# FbDMD¶

Derived module from dmdbase.py for forward/backward dmd.

 `FbDMD.atilde` Get the reduced Koopman operator A, called A tilde. `FbDMD.dmd_timesteps` Get the timesteps of the reconstructed states. `FbDMD.dynamics` Get the time evolution of each mode. `FbDMD.eigs` Get the eigenvalues of A tilde. `FbDMD.fit` Compute the Dynamic Modes Decomposition to the input data. `FbDMD.modes` Get the matrix containing the DMD modes, stored by column. `FbDMD.original_timesteps` Get the timesteps of the original snapshot. `FbDMD.plot_eigs` Plot the eigenvalues. `FbDMD.plot_modes_2D` Plot the DMD Modes. `FbDMD.plot_snapshots_2D` Plot the snapshots. `FbDMD.reconstructed_data` Get the reconstructed data. `FbDMD.snapshots` Get the original input data.
class `FbDMD`(svd_rank=0, tlsq_rank=0, exact=False, opt=False, rescale_mode=None, sorted_eigs=False)[source]

Bases: `pydmd.dmd.DMD`

Forward/backward DMD class.

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 no truncation.

• 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.

• 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.

Reference: Dawson et al. https://arxiv.org/abs/1507.02264