%a矩阵是状态转移矩阵
a = [0.4 0.6 0  ;
     0   0.8 0.2;
     0   0   1  ];
%o矩阵是观察矩阵,观测序列是ABAB
%该o矩阵根据观测序列做了相应的扩展。
o = [0.7 0.3 0.7 0.3;
     0.4 0.6 0.4 0.6;
     0.8 0.2 0.8 0.2];
%pi是初始状态概率矩阵
pi = [1 0 0];

[n,n] = size(a);
[n,T] = size(o);
n = length(pi);

alpha = zeros(n,T);
%初始化t=1时刻的alpha矩阵
for i = 1:n
    alpha(i,1) = pi(i)*o(i,1);
end

for t = 1:T-1
    for i = 1:n
        sum = 0;
        for j = 1:n
            sum = sum + alpha(j,t)*a(j,i);
        end
        alpha(i,t+1) = sum * o(i,t+1);
    end
end

P = 0;
for i = 1:n
    P = P + alpha(i,T);
end
P

%a矩阵是状态转移矩阵
a = [0.4 0.6 0  ;
     0   0.8 0.2;
     0   0   1  ];
%o矩阵是观察矩阵,观测序列是ABAB
%该o矩阵根据观测序列做了相应的扩展。
o = [0.7 0.3 0.7 0.3;
     0.4 0.6 0.4 0.6;
     0.8 0.2 0.8 0.2];
%pi是初始状态概率矩阵
pi = [1 0 0];

[n,n] = size(a);
[n,T] = size(o);
n = length(pi);

derta = zeros(n,T);
pha = zeros(n,T);
maxer = zeros(n,n);
%初始化t=1时刻的alpha矩阵
for i = 1:n
    derta(i,1) = pi(i)*o(i,1);
end

for t = 1:T-1
    for i = 1:n
        nu = 0;
        for j = 1:n
            maxer(j,i) = derta(j,t)*a(j,i);
        end
        if max(maxer(:,i))==0
            pha(i,t+1) = 0;
        else
            [nu,pha(i,t+1)] = max(maxer(:,i));
        end
        derta(i,t+1) = nu * o(i,t+1);
    end
end
derta
pha
P = 0;
q = zeros(1,T);
[P q(T)]= max(derta(:,T));
for i = T-1:-1:1
    q(i) = pha(q(i+1),i+1);
end
q