HMM前向算法

注：该算法即根据观测序列求产生该观测序列的概率

"""HMM model forward algorithm"""
import numpy as np

def possibility(observe):
    """calculate"""
    # 假设有三种状态s1,s2,s3定义一个状态转化矩阵
    state_transform = np.array([[0.5, 0.3, 0.2],
                                [0.2, 0.5, 0.3],
                                [0.3, 0.2, 0.5]])
    # 定义一个观测概率矩阵,每个状态会产生0,1值
    state_transform_observe = np.array([[0.3, 0.7],
                                        [0.5, 0.5],
                                        [0.6, 0.4]])
    # 定义一个初始化变量矩阵
    initial_transform = np.array([0.5, 0.3, 0.2])
    # 初始化第一个观测值的可能性
    alpha_t = initial_transform * state_transform_observe[:, observe[0]]
    for i in range(1, len(observe)):
        state_t = np.dot(alpha_t, state_transform)
        observe_transform = state_transform_observe[:, observe[i]]
        alpha_t = state_t * observe_transform
    return np.sum(alpha_t)

if __name__ == '__main__':
    observe_line = [0, 0, 1, 1, 1]
    print('序列为:' + observe_line.__str__() + '的概率为', possibility(observe_line))