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`	Covariance matrix that is used to parameterize a multivariate Gaussian distribution, resulting in the ellipsoidal shape.
`msm`	Yields the underlying markov state model.
`random_state`	The random state that is used for RNG.
`seed`	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 in `observations()`)
`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.

map_discrete_to_observations(dtraj, n_dim=2, noise=False)¶: Maps a discrete trajectory (see discrete_trajectory()) to an observation trajectory as described in observations())

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.