DMD

Derived module from dmdbase.py for classic dmd.

class DMD(svd_rank=0, tlsq_rank=0, exact=False, opt=False, rescale_mode=None, forward_backward=False, sorted_eigs=False, tikhonov_regularization=None)[source]

Bases: DMDBase

Dynamic Mode Decomposition

Parameters:

  • svd_rank (int or float) – the rank for the truncation; If 0, the method computes the optimal rank and uses it for truncation; if positive interger, the method uses the argument for the truncation; if float between 0 and 1, the rank is the number of the biggest singular values that are needed to reach the ‘energy’ specified by svd_rank; if -1, the method does not compute truncation.

  • tlsq_rank (int) – rank truncation computing Total Least Square. Default is 0, that means TLSQ is not applied.

  • exact (bool) – flag to compute either exact DMD or projected DMD. Default is False.

  • opt (bool or int) – argument to control the computation of DMD modes amplitudes. See DMDBase. Default is False.

  • rescale_mode ({'auto'} or None or numpy.ndarray) – Scale Atilde as shown in 10.1016/j.jneumeth.2015.10.010 (section 2.4) before computing its eigendecomposition. None means no rescaling, ‘auto’ means automatic rescaling using singular values, otherwise the scaling factors.

  • forward_backward (bool) – If True, the low-rank operator is computed like in fbDMD (reference: https://arxiv.org/abs/1507.02264). Default is False.

  • sorted_eigs ({'real', 'abs'} or False) – Sort eigenvalues (and modes/dynamics accordingly) by magnitude if sorted_eigs=’abs’, by real part (and then by imaginary part to break ties) if sorted_eigs=’real’. Default: False.

  • tikhonov_regularization (int or float) – Tikhonov parameter for the regularization. If None, no regularization is applied, if float, it is used as the \lambda tikhonov parameter.

fit(X, Y=None)[source]

Compute the Dynamic Modes Decomposition to the input data.

Parameters:

  • X (numpy.ndarray or iterable) – the input snapshots.

  • Y (numpy.ndarray or iterable) – additional input snapshots such that Y=AX. If not provided, snapshots from X are used.

predict(X)[source]

Predict the output Y given the input X using the fitted DMD model.

Parameters:

X (numpy.ndarray) – the input vector.

Returns:

one time-step ahead predicted output.

Return type:

numpy.ndarray