Havok¶
Derived module from hankeldmd.py for HAVOK.
Reference:  S. L. Brunton, B. W. Brunton, J. L. Proctor,Eurika Kaiser, and J. N. Kutz. Chaos as an intermittently forced linear system. Nature Communications, 8, 2017.

class
HAVOK
(svd_rank=0, tlsq_rank=0, exact=False, opt=False, rescale_mode=None, forward_backward=False, sorted_eigs=False, tikhonov_regularization=None, d=10)[source] Bases:
pydmd.hankeldmd.HankelDMD
Hankel alternative view of Koopman (HAVOK) analysis

property
A
Get the matrix A in the relationship dV/dt = AV + Bu, where V denotes the linear embeddings and u denotes the forcing input.
 Returns
linear dynamics matrix A.
 Return type

property
B
Get the vector B in the relationship dV/dt = AV + Bu, where V denotes the linear embeddings and u denotes the forcing input.
 Returns
forcing dynamics vector B.
 Return type

_dehankel
(X)[source] Given a hankel matrix X as a 2D numpy.ndarray, returns the data as a 1D timeseries.

fit
(x, dt)[source] Perform HAVOK analysis on 1D timeseries data x given the size of the time step dt separating the observations in x.

property
forcing_input
Get the timedelay embedding that forces the linear embeddings.
 Returns
array containing the chaotic forcing term.
 Return type

property
linear_embeddings
Get the timedelay embeddings of the data that are governed by linear dynamics. Emeddings are stored as columns of the returned matrix.
 Returns
matrix containing the linear timedelay embeddings.
 Return type

property
r
Number of timedelay embeddings utilized by the HAVOK model. Note: d is the same as svd_rank if svd_rank is a positive integer.

property
reconstructed_data
Get the reconstructed data.
 Returns
the matrix that contains the reconstructed snapshots.
 Return type

reconstructions_of_timeindex
(timeindex=None)[source] Build a collection of all the available versions of the given timeindex. The indexing of time instants is the same used for
reconstructed_data()
. For each time instant there are at least one and at most d versions. If timeindex is None the function returns the whole collection, for all the time instants. Parameters
timeindex (int) – The index of the time snapshot.
 Returns
a collection of all the available versions for the given time snapshot, or for all the time snapshots if timeindex is None (in the second case, time varies along the first dimension of the array returned).
 Return type
numpy.ndarray or list

property