class Ellipsoids¶
- class deeptime.data.Ellipsoids(laziness: float = 0.97, seed: Optional[int] = None)¶
Example data of a two-state markov chain which can be featurized into two parallel ellipsoids and optionally rotated into higher-dimensional space.
- Parameters:
laziness (float in half-open interval (0.5, 1.], default=0.97) –
The probability to stay in either state rather than transitioning. This yields a transition matrix of
\[P = \begin{pmatrix} \lambda & 1-\lambda \\ 1-\lambda & \lambda \end{pmatrix}, \]where \(\lambda\) is the selected laziness parameter.
seed (int, optional, default=None) – Optional random seed for reproducibility.
Attributes
Covariance matrix that is used to parameterize a multivariate Gaussian distribution, resulting in the ellipsoidal shape.
Yields the underlying markov state model.
The random state that is used for RNG.
Integer value of the seed or None.
state_0_mean
state_1_mean
Methods
discrete_trajectory
(n_steps)Generates a sequence of states 0 and 1 based on the internal markov state model.
map_discrete_to_observations
(dtraj[, n_dim, ...])Maps a discrete trajectory (see
discrete_trajectory()
) to an observation trajectory as described inobservations()
)observations
(n_steps[, n_dim, noise])Generates an observation sequence in n_dim-dimensional space.
- discrete_trajectory(n_steps: int)¶
Generates a sequence of states 0 and 1 based on the internal markov state model.
- Parameters:
n_steps (int) – The number of steps.
- Returns:
dtraj – Time series of states.
- Return type:
(n_steps,) ndarray
- map_discrete_to_observations(dtraj, n_dim=2, noise=False)¶
Maps a discrete trajectory (see
discrete_trajectory()
) to an observation trajectory as described inobservations()
)
- observations(n_steps, n_dim=2, noise=False)¶
Generates an observation sequence in n_dim-dimensional space.
- Parameters:
n_steps (int) – The number of observations.
n_dim (int, default=2) –
The dimension of the observation sequence. In case it is larger than 2, the 2-dimensional sequence is rotated with a random rotation matrix
\[R = \begin{pmatrix} 0 & \cos(\alpha) & -\sin(\alpha) & \cdots \\ 0 & \sin(\alpha) & \cos(\alpha) & \ldots \end{pmatrix} \in\mathbb{R}^{2\times n} \]into \(n\)-dimensional space, where \(\alpha\sim\mathcal{U}(0, 2\pi)\).
noise (bool, default=False) – Optionally equips all observations with additional Gaussian noise of variance 0.2.
- Returns:
ftraj – Observation trajectory.
- Return type:
(n_steps, n_dim) ndarray
- property covariance_matrix¶
Covariance matrix that is used to parameterize a multivariate Gaussian distribution, resulting in the ellipsoidal shape.
- property msm¶
Yields the underlying markov state model.
- property random_state¶
The random state that is used for RNG.
- property seed¶
Integer value of the seed or None.