class EDMDModel

class deeptime.decomposition.EDMDModel(operator: ndarray, basis: Callable[[ndarray], ndarray], eigenvalues, modes)

The EDMD model which can be estimated from a EDMD estimator. It possesses the estimated operator as well as capabilities to project onto modes.

Parameters:

• operator ((n, n) ndarray) – The estimated operator.

• basis (callable) – The basis transform that was used.

• eigenvalues ((n, ) ndarray) – Eigenvalues for the modes.

• modes ((k, n) ndarray) – The EDMD modes.

See also

EDMD

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, **kw)	Transforms the data by first applying the basis and then the estimated modes, i.e.,

__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, **kw)

Transforms the data by first applying the basis and then the estimated modes, i.e.,

\[X \mapsto \Psi(X)\varphi\]

where \(X\) is the input data, \(\Psi\) the basis transform, and \(\varphi\) the Koopman operator’s

Parameters:

data ((T, n) ndarray) – Input data

Returns:

transformed – The forward transform of the input data.

Return type:

(T, n) 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.