Скрытая марковская модель в hmmlearn не сходится ⇐ Python

[Anonymous]

Я использую библиотеку hmmlearn, чтобы подогнать скрытую марковскую модель (HMM) к созданному мной набору данных, но столкнулся с проблемой, из-за которой модель не сходится. Ниже мой код:

Код: Выделить всё

a = np.array([
[0.7, 0.2, 0.1],
[0.3, 0.5, 0.2],
[0.3, 0.3, 0.4]
])

b = np.array(
[[0.6, 0.2, 0.1, 0.1],
[0.2, 0.4, 0.2, 0.2],
[0.1, 0.1, 0.6, 0.2]]
)

pi = np.array([0.3, 0.4, 0.3])

model = MarkovModel(transition_probabilities=a, emission_probabilities=b, initial_state_distribution=pi)

observations = np.array([model.generate_observation_sequence(sequence_length=10) for _ in range(1_000)])

Код: Выделить всё

MarkovModel

- мой класс (https://github.com/SuperrMurlocc/hmm.git), но все, что он делает, это генерирует набор последовательностей наблюдений, вот пример (не совсем 1000 последовательностей из-за ограничения количества символов в stackoverflow) :

Код: Выделить всё

[[2, 0, 1, 0, 0, 3, 0, 0, 2, 0],
[0, 1, 2, 3, 3, 2, 0, 1, 1, 2],
[0, 1, 0, 0, 3, 2, 1, 0, 0, 0],
[2, 2, 3, 1, 2, 1, 1, 0, 3, 3],
[0, 1, 0, 0, 0, 2, 3, 0, 0, 1],
[3, 1, 2, 2, 1, 2, 0, 0, 3, 1],
[0, 0, 2, 1, 0, 3, 0, 2, 0, 1],
[1, 0, 0, 0, 3, 1, 1, 1, 0, 0],
[2, 0, 2, 1, 2, 1, 0, 1, 1, 1],
[0, 1, 0, 0, 3, 2, 2, 0, 3, 3],
[0, 0, 2, 2, 0, 1, 1, 0, 3, 1],
[0, 0, 3, 2, 0, 2, 0, 1, 0, 0],
[0, 0, 0, 1, 2, 1, 1, 3, 0, 0],
[3, 1, 0, 1, 2, 0, 2, 1, 2, 1],
[3, 0, 3, 0, 0, 0, 0, 1, 1, 0],
[2, 2, 3, 2, 2, 1, 2, 1, 1, 1],
[1, 3, 1, 0, 0, 1, 1, 0, 1, 2],
[1, 3, 1, 3, 0, 0, 1, 1, 2, 2],
[2, 3, 0, 3, 2, 1, 2, 2, 2, 2],
[2, 0, 1, 1, 0, 0, 0, 0, 3, 1],
[2, 0, 0, 0, 0, 0, 3, 2, 2, 3],
[2, 3, 1, 1, 2, 3, 0, 0, 0, 2],
[3, 1, 0, 2, 0, 2, 1, 1, 1, 0],
[1, 0, 1, 1, 1, 1, 0, 0, 0, 1],
[2, 2, 2, 0, 0, 0, 0, 1, 2, 0],
[2, 2, 3, 1, 0, 0, 2, 0, 1, 1],
[3, 0, 3, 1, 1, 3, 1, 0, 1, 0],
[2, 0, 2, 3, 0, 0, 0, 2, 0, 3],
[0, 0, 0, 1, 2, 1, 1, 0, 0, 3],
[3, 1, 2, 0, 0, 0, 0, 0, 1, 1],
[0, 1, 0, 0, 3, 0, 0, 0, 1, 1],
[2, 2, 2, 0, 0, 0, 0, 0, 1, 2],
[2, 3, 3, 0, 0, 0, 3, 0, 0, 2],
[3, 2, 2, 1, 0, 0, 1, 0, 0, 0],
[0, 0, 2, 2, 2, 1, 2, 0, 3, 1],
[2, 2, 0, 3, 1, 0, 0, 1, 0, 1],
[0, 0, 0, 1, 0, 0, 0, 1, 0, 0],
[2, 2, 2, 2, 3, 0, 1, 0, 1, 2],
[3, 0, 0, 2, 3, 3, 1, 3, 1, 2],
[0, 1, 0, 2, 0, 1, 0, 0, 1, 0],
[3, 2, 2, 1, 0, 3, 1, 2, 3, 1],
[0, 0, 2, 0, 0, 0, 1, 1, 1, 1],
[0, 2, 0, 3, 3, 1, 2, 1, 1, 0],
[0, 1, 1, 0, 0, 0, 3, 1, 1, 2],
[3, 3, 2, 3, 3, 2, 0, 3, 1, 2],
[0, 0, 2, 0, 2, 0, 3, 0, 2, 0],
[0, 0, 1, 1, 1, 3, 1, 3, 0, 3],
[1, 2, 1, 0, 0, 0, 2, 1, 0, 2],
[0, 0, 0, 0, 0, 2, 1, 1, 1, 3],
[1, 0, 2, 0, 3, 1, 0, 2, 0, 2],
[0, 2, 0, 0, 1, 1, 0, 0, 0, 1],
[1, 2, 1, 0, 1, 0, 0, 3, 2, 0],
[0, 2, 2, 1, 0, 3, 1, 0, 1, 0],
[0, 2, 1, 0, 2, 2, 1, 3, 1, 0],
[1, 3, 0, 2, 1, 2, 1, 0, 3, 3],
[2, 0, 0, 2, 0, 3, 0, 0, 3, 1],
[1, 2, 1, 2, 2, 1, 0, 0, 1, 0],
[0, 0, 0, 1, 0, 0, 0, 3, 2, 3],
[3, 1, 3, 0, 0, 0, 2, 1, 2, 1],
[1, 2, 1, 0, 3, 0, 2, 3, 2, 0],
[0, 0, 2, 2, 1, 2, 1, 1, 2, 2],
[3, 2, 1, 3, 1, 0, 0, 1, 2, 3],
[3, 0, 3, 1, 3, 0, 2, 1, 2, 1],
[0, 3, 2, 0, 0, 2, 0, 3, 0, 1],
[1, 0, 2, 3, 3, 2, 1, 1, 1, 1],
[2, 3, 1, 3, 0, 1, 0, 0, 0, 0],
[2, 0, 0, 1, 3, 0, 0, 2, 0, 2],
[3, 2, 2, 0, 2, 1, 0, 0, 2, 3],
[3, 0, 0, 1, 1, 0, 1, 3, 2, 0],
[0, 0, 0, 2, 2, 1, 0, 0, 0, 1],
[1, 2, 0, 3, 0, 0, 0, 2, 2, 2],
[1, 2, 1, 2, 2, 2, 2, 0, 3, 1],
[1, 1, 1, 1, 0, 2, 1, 2, 0, 0],
[1, 2, 1, 0, 0, 3, 1, 1, 0, 3],
[2, 0, 1, 1, 1, 1, 2, 0, 0, 0],
[1, 2, 2, 3, 1, 0, 3, 1, 0, 2],
