隐马尔可夫模型估值问题&解码问题计算器

模式识别课上，老师没完没了的让算马尔科夫链，为了加快写作业(摸鱼 )的效率，在python上写了两个函数来帮助计算。这里贴贴记录一下。

呆码

import numpy as np
import math

T=4  #序列长度为T
vt=[1,3,2,0]#序列状态
vn=5 #发生事件的个数
c=4  #隐状态个数

A=[[  1,  0,  0,  0],
   [0.2,0.3,0.1,0.4],
   [0.2,0.5,0.2,0.1],
   [0.8,0.1,  0,0.1]]

B=[[1,  0,  0,  0,  0],
   [0,0.3,0.4,0.1,0.2],
   [0,0.1,0.1,0.7,0.1],
   [0,0.5,0.2,0.1,0.2]]

C=[[0 for i in range(T+1)] for j in range(c)]


C[1][0]=1   #假设初始状态是w1

for j in range(1,len(C[0])):
    for i in range(len(C)):
        for k in range(len(C)):
            C[i][j]+=C[k][j-1]*A[k][i]*B[i][vt[j-1]]

print("估值问题")
for i in range(len(C)):
    print(C[i])
    
C=[[0 for i in range(T+1)] for j in range(c)]

C[1][0]=1   #假设初始状态是w1

for j in range(1,len(C[0])):
    for i in range(len(C)):
        for k in range(len(C)):
            if C[i][j]==0:
                C[i][j]=C[k][j-1]*A[k][i]*B[i][vt[j-1]]
            elif C[k][j-1]*A[k][i]*B[i][vt[j-1]]>C[i][j]:
                C[i][j]=C[k][j-1]*A[k][i]*B[i][vt[j-1]]
                
print("解码问题")
for i in range(len(C)):
    print(C[i])

运行效果：

估值Example：

解码Example：

程序计算结果：