state_space = ("sunny", "cloudy", "rainy")
state_info = dict(zip(state_space, np.arange(len(state_space))))
transition_matrix = np.array(((0.6, 0.3, 0.1),
                              (0.3, 0.4, 0.3),
                              (0.2, 0.3, 0.5)))
sample_size = 10000

def generate_markov_chain(state_info, transition_matrix, sample_size=10000):
    initial_state = list(state_info.values())[random.randint(0, len(state_info))]
    states = [initial_state]

    for i in range(sample_size):
        states.append(np.random.choice(tuple(state_info.values()), p=transition_matrix[states[-1]]))
    return np.array(states)

def plot_markov_chain_convergence(state_space, states, sample_size):
    fig, ax = plt.subplots()
    width = 1000
    offsets = range(1, sample_size, 5)
    for i, label in enumerate(state_space): #offset 시점까지 각 상태에 도달했을 확률을 의미.
        ax.plot(offsets, [np.sum(states[:offset] == i) / offset for offset in offsets], label=label)
    ax.set_xlabel("number of steps")
    ax.set_ylabel("likelihood")
    ax.legend(frameon=False)
    plt.show()

states = generate_markov_chain(state_info, transition_matrix, sample_size)
plot_markov_chain_convergence(state_space, states, sample_size)