[0, 2, 3, 1, 0, 0, 0, 1, 0, 0],
[2, 0, 1, 0, 1, 0, 2, 1, 2, 2],
[3, 2, 2, 1, 0, 2, 0, 0, 0, 3],
[1, 0, 2, 0, 2, 0, 0, 0, 0, 1],
[2, 2, 1, 2, 1, 0, 0, 1, 1, 0],
[3, 0, 2, 3, 2, 0, 0, 1, 0, 3],
[3, 1, 0, 1, 2, 1, 2, 3, 3, 0],
[3, 3, 2, 3, 1, 1, 1, 3, 1, 2],
[1, 1, 0, 1, 3, 1, 0, 1, 2, 1],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
[2, 3, 2, 0, 3, 1, 2, 2, 1, 3],
[2, 3, 2, 2, 2, 3, 0, 2, 0, 3],
[0, 1, 2, 3, 1, 0, 3, 1, 1, 1],
[1, 0, 1, 0, 0, 0, 3, 0, 1, 3],
[3, 0, 3, 1, 1, 1, 0, 0, 0, 1],
[3, 2, 1, 3, 0, 3, 3, 0, 0, 0],
[0, 1, 2, 0, 0, 1, 2, 1, 0, 0],
[0, 2, 0, 0, 3, 2, 0, 1, 1, 0],
[1, 0, 2, 0, 1, 1, 1, 1, 2, 0],
[3, 0, 0, 2, 1, 0, 2, 0, 0, 1],
[2, 1, 0, 0, 0, 1, 3, 1, 0, 1],
[1, 2, 1, 2, 0, 2, 2, 0, 0, 0],
[0, 0, 0, 2, 2, 0, 0, 0, 2, 1],
[1, 0, 3, 0, 1, 1, 2, 0, 1, 1],
[0, 0, 2, 1, 0, 1, 1, 0, 1, 3],
[0, 0, 0, 0, 0, 0, 1, 2, 2, 3],
[2, 0, 2, 0, 0, 0, 0, 1, 0, 3],
[0, 0, 0, 0, 0, 3, 2, 1, 2, 0],
[0, 2, 1, 1, 0, 2, 0, 0, 0, 0],
[2, 2, 0, 0, 2, 3, 0, 0, 2, 2],
[0, 1, 2, 0, 2, 0, 0, 1, 2, 2],
[1, 1, 0, 2, 2, 2, 0, 0, 2, 3],
[1, 1, 1, 1, 0, 2, 0, 2, 0, 1],
[3, 2, 3, 2, 2, 1, 3, 0, 0, 3],
[1, 2, 2, 0, 0, 0, 0, 0, 2, 3],
[0, 1, 1, 1, 3, 1, 2, 1, 0, 3],
[1, 1, 2, 0, 2, 0, 0, 1, 1,  0],
[0, 1, 1, 0, 1, 2, 0, 1, 3, 1],
[3, 1, 0, 1, 1, 2, 0, 2, 1, 1],
[0, 2, 1, 0, 0, 0, 0, 1, 0, 0],
[3, 3, 1, 1, 2, 2, 0, 1, 3, 0],
[0, 1, 3, 3, 2, 1, 1, 0, 2, 1],
[2, 3, 0, 2, 3, 2, 0, 1, 0, 0],
[1, 2, 0, 0, 0, 2, 0, 0, 1, 3],
[2, 2, 0, 0, 2, 3, 1, 1, 2, 0],
[0, 2, 3, 3, 1, 3, 1, 1, 0, 1],
[3, 3, 2, 0, 0, 2, 3, 2, 0, 2],
[3, 2, 3, 3, 3, 0, 0, 0, 1, 0],
[2, 2, 3, 0, 1, 3, 0, 3, 1, 1],
[3, 1, 1, 2, 1, 2, 0, 3, 3, 3],
[2, 1, 0, 1, 1, 1, 3, 1, 0, 0],
[1, 0, 3, 3, 0, 2, 0, 1, 1, 2],
[3, 3, 3, 0, 0, 2, 1, 0, 1, 2],
[0, 0, 2, 2, 3, 3, 2, 0, 2, 2],
[1, 0, 1, 0, 2, 1, 0, 0, 0, 0],
[1, 0, 1, 3, 0, 1, 2, 0, 0, 3],
[2, 0, 0, 2, 0, 2, 0, 1, 1, 0],
[2, 1, 2, 2, 3, 3, 2, 2, 2, 0],
[2, 0, 1, 0, 0, 2, 0, 1, 3, 3],
[2, 1, 2, 0, 0, 1, 3, 2, 0, 2],
[0, 1, 0, 0, 0, 0, 3, 3, 3, 1],
[2, 1, 1, 2, 1, 1, 2, 2, 1, 2],
[2, 2, 2, 2, 2, 2, 2, 1, 3, 3],
[3, 0, 0, 0, 2, 2, 0, 3, 1, 1],
[1, 0, 2, 1, 3, 1, 1, 0, 0, 3],
[1, 0, 1, 1, 1, 2, 3, 3, 0, 1],
[1, 2, 1, 0, 0, 2, 3, 0, 1, 2],
[3, 1, 2, 3, 0, 3, 1, 0, 0, 2],
[2, 2, 2, 1, 3, 3, 0, 3, 2, 3],
[0, 3, 3, 0, 0, 0, 2, 1, 2, 0],
[1, 0, 0, 2, 2, 2, 1, 2, 2, 0],
[3, 0, 3, 0, 1, 1, 0, 0, 1, 1],
[2, 1, 0, 2, 1, 2, 2, 2, 3, 0],
[2, 1, 2, 1, 2, 3, 3, 1, 2, 0],
[0, 1, 3, 0, 1, 0, 3, 0, 2, 3],
[1, 1, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 1, 0, 2, 0, 2, 1, 0, 1, 0],
[0, 1, 0, 0, 2, 3, 0, 2, 0, 2],
[3, 0, 1, 3, 2, 3, 3, 0, 0, 3],
[2, 3, 0, 1, 0, 3, 2, 2, 2, 3],
[2, 2, 1, 2, 3, 0, 0, 0, 0, 0],
[0, 3, 0, 2, 0, 0, 0, 2, 2, 2],
[1, 3, 1, 3, 2, 3, 3, 0, 2, 0],
[3, 2, 0, 0, 0, 2, 1, 1, 0, 3],
[3, 1, 0, 0, 0, 0, 0, 1, 0, 3],
[3, 0, 0, 0, 0, 1, 1, 0, 2, 3],
[2, 0, 2, 0, 3, 1, 3, 0, 3, 1],
[1, 2, 3, 0, 0, 0, 1, 2, 2, 2],
[2, 3, 2, 0, 3, 3, 2, 3, 2, 2],
[2, 3, 0, 1, 0, 1, 0, 0, 3, 0],
[1, 2, 3, 2, 1, 2, 0, 1, 0, 1],
[2, 1, 2, 1, 2, 0, 1, 3, 3, 0],
[0, 1, 0, 0, 2, 0, 1, 2, 3, 1],
[2, 1, 2, 1, 0, 0, 2, 3, 0, 0],
[0, 2, 2, 1, 1, 1, 2, 0, 1, 0],
[2, 2, 0, 1, 0, 3, 2, 2, 1, 0],
[1, 0, 2, 2, 1, 3, 0, 1, 0, 0],
[2, 0, 2, 1, 0, 2, 0, 0, 0, 0],
[0, 1, 0, 2, 3, 2, 3, 2, 2, 0],
[1, 2, 0, 1, 3, 2, 2, 3, 3, 2],
[0, 0, 1, 0, 0, 0, 0, 0, 2, 3],
[0, 2, 2, 2, 2, 0, 0, 2, 1, 1],
[0, 1, 3, 1, 1, 3, 0, 1, 0, 3],
[0, 0, 0, 2, 2, 2, 1, 0, 0, 0],
