Continuation Backends

The backends module provides the core numerical algorithms that drive the continuation process.

Base Backend

_ContinuationBackend()

Abstract base class for continuation backends.

class hiten.algorithms.continuation.backends._ContinuationBackend

Bases: _HitenBaseBackend

abstractmethod run(*, seed_repr, stepper, parameter_getter, corrector, representation_of, step, target, max_members, max_retries_per_step, shrink_policy, step_min, step_max)

Run continuation using purely numerical inputs and callables.

Parameters:

• seed_repr (np.ndarray) – Numerical representation of the seed solution.

• stepper (callable) – stepper(last_repr, step) -> (next_prediction: np.ndarray, step_hint: np.ndarray)

• parameter_getter (callable) – parameter_getter(repr) -> np.ndarray of continuation parameters.

• corrector (callable) – corrector(prediction_repr) -> (corrected_repr, residual_norm, converged).

• representation_of (callable, optional) – Maps a domain solution to its numerical representation (for secant updates).

• step (np.ndarray) – Initial step vector (m,).

• target (ndarray) – Bounds array shaped (2, m): [mins; maxs].

• max_members (int) – Maximum number of accepted members (including the seed).

• max_retries_per_step (int) – Maximum retries allowed when correction fails at a step.

• shrink_policy (callable, optional) – Function to produce a reduced step on failure.

• step_min (float) – Minimum allowed |step| magnitude.

• step_max (float) – Maximum allowed |step| magnitude.

Returns:

• family_repr (list of np.ndarray) – Accepted member representations in order (including seed as first).

• info (dict) – Backend-specific telemetry (e.g., parameter history, counts, timings).

Return type:

tuple[list[ndarray], dict]

get_tangent()

Return the current tangent vector maintained by the backend.

Stateless backends may return None.

Return type:

ndarray | None

seed_tangent(tangent)

Seed the backend with an initial tangent vector prior to run().

Engines may call this at most once. Default implementation is a no-op.

Parameters:

tangent (ndarray | None)

Return type:

None

Predict-Correct Backend

_PCContinuationBackend()

Implement a predict-correct continuation backend.

class hiten.algorithms.continuation.backends._PCContinuationBackend

Bases: _ContinuationBackend

Implement a predict-correct continuation backend.

This backend drives a simple predict-correct-accept loop using a user-provided predictor and corrector, adapting the step size based on success/failure and stopping when either the member limit is reached or parameters exit the configured bounds.

Parameters:

• tangent (np.ndarray | None) – The initial tangent vector.

• last_residual (float) – The last residual.

get_tangent()

Return the current tangent vector maintained by the backend.

Return type:

ndarray | None

seed_tangent(tangent)

Seed the backend with an initial tangent vector prior to run().

Parameters:

tangent (ndarray | None)

Return type:

None

run(*, seed_repr, stepper, parameter_getter, corrector, representation_of, step, target, max_members, max_retries_per_step, shrink_policy, step_min, step_max)

Run continuation using purely numerical inputs and callables.

This backend implements a simple predict-correct-accept loop using a user-provided predictor and corrector, adapting the step size based on success/failure and stopping when either the member limit is reached or parameters exit the configured bounds.

Parameters:

• seed_repr (np.ndarray) – Numerical representation of the seed solution.

• stepper (Callable[[np.ndarray, np.ndarray], tuple[np.ndarray, np.ndarray]]) – Stepper function that takes the last representation and step vector and returns the next prediction and step hint.

• parameter_getter (Callable[[np.ndarray], np.ndarray]) – Function that takes a representation and returns the parameter values.

• corrector (Callable[[np.ndarray], tuple[np.ndarray, float, bool]]) – Function that takes a prediction and returns the corrected representation, residual norm, and convergence flag.

• representation_of (Callable[[np.ndarray], np.ndarray] | None) – Function that takes a representation and returns the numerical representation.

• step (np.ndarray) – Initial step vector.

• target (np.ndarray, shape (2, m)) – Target parameter range.

• max_members (int) – Maximum number of accepted members.

• max_retries_per_step (int) – Maximum number of retries per step.

• shrink_policy (Callable[[np.ndarray], np.ndarray] | None) – Function that takes a step vector and returns a shrunk step vector.

• step_min (float) – Minimum step size.

• step_max (float) – Maximum step size.

Returns:

• family (list of np.ndarray) – List of accepted member representations.

• info (dict) – Dictionary containing the accepted count, rejected count, iterations, parameter values, and final step vector.

Return type:

tuple[list[ndarray], dict]