conatus.expert.KSDomainContinuation

class conatus.expert.KSDomainContinuation(*, N, dealias, dp_fd, marginal_tol, eig_count, cache=6)

Bases: object

Equilibria of KS continued in L within R u = u; every numerical choice is an argument.

Parameters:

• N (int)

• dealias (float)

• dp_fd (float)

• marginal_tol (float)

• eig_count (int)

• cache (int)

at(L)

Solver, vector field and Fourier operators at domain length L (small LRU cache).

Parameters:

L (float)

Return type:

_AtL

full(x, L)

Full state from the antisymmetric-subspace unknowns (other entries zero).

Parameters:

• x (ndarray)

• L (float)

Return type:

ndarray

active(X, L)

Unknowns of the antisymmetric subspace (sin components) of a full state.

Parameters:

• X (ndarray)

• L (float)

Return type:

ndarray

residual(x, L)

G(x, L): the KS vector field restricted to the subspace.

Parameters:

• x (ndarray)

• L (float)

Return type:

ndarray

jacobian(x, L)

Dense Jacobian of residual from exact JVPs (one per unknown).

Parameters:

• x (ndarray)

• L (float)

Return type:

ndarray

eigenvalues(x, L)

Leading eigenvalues of the full-space Jacobian (mean frozen); |Re| ≤ marginal_tol → 0.

Parameters:

• x (ndarray)

• L (float)

Return type:

ndarray

energy(x, L)

E = (1/L) ∫ u²/2 dx (Cvitanović et al. 2010, eq. 3.6); only sin components here.

Parameters:

• x (ndarray)

• L (float)

Return type:

float

continuation(settings, *, eigen)

The PseudoArclength driver on these callbacks (stability if eigen).

Parameters:

• settings (ContinuationSettings)

• eigen (bool)

Return type:

PseudoArclength

run(x0, L0, settings, *, direction, L_bounds, eigen=True)

Continue the equilibrium x0 (full state at L0, must satisfy R u = u) in L.

Parameters:

• x0 (ndarray)

• L0 (float)

• settings (ContinuationSettings)

• direction (float)

• L_bounds (tuple[float, float])

• eigen (bool)

Return type:

Branch

explain()

Discretization, unknowns, Jacobian, G_L and stability settings.

Return type:

str