[1, 0, 2, 3, 1, 3, 1, 1, 0, 1],
[0, 0, 1, 0, 0, 0, 1, 1, 1, 0],
[3, 2, 1, 3, 0, 3, 1, 0, 0, 3],
[2, 1, 2, 0, 0, 0, 0, 0, 0, 1],
[1, 1, 1, 3, 3, 2, 0, 1, 0, 3],
[1, 1, 1, 3, 0, 2, 1, 0, 0, 3],
[2, 0, 0, 3, 1, 0, 0, 0, 1, 0],
[3, 2, 1, 1, 1, 0, 3, 0, 0, 0],
[2, 2, 3, 0, 0, 2, 1, 0, 1, 0],
[2, 0, 0, 2, 3, 3, 2, 1, 2, 1],
[0, 1, 0, 0, 1, 3, 0, 0, 1, 3],
[2, 3, 1, 2, 0, 3, 3, 3, 2, 1],
[1, 2, 2, 0, 0, 0, 2, 1, 0, 3],
[1, 2, 0, 0, 0, 3, 0, 0, 2, 1],
[0, 1, 0, 3, 3, 0, 3, 0, 2, 3],
[2, 3, 1, 2, 1, 1, 1, 3, 1, 1],
[3, 3, 1, 1, 0, 1, 2, 1, 1, 1],
[1, 0, 1, 0, 1, 2, 0, 0, 0, 3],
[1, 1, 1, 1, 1, 1, 0, 0, 1, 0],
[1, 3, 0, 0, 1, 2, 1, 3, 0, 3],
[1, 2, 3, 2, 1, 0, 2, 0, 1, 3],
[0, 1, 1, 0, 0, 0, 0, 1, 3, 1],
[0, 0, 2, 1, 3, 2, 2, 1, 2, 1],
[0, 1, 0, 2, 1, 0, 0, 3, 0, 0],
[0, 2, 0, 1, 0, 0, 1, 2, 1, 1],
[3, 3, 2, 1, 1, 2, 1, 0, 2, 0],
[0, 0, 1, 0, 2, 0, 0, 2, 0, 1],
[1, 0, 2, 3, 0, 1, 3, 1, 1, 1],
[1, 1, 1, 0, 1, 0, 3, 1, 1, 1],
[3, 1, 2, 2, 0, 0, 1, 0, 0, 2],
[1, 0, 1, 0, 0, 3, 0, 0, 1, 3],
[2, 2, 2, 0, 1, 2, 2, 3, 0, 0],
[0, 2, 0, 1, 0, 1, 2, 0, 0, 2],
[3, 0, 2, 1, 2, 2, 2, 0, 3, 1],
[0, 3, 0, 3, 2, 3, 3, 0, 3, 3],
[1, 0, 0, 2, 0, 3, 1, 2, 3, 0],
[3, 2, 2, 1, 2, 1, 0, 0, 2, 2],
[1, 0, 2, 2, 2, 1, 2, 3, 1, 1],
[0, 1, 1, 2, 0, 1, 1, 0, 2, 3],
[0, 0, 0, 0, 1, 0, 0, 1, 2, 0],
[0, 2, 0, 0, 0, 0, 1, 2, 0, 3],
[0, 2, 3, 0, 1, 0, 3, 2, 0, 2],
[0, 1, 0, 2, 0, 0, 2, 0, 1, 3],
[0, 1, 1, 0, 2, 3, 0, 3, 1, 1],
[2, 2, 3, 0, 2, 3, 1, 0, 3, 2],
[0, 0, 0, 0, 2, 1, 3, 0, 0, 1],
[2, 0, 1, 2, 0, 3, 3, 1, 0, 2],
[1, 0, 3, 2, 1, 1, 2, 0, 3, 0],
[0, 0, 2, 3, 1, 0, 2, 1, 1, 2],
[1, 2, 0, 0, 3, 0, 3, 0, 3, 3],
[2, 3, 2, 3, 1, 2, 3, 0, 1, 2],
[3, 1, 0, 0, 0, 0, 1, 1, 2, 1],
[2, 3, 2, 1, 1, 3, 1, 1, 0, 1],
[3, 2, 2, 0, 1, 1, 0, 0, 0, 0],
[0, 3, 0, 3, 0, 1, 2, 2, 0, 0],
[0, 2, 3, 0, 3, 1, 3, 0, 1, 1],
[3, 2, 1, 1, 1, 0, 1, 1, 1, 3],
[2, 1, 1, 0, 1, 0, 0, 0, 2, 1],
[2, 2, 1, 1, 1, 2, 0, 0, 2, 0],
[1, 1, 0, 0, 2, 0, 0, 0, 0, 2],
[3, 0, 1, 0, 0, 2, 0, 0, 0, 0],
[1, 3, 2, 0, 2, 3, 1, 1, 0, 1],
[3, 0, 0, 0, 0, 2, 1, 1, 1, 3],
[1, 0, 2, 0, 2, 3, 2, 0, 3, 2],
[2, 2, 2, 1, 2, 3, 0, 2, 0, 1],
[3, 1, 3, 2, 2, 2, 3, 3, 1, 1],
[2, 1, 3, 2, 3, 2, 0, 1, 3, 2],
[2, 2, 1, 1, 1, 0, 1, 2, 1,  1],
[1, 2, 0, 0, 0, 2, 1, 2, 0, 0],
[0, 0, 3, 2, 2, 2, 2, 1, 1, 0],
[3, 2, 3, 0, 3, 0, 2, 0, 0, 1],
[3, 1, 2, 1, 0, 1, 1, 3, 2, 3],
[2, 0, 2, 0, 1, 3, 0, 1, 3, 0],
[2, 3, 2, 0, 0, 2, 2, 2, 3, 1],
[3, 3, 1, 0, 1, 3, 3, 0, 2, 2],
[1, 3, 0, 2, 2, 2, 2, 3, 0, 2],
[0, 0, 1, 1, 0, 1, 2, 0, 1, 1],
[3, 0, 2, 2, 3, 1, 1, 2, 0, 0],
[2, 1, 0, 2, 3, 0, 0, 3, 2, 0],
[0, 3, 3, 1, 0, 2, 3, 1, 1, 2],
[1, 2, 3, 2, 3, 3, 0, 0, 3, 1],
[0, 0, 0, 1, 0, 0, 3, 1, 0, 1],
[1, 1, 3, 2, 3, 0, 1, 0, 0, 2],
[3, 3, 2, 0, 1, 1, 2, 1, 0, 2],
[1, 1, 1, 2, 3, 1, 2, 0, 1, 2],
[2, 2, 0, 2, 0, 1, 1, 0, 0, 1],
[2, 0, 1, 1, 2, 1, 1, 0, 1, 1],
[0, 1, 3, 0, 1, 0, 0, 3, 3, 0],
[1, 0, 1, 2, 3, 2, 2, 0, 2, 0],
[2, 1, 0, 1, 1, 2, 1, 1, 0, 2],
[2, 0, 0, 0, 0, 3, 1, 2, 2, 0],
[2, 1, 0, 0, 2, 1, 2, 1, 3, 1],
[1, 3, 0, 0, 0, 1, 1, 2, 0, 2],
[1, 0, 1, 1, 3, 2, 1, 1, 3, 0],
[2, 1, 0, 2, 1, 2, 1, 2, 0, 0],
[0, 3, 2, 2, 0, 1, 1, 0, 0, 2],
[0, 1, 2, 1, 2, 2, 0, 3, 2, 1],
[0, 0, 2, 0, 2, 1, 0, 3, 0, 2],
[2, 2, 0, 3, 3, 3, 3, 2, 0, 3],
[0, 3, 2, 2, 2, 2, 3, 2, 0, 0],
[0, 0, 3, 1, 3, 0, 0, 0, 0, 0],
[0, 1, 0, 2, 3, 1, 2, 3, 0, 0],
[0, 0, 0, 1, 0, 1, 0, 0, 2, 1],
[3, 2, 2, 0, 1, 0, 1, 3, 2, 2],
[0, 0, 1, 0, 1, 0, 2, 2, 1, 0],
[3, 1, 2, 2, 0, 1, 0, 3, 2, 0],
