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.

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 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.

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.