dymad.sako.base

Functions

encode_runtime_batch(model, batch)	Encode one trainer batch via typed-runtime payloads.
filter_spectrum(sako, eigs[, order, remove_one])	Apply SAKO to the identified eigenpairs to compute the corresponding residuals

Classes

SAInterface(model_class, checkpoint_path[, ...])	Interface for spectral analysis of KBF and DKBF models.
SpectralAnalysis(model_class, checkpoint_path)	The base class for Spectral Analysis based on Koopman operator theory.

class dymad.sako.base.SAInterface(model_class, checkpoint_path, device=None)

Bases: DataInterface

Interface for spectral analysis of KBF and DKBF models.

get_weights()

Get the linear weights of the dynamics model.

Return type:

tuple[ndarray, ...]

property snapshot: SpectralSnapshot

Typed spectral snapshot extracted from checkpoint-backed model state.

class dymad.sako.base.SpectralAnalysis(model_class, checkpoint_path, forder='full', dt=1.0, reps=1e-10, remove_one=True, etol=1e-13, exec_context=None)

Bases: object

The base class for Spectral Analysis based on Koopman operator theory.

The formulation is based on the following convention: Psi_0 A = Psi_1 where A is the finite-dimensional approximation of Koopman operator, Psi’s are data matrices with each row containing one time step.

Parameters:

dt (float) – Time step size.

estimate_measure(fobs, order, eps, thetas=101)

Estimate the measure of the observable along the unit circle.

estimate_ps(grid=None, return_vec=False, mode='cont', method='standard')

Estimate pseudospectrum over a grid.

In disc mode, the grid is assumed to be on discrete-time complex plane; the estimator should perform discrete-time resolvent analysis, using time step size of data In cont mode, the grid is assumed to be on continuous-time complex plane; the estimator should perform continuous-time resolvent analysis

Parameters:

• grid – Mode disc: points on discrete-time plane (Re, Im) Mode cont: points on continuous-time plane (zeta, omega)

• return_vec – If return I/O modes

• mode – ‘cont’ or ‘disc’

eval_eigfun(X, idx, rng=None)

Evaluate the eigenfunctions at given locations, possibly in embedded space

eval_eigfun_par(par, idx, func, rng=None)

Evaluate the eigenfunctions at given parametrization

eval_eigfunc_jac(ref=None, rng=None, **kwargs)

Return type:

ndarray

eval_eigmode_jac(ref=None, rng=None, **kwargs)

Return type:

ndarray

filter_spectrum(order='full', remove_one=True)

Apply SAKO to the identified eigenpairs to compute the corresponding residuals

plot_eigfun_2d(rngs, Ns, idx, mode='angle', space='full', ncols=2, figsize=(6, 10), fig=None)

Plot the 2D eigenfunctions as contours.

plot_eigjac_contour(ref=None, rng=None, eig='func', lam='ct', comp='ri', idx='all', shape=(), contour_args=None, **kwargs)

Plot contour maps for Jacobian eigfunction/eigmode components.

plot_eigs(fig=None, plot_full='bo', plot_filt='r^', mode='disc')

Plot the eigenvalues in the complex plane.

plot_pred(x0s, ts, ref=None, ifobs=False, idx='all', ncols=1, figsize=(6, 8), title=None, fig=None)

Plot the predicted trajectories in data space or latent space.

plot_vec_line(idx, which='func', modes=None, ncols=1, figsize=(6, 10))

Plot slices of eigenfunctions/eigenmodes as vectors.

predict(x0, tseries, return_obs=False)

Make time-domain prediction.

Parameters:

• x0 – Initial states

• tseries – Time series at which to evaluate the solutions.

• return_obs – If return observables over time as well

resolvent_analysis(z, return_vec, mode, method)

Perform resolvent analysis of the DMD operator.

Parameters:

method – ‘standard’ - The projected approach where I/O modes are all in DMD mode space, which is true for a low-rank DMD operator.

set_conj_map(J)

Compute the conjugacy map assuming an equilibrium point at x=0 with Jacobian J. Consider eigendecomposition: J = W * L * V^H locally a principal eigenfunction is approximately phi_i(x) = v_i^H x

dymad.sako.base.encode_runtime_batch(model, batch)

Encode one trainer batch via typed-runtime payloads.

Return type:

ndarray

dymad.sako.base.filter_spectrum(sako, eigs, order='full', remove_one=True)

Apply SAKO to the identified eigenpairs to compute the corresponding residuals