[0, 3, 1, 3, 2, 2, 0, 1, 2, 0],
[2, 1, 3, 3, 0, 2, 3, 0, 0, 1],
[2, 2, 2, 2, 1, 0, 0, 0, 0, 2],
[1, 2, 0, 2, 3, 2, 3, 2, 2, 1],
[2, 1, 2, 0, 0, 0, 0, 1, 0, 1],
[1, 2, 0, 0, 2, 3, 0, 0, 0, 0],
[2, 0, 0, 3, 3, 0, 1, 0, 2, 2],
[3, 3, 1, 0, 0, 2, 2, 2, 2, 2],
[1, 2, 1, 1, 3, 0, 3, 0, 1, 2],
[2, 2, 2, 3, 0, 0, 0, 1, 0, 1],
[0, 1, 2, 2, 3, 0, 0, 1, 1, 2],
[0, 0, 3, 0, 2, 0, 0, 1, 0, 0],
[3, 0, 3, 0, 0, 0, 0, 1, 1, 2],
[0, 1, 0, 1, 0, 1, 0, 0, 1, 2],
[1, 3, 1, 3, 3, 1, 3, 0, 0, 2],
[3, 2, 0, 0, 0, 0, 1, 0, 0, 0],
[0, 2, 3, 2, 2, 3, 1, 1, 3, 3],
[1, 3, 0, 2, 0, 1, 1, 1, 1, 0],
[0, 2, 2, 2, 2, 1, 3, 2, 2, 2],
[2, 3, 1, 0, 1, 1, 1, 1, 1, 0],
[2, 3, 2, 0, 0, 3, 3, 1, 3, 1],
[0, 0, 2, 1, 2, 0, 1, 1, 3, 3],
[2, 2, 0, 0, 3, 0, 0, 1, 0, 3],
[2, 2, 1, 2, 0, 3, 1, 0, 3, 2],
[3, 2, 0, 0, 1, 0, 1, 2, 2, 2],
[0, 2, 0, 1, 0, 1, 3, 2, 1, 2],
[0, 0, 2, 1, 1, 0, 3, 1, 0, 0],
[2, 2, 0, 0, 0, 1, 1, 1, 0, 2],
[1, 2, 3, 3, 1, 2, 0, 0, 1, 1],
[1, 1, 3, 3, 0, 3, 1, 3, 3, 0],
[3, 2, 0, 1, 3, 2, 0, 2, 1, 2],
[2, 2, 1, 1, 0, 0, 0, 0, 0, 3],
[0, 0, 3, 2, 1, 3, 2, 3, 2, 1],
[3, 2, 0, 0, 3, 1, 0, 1, 0, 0],
[2, 0, 0, 0, 0, 0, 0, 0, 1, 3],
[3, 2, 1, 0, 1, 3, 0, 0, 1, 0],
[1, 1, 2, 0, 0, 0, 0, 1, 0, 2],
[1, 0, 1, 0, 0, 0, 3, 3, 1, 1],
[0, 2, 1, 1, 0, 0, 0, 2, 1, 3],
[2, 0, 1, 1, 0, 0, 1, 3, 2, 2],
[3, 3, 3, 2, 2, 3, 0, 3, 0, 2],
[0, 1, 0, 3, 2, 2, 1, 1, 0, 2],
[2, 0, 3, 1, 1, 3, 0, 3, 1, 1],
[3, 0, 0, 2, 3, 3, 2, 2, 2, 0],
[0, 2, 1, 3, 0, 2, 1, 3, 2, 1],
[2, 0, 1, 1, 3, 2, 3, 0, 0, 3],
[0, 1, 3, 1, 0, 0, 3, 0, 0, 1],
[2, 2, 0, 0, 1, 1, 0, 0, 3, 0],
[0, 1, 1, 2, 2, 2, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 3, 0, 0, 3, 1],
[0, 0, 0, 0, 0, 3, 1, 0, 1, 2],
[3, 1, 3, 0, 0, 2, 2, 0, 0, 2],
[0, 2, 1, 1, 0, 0, 0, 1, 0, 0],
[3, 3, 3, 3, 2, 3, 1, 1, 0, 2],
[0, 2, 2, 3, 1, 1, 1, 0, 0, 0],
[0, 0, 3, 0, 0, 1, 2, 1, 1, 0],
[3, 2, 0, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 0, 1, 3, 3, 2, 2, 0, 2],
[2, 3, 3, 1, 0, 0, 3, 0, 0, 0],
[0, 1, 0, 0, 3, 3, 1, 2, 0, 1],
[2, 1, 2, 3, 0, 3, 3, 2, 1, 1],
[0, 0, 3, 1, 1, 1, 1, 2, 1, 0],
[2, 2, 0, 0, 0, 1, 0, 1, 3, 2],
[0, 1, 3, 2, 1, 3, 3, 0, 0, 0],
[2, 0, 3, 2, 3, 0, 2, 2, 0, 2],
[3, 3, 0, 0, 2, 1, 0, 0, 2, 2],
[1, 3, 1, 2, 2, 2, 1, 2, 1, 1],
[1, 0, 3, 0, 2, 1, 3, 0, 3, 3],
[2, 2, 2, 1, 2, 2, 0, 0, 0, 0],
[2, 0, 1, 3, 0, 0, 0, 3, 1, 2],
[0, 0, 1, 1, 0, 0, 0, 2, 0, 1],
[2, 0, 0, 0, 1, 0, 0, 1, 1, 1],
[3, 2, 0, 3, 3, 1, 0, 3, 1, 3],
[0, 0, 2, 2, 2, 0, 1, 0, 2, 1],
[2, 0, 2, 0, 3, 0, 0, 0, 1, 0],
[1, 0, 0, 2, 1, 2, 3, 1, 1, 1],
[3, 0, 0, 2, 3, 1, 2, 2, 3, 1],
[2, 3, 3, 3, 0, 3, 1, 2, 3, 1],
[1, 1, 3, 1, 1, 0, 0, 2, 1, 0],
[0, 1, 1, 0, 1, 0, 3, 2, 1, 0],
[3, 3, 0, 3, 0, 0, 1, 0, 0, 1],
[0, 2, 1, 2, 2, 2, 2, 0, 1, 2],
[0, 0, 3, 0, 0, 0, 0, 3, 2, 0],
[2, 0, 2, 0, 1, 2, 1, 2, 0, 0],
[2, 3, 1, 0, 3, 1, 1, 0, 0, 0],
[1, 2, 3, 1, 2, 1, 1, 2, 3, 0],
[3, 0, 2, 0, 0, 2, 0, 1, 0, 0],
[2, 0, 1, 0, 2, 1, 1, 3, 1, 0],
[3, 2, 0, 2, 3, 2, 0, 0, 0, 2],
[3, 2, 1, 2, 0, 0, 3, 0, 2, 0],
[2, 1, 2, 3, 1, 0, 1, 0, 1, 3],
[0, 2, 2, 2, 2, 1, 1, 1, 3, 2],
[2, 3, 1, 3, 0, 0, 0, 0, 2, 0],
[2, 1, 2, 2, 1, 0, 0, 0, 0, 3],
[1, 0, 1, 0, 1, 1, 2, 1, 0, 0],
[3, 1, 2, 2, 2, 0, 1, 0, 3, 0],
[0, 0, 1, 1, 0, 2, 0, 0, 2,  3],
[3, 1, 2, 1, 0, 0, 1, 1, 1, 1],
[1, 3, 0, 1, 0, 0, 2, 0, 3, 0],
[3, 0, 2, 2, 2, 3, 2, 3, 2, 0],
[1, 1, 0, 1, 2, 0, 1, 2, 1, 2],
[2, 3, 1, 0, 1, 3, 3, 1, 2, 0],
[2, 0, 1, 1, 1, 2, 3, 3, 3, 1],
[2, 1, 0, 2, 2, 1, 3, 3, 0, 0],
