 2, 2, 3, 1, 1, 2, 2, 3, 3, 2, 1, 2, 2, 2, 2, 1, 1, 1, 3, 3, 1, 3, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 3, 2, 3, 1, 1, 3, 3, 3, 1, 3, 1, 1, 3, 3, 1, 1, 2, 2, 3, 3, 1, 1, 3, 3, 2, 2, 2, 1, 2, 1, 3, 1, 3, 3, 3, 2, 3, 3, 2, 3, 1, 3, 2, 3, 3, 3, 1, 2, 2, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 2, 3, 3, 2, 3, 2, 2, 1, 3, 1, 2, 2, 2, 3, 3, 3, 1, 3, 3, 2, 2, 3, 1, 2, 3, 3, 2, 3, 2, 3, 3, 3, 3, 1, 1, 3, 3, 1, 3, 3, 2, 3, 1, 3, 3, 3, 3, 1, 3, 3, 1, 1, 3, 3, 1, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 2, 1, 3, 3, 2, 3, 2, 2, 1, 2, 3, 1, 1, 2, 3, 2, 1, 2, 2, 1, 3, 2, 1, 3, 3, 3, 2, 2, 3, 3, 3, 1, 3, 3, 3, 3, 1, 3, 1, 1, 1, 1, 3, 2, 2, 2, 2, 1, 3, 2, 1, 3, 3, 3, 3, 1, 1, 1, 2, 3, 3, 1, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 1, 3, 3, 1, 3, 3, 2, 3, 2, 1, 3, 2, 2, 1, 2, 1, 1, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 3, 2, 3, 1, 3, 3, 2, 2, 2, 3, 3, 3, 1, 2]\n", "-------------\n", "第300个状态的分布为:[0.302,0.222,0.476]\n" ] } ], "source": [ "import numpy as np\n", "import numpy.random as nprd\n", "\n", "Q=np.array([[0.3,0.4,0.3],[0.3,0.1,0.6],[0.3,0.2,0.5]])\n", "\n", "def get_path(N):\n", " states=[0,1,2] # 状态空间,讲义中为1、2、3,这里方便起见记为0、1、2,最后画图的时候+1即可。\n", " current_state=0 # 从0出发\n", " Path=[0] # 初始化路径\n", " ## 定义转移函数\n", " def trans(x,Q):\n", " prob=Q[x] #提取出Q矩阵的第x行,比如第0行为[0.3,0.4,0.3]\n", " cum_prob=np.add.accumulate(prob) #将prob累加,比如第0行累加后得到[0.3,0.7,1.0]\n", " u=nprd.random() #产生一个(0,1)上的均匀分布随机数\n", " s=0\n", " while u>=cum_prob[s]:\n", " s+=1\n", " return s\n", "\n", " for i in range(N-1):\n", " current_state=trans(current_state, Q)\n", " Path.append(current_state)\n", " return [i+1 for i in Path]\n", "\n", "M=1000 ##产生1000条马尔可夫链\n", "N=400 ##每条马尔可夫链的长度\n", "Xfinal=[]\n", "for i in range(M):\n", " path=get_path(N) ##获取路径\n", " x=path[300] ##每条马尔可夫链第300个状态\n", " Xfinal.append(x)\n", "print(\"%s条马尔可夫链路径的第300个状态:\" % M)\n", "print(Xfinal)\n", "## 计算每个状态的分布\n", "print(\"-------------\")\n", "p1=sum([i==1 for i in Xfinal])/len(Xfinal)\n", "p2=sum([i==2 for i in Xfinal])/len(Xfinal)\n", "p3=sum([i==3 for i in Xfinal])/len(Xfinal)\n", "print(\"第300个状态的分布为:[%s,%s,%s]\" % (p1,p2,p3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 平稳分布的计算\n", "\n", "根据理论,马尔可夫链的平稳分布应该满足:$$\\pi Q=\\pi$$对于遍历的马尔可夫链,为了计算平稳分布,可以通过:$$Q'\\pi'=\\pi'$$即计算$Q'$的特征向量实现:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Q的转置:\n", " [[0.3 0.3 0.3]\n", " [0.4 0.1 0.2]\n", " [0.3 0.6 0.5]]\n", "特征值: [ 1.00000000e+00 -2.10335221e-17 -1.00000000e-01]\n", "特征向量:\n", " [[ 0.49942707 0.26726124 0. ]\n", " [ 0.39348799 0.53452248 -0.70710678]\n", " [ 0.77184183 -0.80178373 0.70710678]]\n", "平稳分布: [0.3 0.23636364 0.46363636]\n", "-------------\n", "Q的2次方:\n", " [[0.3 0.22 0.48]\n", " [0.3 0.25 0.45]\n", " [0.3 0.24 0.46]]\n", "Q的4次方:\n", " [[0.3 0.2362 0.4638]\n", " [0.3 0.2365 0.4635]\n", " [0.3 0.2364 0.4636]]\n", "Q的8次方:\n", " [[0.3 0.23636362 0.46363638]\n", " [0.3 0.23636365 0.46363635]\n", " [0.3 0.23636364 0.46363636]]\n", "Q的16次方:\n", " [[0.3 0.23636364 0.46363636]\n", " [0.3 0.23636364 0.46363636]\n", " [0.3 0.23636364 0.46363636]]\n" ] } ], "source": [ "import numpy as np\n", "\n", "Q=np.array([[0.3,0.4,0.3],[0.3,0.1,0.6],[0.3,0.2,0.5]])\n", "Qt=np.transpose(Q)\n", "print(\"Q的转置:\\n\",Qt)\n", "eig_value,eig_vector=np.linalg.eig(Qt)\n", "print(\"特征值:\",eig_value)\n", "print(\"特征向量:\\n\",eig_vector)\n", "pi=eig_vector[:,0] ##取出第一列\n", "pi=pi/sum(pi) ##标准化为概率分布\n", "print(\"平稳分布:\",pi)\n", "print(\"-------------\")\n", "Q2=np.dot(Q,Q)\n", "print(\"Q的2次方:\\n\",Q2)\n", "Q4=np.dot(Q2,Q2)\n", "print(\"Q的4次方:\\n\",Q4)\n", "Q8=np.dot(Q4,Q4)\n", "print(\"Q的8次方:\\n\",Q8)\n", "Q16=np.dot(Q8,Q8)\n", "print(\"Q的16次方:\\n\",Q16)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }