class KernelEDMDModel¶

class deeptime.decomposition.KernelEDMDModel(data: ndarray, eigenvalues: ndarray, eigenvectors: ndarray, kernel: Kernel)¶

The kEDMD model containing eigenvalues and eigenfunctions evaluated in the instantaneous data.

Parameters:

eigenvalues ((d,) ndarray) – The eigenvalues.
eigenvectors ((T, d) ndarray) – The eigenfunction evaluation.
kernel (Kernel) – The kernel that was used for estimation.

See also

KernelEDMD

Attributes

`instantaneous_obs`	Transforms the current state \(x_t\) to \(f(x_t)\).
`koopman_matrix`	Same as `operator`.
`operator`	The operator \(K\) so that \(\mathbb{E}[g(x_{t+\tau})] = K^\top \mathbb{E}[f(x_t)]\) in transformed bases.
`operator_inverse`	Inverse of the operator \(K\), i.e., \(K^{-1}\).
`output_dimension`	The dimension of data after propagation by \(K\).
`timelagged_obs`	Transforms the future state \(x_{t+\tau}\) to \(g(x_{t+\tau})\).

Methods

`backward`(data[, propagate])	Maps data backward in time.
`copy`()	Makes a deep copy of this model.
`forward`(data[, propagate])	Maps data forward in time.
`get_params`([deep])	Get the parameters.
`set_params`(**params)	Set the parameters of this estimator.
`transform`(data[, propagate])	Transforms data by applying the observables to it and then mapping them onto the modes of \(K\).

__call__(*args, **kwargs)¶: Call self as a function.

backward(data: ndarray, propagate=True)¶

Maps data backward in time.

Parameters:

data ((T, n) ndarray) – Input data
propagate (bool, default=True) – Whether to apply the Koopman operator to the featurized data.

Returns:

mapped_data – Mapped data.

Return type:

(T, m) ndarray

copy() → Model¶

Makes a deep copy of this model.

Returns:: A new copy of this model.
Return type:: copy

forward(data: ndarray, propagate=True)¶

Maps data forward in time.

Parameters:

data ((T, n) ndarray) – Input data
propagate (bool, default=True) – Whether to apply the Koopman operator to the featurized data.

Returns:

mapped_data – Mapped data.

Return type:

(T, m) ndarray

get_params(deep=False)¶

Get the parameters.

Returns:: params – Parameter names mapped to their values.
Return type:: mapping of string to any

set_params(**params)¶

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:: **params (dict) – Estimator parameters.
Returns:: self – Estimator instance.
Return type:: object

transform(data: ndarray, propagate=True)¶

Transforms data by applying the observables to it and then mapping them onto the modes of \(K\).

Parameters:: data ((T,n) ndarray) – Input data.
Returns:: transformed_data – The transformed data.
Return type:: (T,m) ndarray

property instantaneous_obs: Callable[[ndarray], ndarray]¶: Transforms the current state \(x_t\) to \(f(x_t)\). Defaults to f(x) = x.

property koopman_matrix: ndarray¶: Same as operator.

property operator: ndarray¶: The operator \(K\) so that \(\mathbb{E}[g(x_{t+\tau})] = K^\top \mathbb{E}[f(x_t)]\) in transformed bases.

property operator_inverse: ndarray¶: Inverse of the operator \(K\), i.e., \(K^{-1}\). Potentially pseudo-inverse instead of true inverse.

property output_dimension¶: The dimension of data after propagation by \(K\).

property timelagged_obs: Callable[[ndarray], ndarray]¶: Transforms the future state \(x_{t+\tau}\) to \(g(x_{t+\tau})\). Defaults to f(x) = x.