[3, 0, 0, 0, 0, 1, 2, 0, 0, 1],
[1, 0, 1, 2, 3, 0, 1, 3, 1, 0],
[0, 0, 1, 1, 1, 0, 0, 0, 1, 3],
[2, 3, 1, 3, 3, 1, 0, 1, 3, 3],
[0, 0, 0, 0, 2, 2, 3, 2, 2, 1],
[0, 1, 0, 1, 0, 0, 3, 0, 0, 1],
[2, 2, 1, 2, 3, 1, 3, 3, 2, 0],
[0, 3, 2, 0, 1, 0, 0, 2, 0, 1],
[1, 2, 3, 1, 0, 1, 1, 0, 2, 1],
[2, 2, 2, 0, 0, 0, 1, 0, 1, 2],
[0, 0, 0, 0, 1, 0, 0, 1, 2, 3],
[2, 0, 1, 2, 1, 3, 0, 2, 2, 2],
[2, 0, 1, 1, 2, 2, 3, 1, 1, 2],
[1, 0, 0, 2, 0, 2, 0, 3, 1, 0],
[1, 0, 0, 3, 1, 0, 2, 1, 0, 1],
[1, 0, 0, 1, 1, 0, 3, 0, 0, 1],
[3, 1, 1, 0, 2, 0, 0, 0, 1, 2],
[1, 2, 2, 3, 0, 2, 2, 2, 1, 0],
[0, 3, 0, 2, 1, 0, 3, 1, 0, 0],
[1, 3, 0, 1, 3, 1, 0, 0, 1, 0],
[1, 2, 0, 3, 2, 3, 1, 0, 0, 0],
[0, 1, 0, 0, 0, 2, 2, 0, 0, 2],
[0, 1, 3, 2, 2, 0, 1, 3, 1, 2],
[2, 2, 2, 1, 3, 1, 0, 2, 0, 0],
[0, 2, 0, 2, 0, 2, 2, 1, 0, 3],
[3, 0, 1, 1, 2, 0, 0, 3, 3, 1],
[0, 1, 1, 1, 0, 0, 0, 2, 3, 2],
[0, 2, 3, 1, 0, 2, 2, 3, 1, 0],
[2, 0, 3, 0, 1, 1, 1, 3, 0, 1],
[0, 0, 2, 0, 0, 0, 2, 2, 1, 2],
[1, 1, 3, 2, 1, 0, 3, 2, 3, 1],
[0, 2, 0, 0, 0, 0, 3, 2, 0, 3],
[2, 0, 1, 3, 0, 0, 2, 0, 0, 3],
[2, 0, 3, 2, 0, 0, 0, 0, 0, 1],
[1, 2, 1, 0, 2, 3, 2, 2, 3, 1],
[3, 0, 1, 3, 2, 0, 2, 0, 1, 1],
[2, 0, 0, 3, 1, 2, 1, 1, 3, 1],
[3, 0, 0, 0, 0, 1, 1, 3, 2, 2],
[1, 0, 1, 1, 0, 2, 0, 3, 1, 3],
[2, 1, 2, 2, 1, 1, 0, 0, 0, 0],
[2, 2, 3, 0, 3, 0, 1, 1, 1, 0],
[2, 3, 0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 3, 0, 3, 1],
[0, 3, 2, 0, 2, 3, 2, 3, 0, 0],
[2, 2, 2, 2, 2, 1, 2, 0, 0, 0],
[0, 2, 0, 2, 2, 3, 3, 2, 2, 0],
[1, 0, 1, 0, 0, 0, 3, 2, 1, 1],
[1, 0, 1, 0, 0, 0, 2, 1, 3, 3],
[2, 0, 0, 0, 0, 0, 0, 0, 3, 0],
[1, 1, 0, 1, 1, 2, 0, 0, 2, 3],
[2, 2, 2, 2, 0, 2, 3, 0, 0, 2],
[3, 0, 0, 3, 3, 3, 1, 1, 1, 2],
[3, 1, 0, 0, 2, 0, 2, 1, 2, 0],
[0, 0, 3, 0, 1, 0, 0, 1, 2, 0],
[0, 0, 1, 3, 1, 2, 1, 3, 0, 0],
[0, 0, 1, 1, 0, 1, 0, 0, 0, 0],
[3, 0, 0, 2, 0, 2, 1, 0, 2, 0],
[3, 3, 1, 0, 0, 0, 0, 0, 3, 2],
[0, 0, 2, 1, 3, 3, 3, 1, 0, 0],
[3, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[3, 1, 1, 3, 3, 2, 1, 0, 3, 2],
[0, 0, 0, 0, 3, 1, 2, 2, 3, 0],
[2, 0, 1, 3, 0, 0, 1, 0, 1, 0],
[0, 2, 0, 0, 0, 0, 0, 0, 3, 0],
[3, 3, 0, 1, 1, 3, 2, 0, 0, 1],
[1, 3, 1, 1, 3, 2, 2, 1, 2, 2],
[0, 1, 3, 2, 0, 1, 3, 1, 2, 1],
[0, 0, 2, 0, 3, 0, 2, 2, 1, 0],
[2, 3, 3, 0, 2, 1, 0, 2, 1, 0],
[0, 0, 2, 1, 1, 1, 0, 0, 1, 2],
[0, 0, 0, 2, 0, 3, 0, 0, 1, 2],
[1, 0, 3, 3, 1, 0, 1, 3, 1, 2],
[1, 0, 3, 3, 1, 3, 0, 3, 2, 2],
[3, 0, 2, 1, 0, 2, 1, 2, 2, 0],
[0, 2, 3, 0, 0, 3, 0, 3, 0, 0],
[2, 2, 2, 1, 2, 0, 0, 1, 1, 1],
[2, 2, 3, 3, 0, 1, 1, 1, 2, 2],
[2, 1, 2, 3, 1, 3, 2, 2, 0, 0],
[1, 0, 0, 2, 2, 0, 2, 1, 0, 0],
[0, 0, 3, 3, 2, 0, 1, 0, 0, 2],
[0, 0, 0, 0, 3, 1, 3, 0, 2, 0],
[0, 3, 2, 2, 0, 1, 1, 1, 3, 2],
[1, 2, 0, 3, 2, 1, 3, 2, 0, 0],
[0, 2, 2, 2, 2, 0, 0, 1, 0, 0],
[2, 2, 0, 1, 2, 0, 0, 0, 0, 1],
[2, 0, 1, 3, 2, 2, 0, 0, 0, 3],
[1, 2, 1, 2, 2, 0, 1, 1, 0, 0],
[2, 0, 2, 3, 3, 1, 3, 1, 0, 1],
[2, 2, 0, 0, 0, 3, 0, 1, 2, 3],
[1, 2, 0, 3, 0, 1, 2, 0, 2, 1],
[0, 1, 0, 2, 0, 1, 2, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 2, 1, 2, 0],
[0, 1, 2, 3, 2, 1, 1, 0, 0, 2],
[0, 1, 2, 2, 1, 2, 0, 0, 0, 0],
[1, 2, 0, 1, 0, 1, 1, 1, 0, 2],
[2, 0, 0, 1, 0, 3, 0, 0, 1, 1],
[0, 1, 2, 0, 3, 1, 2, 1, 0, 0],
[1, 3, 3, 0, 1, 2, 2, 3, 2, 0],
[2, 2, 0, 0, 2, 1, 0, 0, 0, 1],
[1, 0, 1, 2, 0, 2, 0, 2, 0, 1],
[2, 0, 0, 1, 2, 2, 1, 3, 1, 0],
[1, 1, 2, 0, 0, 0, 0, 1, 0, 2],
[3, 0, 0, 3, 0, 1, 1, 0, 1, 2],
[3, 3, 0, 1, 3, 0, 1, 1, 1, 0],
[3, 0, 0, 1, 0, 0, 2, 1, 1, 0],
[1, 3, 0, 0, 0, 0, 1, 2, 2, 3],
[1, 3, 1, 1, 3, 0, 0, 1, 0, 3],
[2, 2, 2, 0, 1, 1, 0, 3, 3, 0],
[3, 0, 2, 2, 3, 3, 2, 0, 0, 1],
[3, 1, 0, 0, 3, 0, 0, 2, 2, 2],
[1, 0, 2, 1, 1, 2, 0, 0, 2, 0],
[0, 3, 1, 0, 3, 1, 2, 3, 0, 2],
[2, 1, 0, 2, 2, 1, 0, 1, 0, 0],
[0, 2, 0, 2, 1, 0, 0, 1, 2, 0],
[1, 2, 1, 1, 2, 2, 1, 3, 1, 0],
[0, 0, 0, 1, 0, 2, 0, 2, 0, 1],
[2, 1, 2, 2, 3, 2, 1, 1, 2, 0],
[2, 1, 2, 1, 0, 0, 3, 0, 2, 1],
[0, 3, 3, 3, 2, 2, 3, 1, 1, 0],
[0, 3, 3, 0, 1, 2, 3, 1, 0, 1],
[3, 0, 1, 1, 0, 0, 0, 3, 0, 1],
[2, 1, 2, 3, 3, 1, 2, 1, 1, 0],
[0, 0, 3, 2, 1, 0, 2, 1, 2, 2],
[2, 0, 1, 1, 0, 0, 2, 0, 0, 1],
[0, 3, 2, 2, 0, 0, 1, 2, 1, 0],
[3, 3, 0, 1, 1, 2, 0, 2, 0, 3],
[0, 0, 3, 1, 1, 2, 0, 0, 1, 0],
[0, 0, 2, 2, 1, 0, 2, 1, 3,  1],
[0, 1, 1, 0, 0, 3, 1, 2, 1, 0],
[1, 0, 2, 1, 2, 0, 0, 2, 2, 2],
[2, 3, 3, 2, 3, 2, 1, 1, 2, 0],
[0, 0, 2, 1, 2, 0, 3, 2, 1, 1],
[0, 0, 3, 1, 0, 0, 0, 0, 1, 0],
[3, 0, 3, 2, 2, 1, 2, 2, 3, 3],
[2, 2, 2, 0, 1, 0, 2, 0, 3, 1],
[0, 0, 0, 3, 0, 3, 1, 0, 0, 1],
[0, 3, 2, 2, 3, 0, 0, 0, 1, 1],
[2, 1, 3, 1, 1, 0, 0, 3, 3, 0],
[2, 0, 2, 1, 2, 2, 2, 1, 3, 2],
[2, 2, 2, 1, 1, 1, 0, 3, 3, 0],
[1, 2, 1, 3, 1, 1, 3, 0, 1, 3],
[2, 0, 1, 0, 0, 0, 3, 1, 0, 0],
[2, 3, 0, 0, 0, 0, 2, 0, 1, 3],
[1, 2, 1, 1, 3, 1, 0, 2, 0, 2],
[0, 2, 2, 2, 1, 2, 0, 2, 1, 0],
[1, 1, 0, 0, 0, 0, 3, 0, 3, 2],
[0, 1, 2, 1, 0, 2, 1, 1, 0, 0],
[0, 1, 3, 0, 3, 2, 0, 0, 1, 3],
[2, 0, 1, 0, 0, 3, 2, 2, 1, 3],
[0, 0, 3, 1, 0, 0, 1, 2, 0, 1],
[0, 2, 1, 2, 3, 3, 0, 0, 0, 0],
[0, 3, 2, 0, 3, 2, 3, 1, 0, 2],
[2, 1, 0, 2, 0, 2, 2, 3, 1, 0],
[2, 3, 2, 0, 2, 2, 3, 1, 2, 2],
[1, 0, 0, 0, 0, 0, 1, 0, 2, 1],
[3, 1, 0, 0, 0, 0, 2, 0, 0, 2],
[2, 3, 0, 3, 3, 3, 0, 2, 0, 0],
[1, 2, 1, 1, 0, 1, 0, 2, 3, 1],
[3, 3, 0, 0, 3, 0, 2, 3, 0, 3],
[2, 0, 2, 2, 2, 3, 0, 2, 0, 0],
[0, 1, 2, 1, 1, 2, 1, 0, 2, 0],
[2, 0, 3, 2, 1, 1, 1, 2, 2, 2],
[0, 1, 0, 3, 0, 1, 2, 0, 2, 2],
[0, 0, 1, 2, 0, 3, 2, 0, 3, 2],
[2, 2, 0, 2, 0, 0, 0, 2, 2, 3],
[0, 0, 2, 2, 3, 2, 2, 0, 2, 0],
[2, 0, 1, 2, 1, 0, 1, 1, 2, 0],
[3, 2, 2, 1, 0, 1, 0, 2, 1, 2],
[2, 1, 1, 3, 3, 1, 1, 0, 0, 3],
[3, 1, 1, 0, 2, 0, 3, 1, 1, 2],
[0, 0, 1, 1, 0, 0, 0, 0, 2, 2],
[0, 2, 2, 3, 3, 2, 2, 2, 3, 1],
[2, 3, 1, 2, 0, 0, 2, 1, 2, 2],
[3, 2, 3, 1, 2, 1, 1, 1, 1, 0],
[2, 3, 3, 0, 1, 0, 1, 3, 1, 0],
[1, 3, 3, 1, 1, 0, 0, 1, 2, 0],
[0, 0, 2, 0, 1, 0, 3, 2, 1, 2],
[0, 1, 0, 2, 2, 0, 2, 1, 2, 2],
[2, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[2, 2, 1, 3, 2, 1, 2, 1, 3, 0],
[1, 3, 2, 1, 0, 3, 2, 2, 1, 0],
[0, 0, 2, 1, 1, 0, 2, 1, 3, 1],
[2, 2, 2, 1, 1, 2, 1, 1, 0, 1],
[0, 0, 1, 1, 2, 1, 1, 2, 3, 1],
[3, 2, 1, 2, 1, 3, 0, 3, 2, 0],
[0, 1, 0, 2, 3, 2, 1, 1, 3, 0],
[2, 1, 2, 1, 2, 2, 0, 0, 1, 0],
[2, 0, 0, 1, 2, 3, 1, 2, 2, 3],
[3, 0, 2, 1, 1, 1, 2, 0, 0, 1],
[1, 1, 1, 0, 0, 1, 0, 2, 1, 1],
[2, 1, 2, 2, 2, 1, 1, 1, 2, 0],
[0, 1, 1, 0, 3, 2, 0, 0, 0, 1],
[2, 2, 2, 3, 1, 2, 2, 2, 0, 0],
[1, 0, 3, 3, 0, 0, 0, 1, 1, 1],
[3, 0, 0, 0, 0, 0, 2, 0, 1, 2],
[0, 2, 2, 1, 2, 3, 2, 1, 1, 0],
[0, 3, 2, 1, 0, 2, 0, 2, 3, 1],
[2, 2, 2, 0, 2, 0, 0, 0, 1, 0],
[1, 1, 0, 1, 2, 0, 0, 1, 1, 3],
[1, 1, 0, 3, 1, 2, 0, 0, 0, 0],
[3, 1, 3, 1, 1, 2, 2, 0, 1, 0],
[2, 1, 0, 1, 0, 3, 1, 2, 1, 0],
[1, 0, 2, 0, 3, 3, 2, 2, 1, 0],
[2, 3, 3, 0, 2, 2, 1, 2, 1, 0],
[1, 1, 1, 0, 0, 2, 0, 0, 2, 0],
[2, 1, 2, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 1, 0, 3, 2, 2, 2, 3, 0],
[0, 1, 0, 0, 2, 1, 3, 0, 2, 2],
[1, 0, 1, 0, 3, 2, 3, 3, 0, 0],
[2, 0, 2, 0, 0, 0, 1, 2, 1, 0],
[0, 3, 0, 3, 1, 0, 0, 1, 0, 0],
[0, 0, 3, 0, 1, 2, 2, 1, 0, 0],
[2, 0, 0, 0, 1, 0, 2, 1, 1, 0],
[2, 1, 0, 1, 0, 1, 2, 1, 0, 2],
[3, 2, 2, 0, 0, 0, 1, 2, 2, 2],
[1, 0, 1, 0, 0, 0, 1, 2, 1, 0],
[2, 1, 1, 3, 2, 1, 1, 0, 2, 1],
[2, 1, 0, 0, 0, 0, 0, 0, 0, 2],
[0, 3, 0, 1, 1, 3, 2, 0, 1, 0],
[0, 2, 3, 0, 0, 0, 2, 2, 0, 1],
[0, 1, 3, 0, 1, 2, 0, 0, 0, 1],
[3, 3, 1, 1, 2, 2, 2, 0, 0, 1],
[1, 1, 0, 2, 1, 1, 0, 2, 1, 0],
[3, 0, 1, 1, 2, 0, 0, 0, 0, 0],
[0, 0, 1, 3, 0, 3, 3, 2, 0, 1],
[1, 0, 1, 0, 0, 1, 3, 2, 1, 1],
[3, 1, 0, 3, 3, 0, 0, 0, 1, 1],
[1, 2, 0, 0, 3, 2, 3, 1, 1, 3],
[2, 1, 1, 1, 1, 1, 0, 0, 0, 0],
[1, 3, 3, 0, 2, 3, 3, 0, 0, 3],
[1, 3, 2, 2, 1, 0, 1, 1, 0, 2],
[0, 3, 0, 3, 1, 3, 3, 3, 1, 2],
[0, 0, 3, 2, 3, 0, 1, 0, 0, 0],
[1, 2, 1, 0, 3, 2, 3, 3, 0, 2],
[1, 0, 2, 1, 1, 0, 1, 0, 0, 3],
[3, 3, 0, 3, 1, 1, 1, 1, 3, 1],
[0, 3, 0, 2, 0, 1, 0, 0, 2, 2],
[2, 0, 1, 0, 3, 0, 0, 0, 0, 1],
[1, 0, 2, 0, 2, 0, 0, 3, 2, 0],
[2, 2, 3, 0, 2, 0, 2, 2, 3, 2],
[0, 2, 0, 0, 3, 0, 0, 0, 0, 3],
[0, 1, 1, 0, 3, 1, 3, 0, 1, 0],
[1, 0, 0, 3, 3, 1, 0, 2, 3, 1],
[3, 1, 2, 3, 0, 2, 0, 2, 2, 0],
[1, 1, 1, 1, 3, 0, 3, 2, 0, 2],
[3, 3, 3, 0, 0, 0, 1, 0, 0, 0],
[2, 0, 0, 0, 2, 0, 2, 2, 0, 3],
[0, 3, 3, 2, 1, 0, 2, 1, 1, 2],
[2, 2, 1, 1, 1, 0, 0, 3, 1, 3],
[3, 0, 3, 3, 2, 2, 2, 2, 3, 0],
[1, 2, 2, 2, 3, 3, 2, 1, 1, 0],
[0, 3, 1, 3, 0, 0, 0, 2, 1, 0],
[3, 2, 2, 2, 1, 1, 2, 0, 2, 0],
[0, 3, 3, 1, 0, 1, 1, 0, 1, 3],
[2, 0, 3, 1, 1, 1, 1, 2, 1, 2],
[2, 2, 2, 0, 1, 0, 0, 0, 0, 1],
[0, 1, 1, 0, 2, 2, 2, 0, 2, 1],
[1, 3, 1, 0, 3, 0, 3, 1, 0, 1],
[1, 0, 1, 0, 0, 2, 1, 1, 2, 0],
[2, 3, 0, 1, 2, 2, 1, 1, 0, 3],
[2, 2, 1, 1, 1, 0, 3, 0, 2, 1],
[0, 0, 0, 2, 0, 3, 2, 1, 2, 2],
[1, 0, 2, 0, 0, 0, 2, 1, 1,  1],
[2, 2, 1, 1, 0, 0, 1, 2, 1, 0],
[3, 1, 2, 1, 2, 3, 1, 0, 0, 0],
[2, 0, 1, 2, 0, 0, 0, 1, 1, 2],
[2, 3, 1, 1, 1, 1, 1, 2, 1, 1],
[2, 2, 1, 0, 0, 0, 0, 0, 2, 0],
[0, 3, 0, 3, 0, 1, 0, 1, 3, 0],
[1, 2, 0, 2, 3, 1, 1, 0, 0, 0],
[1, 2, 2, 2, 1, 3, 0, 1, 2, 2],
[1, 2, 2, 0, 1, 1, 0, 3, 2, 1],
[1, 1, 2, 1, 0, 1, 1, 3, 1, 0],
[1, 0, 0, 3, 0, 0, 0, 3, 2, 3],
[2, 2, 0, 1, 2, 0, 0, 0, 0, 1],
[2, 2, 1, 1, 0, 0, 0, 0, 0, 1],
[2, 3, 2, 3, 0, 0, 0, 3, 0, 1],
[1, 0, 0, 3, 2, 0, 2, 0, 0, 3],
[0, 3, 0, 0, 0, 2, 0, 0, 1, 3],
[0, 3, 2, 3, 2, 0, 0, 1, 0, 1],
[1, 0, 1, 2, 1, 3, 0, 0, 0, 2],
[3, 1, 3, 2, 0, 0, 2, 1, 3, 2],
[2, 2, 0, 2, 1, 1, 2, 2, 2, 0],
[0, 3, 3, 1, 0, 0, 3, 1, 1, 2],
[0, 3, 0, 2, 1, 1, 0, 1, 2, 0],
[0, 2, 1, 3, 0, 0, 2, 0, 2, 3],
[0, 0, 0, 0, 3, 1, 2, 1, 1, 2],
[1, 2, 0, 2, 1, 0, 0, 0, 0, 2],
[1, 1, 0, 1, 0, 0, 2, 2, 0, 2],
[1, 2, 1, 3, 1, 1, 0, 3, 0, 0],
[3, 3, 3, 3, 2, 0, 3, 3, 3, 2],
[2, 1, 2, 0, 1, 2, 2, 0, 0, 2],
[0, 2, 0, 0, 2, 0, 1, 0, 0, 1],
[3, 2, 3, 1, 0, 0, 0, 0, 0, 0],
[3, 1, 1, 1, 1, 2, 1, 2, 2, 1],
[0, 1, 2, 3, 1, 1, 3, 0, 0, 3],
[1, 0, 0, 0, 1, 0, 3, 1, 0, 1],
[3, 2, 0, 3, 0, 0, 2, 0, 1, 2],
[0, 0, 0, 0, 0, 2, 0, 0, 2, 1],
[1, 0, 3, 0, 2, 1, 1, 1, 0, 1],
[2, 3, 2, 0, 2, 2, 0, 0, 3, 1],
[0, 2, 2, 3, 0, 3, 0, 0, 3, 0],
[2, 3, 2, 1, 2, 0, 1, 3, 2, 2],
[1, 1, 0, 3, 2, 0, 2, 2, 0, 1],
[0, 3, 2, 0, 0, 0, 1, 1, 0, 1],
[1, 0, 2, 2, 0, 2, 3, 1, 1, 3],
[1, 2, 2, 1, 1, 0, 2, 2, 1, 0],
[0, 0, 1, 0, 0, 0, 1, 3, 3, 2],
[3, 0, 0, 0, 3, 0, 0, 0, 0, 1],
[0, 3, 1, 0, 2, 0, 0, 2, 2, 0],
[1, 0, 3, 3, 1, 3, 0, 2, 2, 2],
[3, 1, 0, 1, 3, 3, 0, 2, 0, 1],
[1, 3, 3, 0, 2, 3, 3, 3, 0, 1],
[1, 0, 0, 0, 0, 0, 1, 0, 3, 0],
[3, 1, 1, 1, 0, 0, 0, 0, 0, 0],
[1, 3, 2, 2, 2, 2, 1, 1, 2, 2],
[2, 3, 3, 2, 2, 2, 2, 2, 2, 1],
[2, 0, 1, 0, 2, 0, 3, 2, 1, 0],
[0, 0, 2, 1, 2, 1, 0, 1, 0, 3],
[2, 0, 1, 0, 0, 0, 0, 3, 2, 0],
[1, 1, 0, 1, 2, 1, 3, 3, 0, 3],
[0, 3, 1, 3, 0, 0, 3, 3, 1, 0],
[0, 1, 0, 2, 2, 0, 3, 0, 0, 0],
[2, 1, 1, 1, 1, 0, 0, 2, 0, 3],
[2, 3, 1, 1, 2, 0, 2, 1, 1, 0],
[3, 0, 2, 3, 2, 2, 2, 2, 2, 2],
[2, 0, 0, 3, 0, 1, 0, 2, 1, 0],
[2, 3, 0, 0, 0, 2, 0, 1, 0, 2],
[3, 1, 3, 3, 3, 1, 2, 1, 0, 0],
[2, 2, 0, 1, 2, 0, 0, 3, 3, 2],
[1, 1, 2, 1, 2, 2, 1, 2, 0, 0],
[0, 3, 3, 1, 1, 2, 0, 3, 0, 2],
[3, 2, 2, 3, 3, 1, 0, 0, 3, 2],
[0, 1, 0, 0, 2, 1, 1, 0, 2, 0],
[2, 1, 0, 2, 2, 2, 2, 1, 2, 1],
[0, 0, 0, 3, 3, 3, 0, 1, 0, 2],
[2, 0, 0, 0, 1, 1, 1, 0, 0, 1],
[2, 3, 1, 1, 3, 0, 0, 2, 0, 0],
[1, 0, 0, 2, 0, 3, 0, 0, 0, 1],
[0, 2, 3, 3, 1, 0, 0, 0, 1, 0],
[0, 1, 2, 3, 2, 3, 0, 0, 3, 0],
[1, 3, 3, 3, 0, 1, 3, 0, 2, 3],
[1, 0, 0, 0, 0, 0, 0, 2, 0, 0],
[0, 3, 1, 0, 2, 3, 1, 1, 2, 2],
[2, 1, 3, 0, 1, 3, 0, 0, 1, 3],
[1, 0, 1, 2, 1, 2, 2, 1, 1, 0],
[1, 3, 3, 3, 0, 3, 1, 1, 1, 0],
[0, 0, 0, 0, 3, 1, 0, 0, 2, 0],
[3, 0, 2, 2, 0, 1, 0, 0, 0, 1],
[0, 0, 0, 2, 0, 0, 0, 0, 2, 3],
[1, 2, 1, 2, 0, 1, 3, 2, 0, 1],
[2, 1, 1, 2, 3, 2, 3, 1, 2, 3],
[2, 2, 1, 2, 0, 0, 0, 3, 2, 1],
[1, 0, 1, 1, 2, 0, 0, 1, 2, 0],
[1, 0, 0, 1, 0, 2, 2, 0, 1, 2],
[1, 0, 1, 1, 1, 0, 1, 3, 2, 0],
[2, 2, 1, 2, 2, 0, 0, 2, 1, 0],
[2, 2, 1, 0, 1, 1, 1, 0, 2, 0],
[0, 1, 2, 0, 0, 0, 0, 2, 2, 3],
[0, 2, 2, 0, 0, 0, 1, 0, 1, 2],
[1, 0, 2, 1, 0, 0, 2, 0, 0, 0],
[0, 0, 0, 3, 0, 0, 0, 3, 3, 0],
[0, 0, 1, 1, 0, 0, 2, 2, 3, 0],
[0, 3, 0, 3, 0, 0, 2, 0, 2, 2],
[0, 0, 2, 1, 0, 1, 0, 2, 2, 0],
[2, 2, 2, 0, 0, 0, 0, 0, 1, 0],
[3, 0, 0, 0, 3, 3, 0, 0, 0, 1],
[3, 0, 3, 3, 0, 0, 0, 2, 3, 1],
[0, 0, 1, 1, 2, 0, 1, 1, 1, 1],
[2, 0, 2, 3, 2, 1, 1, 2, 3, 0],
[0, 0, 1, 1, 0, 2, 2, 1, 3, 1],
[1, 2, 3, 3, 0, 1, 2, 3, 2, 2],
[1, 1, 3, 1, 0, 0, 0, 0, 0, 2],
[2, 0, 1, 2, 2, 1, 0, 0, 2, 0],
[1, 0, 0, 0, 0, 2, 2, 0, 3, 0],
[1, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[2, 2, 2, 0, 1, 2, 2, 3, 2, 2],
[1, 0, 2, 2, 3, 1, 0, 3, 2, 0],
[0, 0, 3, 1, 3, 0, 0, 0, 3, 0],
[2, 0, 0, 3, 1, 0, 3, 2, 2, 0],
[1, 2, 0, 0, 1, 0, 0, 2, 2, 3],
[1, 2, 2, 2, 0, 1, 1, 2, 3, 1],
[0, 2, 3, 0, 1, 0, 0, 0, 2, 1],
[1, 0, 1, 3, 2, 0, 0, 0, 0, 1],
[0, 0, 0, 2, 1, 0, 0, 3, 2, 1],
[0, 0, 3, 2, 1, 3, 0, 1, 0, 2],
[1, 1, 1, 0, 1, 0, 0, 1, 0, 0],
[2, 3, 0, 2, 1, 0, 1, 0, 0, 1],
[3, 3, 2, 2, 2, 0, 0, 3, 1, 2],

и остальной код, поэтому пытаемся переделать:

Код: Выделить всё

concatenated = np.concatenate(observations.reshape(10, 1_000))

remodel = hmm.CategoricalHMM(n_components=3, n_iter=100, verbose=True)

remodel.fit(concatenated.reshape(-1, 1),  lengths=[10 for _ in range(1_000)])

Что бы я ни пытался, я получаю дерьмовые remodel.emissionprob_ и remodel.transmat_, очень близкие к

Код: Выделить всё

[[.33 .33. 33],
[.33 .33. 33],
[.33 .33. 33]]

Также очень часто появляется следующее предупреждение:

Код: Выделить всё

Model is not converging.

Я уже пробовал:

[*]генерировать последовательности с помощью CategoricalHMM;
[*]инициализация transmat_,missionprob_ и start_prob вручную путем добавления параметра init_params;
[*]изменение формы набора последовательности наблюдений (1000x10, 10x1000, 1x10000 и т. д.);
[*]с использованием MultinomialHMM и remodel.fit(observations).


Подробнее здесь: https://stackoverflow.com/questions/787 ... converging