class DMD

class deeptime.decomposition.DMD(mode='exact', rank=None, driver='scipy')

Dynamic mode decomposition estimator. [1]

There are two supported modes:

  • standard, which produces “projected” DMD modes (following the original formulation of DMD),

  • exact, which produces DMD modes that do not required ordered data but just matched pairs of data [2].

Parameters:

  • mode (str) – The estimation mode, see available_modes for available modes.

  • rank (int or None, optional, default=None) – Truncation of the rank after performing SVD.

  • driver (str, default='numpy') – Which package to use for the SVD. Defaults to numpy, can also be ‘scipy’.

Notes

In standard DMD, one considers a temporally ordered list of data vectors \((z_0,\ldots,z_T)\in\mathbb{R}^{T\times d}\). The data is split into the pair

\[X = (z_0, \ldots, z_{T-1}),\quad Y=(z_1,\ldots, z_T).\]

If the mode is exact, the list does not need to be temporally ordered but just the pairs \((X_i, Y_i)\) have to match. The underlying assumption is that the data are generated by a linear relationship

\[z_{t+1} = A z_t\]

for some matrix \(A\).

The so-called DMD modes and eigenvalues are then the (potentially scaled) eigenvectors and eigenvalues of \(A\).

References

Attributes

available_drivers

The available drivers.

available_modes

The available estimation modes.

has_model

Property reporting whether this estimator contains an estimated model.

mode

model

Shortcut to fetch_model().

Methods

fetch_model()

Yields the estimated model if fit() was called.

fit(data, **kwargs)

Fit this estimator instance onto data.

fit_fetch(data, **kwargs)

Fits the internal model on data and subsequently fetches it in one call.

fit_transform(data[, fit_options, ...])

Fits a model which simultaneously functions as transformer and subsequently transforms the input data.

get_params([deep])

Get the parameters.

set_params(**params)

Set the parameters of this estimator.

transform(data, **kwargs)

See DMDModel.transform().
__call__(*args, **kwargs)

Call self as a function.

fetch_model() → Optional[DMDModel]

Yields the estimated model if fit() was called.

Returns:

model – The model or None.

Return type:

DMDModel or None

fit(data, **kwargs)

Fit this estimator instance onto data.

Parameters:

  • data – Input data, see to_dataset for options.

  • **kwargs – Kwargs, may contain lagtime.

Returns:

self – Reference to self.

Return type:

DMD

fit_fetch(data, **kwargs)

Fits the internal model on data and subsequently fetches it in one call.

Parameters:

  • data (array_like) – Data that is used to fit the model.

  • **kwargs – Additional arguments to fit().

Returns:

The estimated model.

Return type:

model

fit_transform(data, fit_options=None, transform_options=None)

Fits a model which simultaneously functions as transformer and subsequently transforms the input data. The estimated model can be accessed by calling fetch_model().

Parameters:

  • data (array_like) – The input data.

  • fit_options (dict, optional, default=None) – Optional keyword arguments passed on to the fit method.

  • transform_options (dict, optional, default=None) – Optional keyword arguments passed on to the transform method.

Returns:

output – Transformed data.

Return type:

array_like

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, **kwargs)

See DMDModel.transform().

Parameters:

data ((T, d) np.ndarray) – Input data

Returns:

result – Propagated input data

Return type:

(T, d) np.ndarray

available_drivers = ('numpy', 'scipy')

The available drivers.

available_modes = ('exact', 'standard')

The available estimation modes.

property has_model: bool

Property reporting whether this estimator contains an estimated model. This assumes that the model is initialized with None otherwise.

Type:

bool

property model

Shortcut to fetch_model().