Linear Algebra Base

The base module provides the main facade for linear stability analysis.

Main Classes

class hiten.algorithms.linalg.base.StabilityPipeline[source]

Bases: _HitenBasePipeline, Generic[DomainT, InterfaceT, ConfigT, ResultT]

Facade exposing linear stability results on demand.

Parameters:
classmethod with_default_engine(*, config, interface=None, backend=None)[source]

Create a facade instance with a default engine (factory).

Parameters:

  • config (ConfigT) – Configuration object.

  • interface (InterfaceT) – Interface object.

  • backend (_LinalgBackend, optional) – Backend object. If None, uses the default _LinalgBackend.

Returns:

A stability pipeline instance with a default engine injected.

Return type:

StabilityPipeline

compute(domain_obj, options=None)[source]

Compose a problem from domain_obj and run the engine.

Parameters:

  • domain_obj (DomainT) – Domain object.

  • options (EigenDecompositionOptions, optional) – Runtime options for eigenvalue decomposition. If None, uses defaults.

Returns:

Eigen decomposition results.

Return type:

EigenDecompositionResults

property is_stable: bool

Check if the system is stable.

Returns:

True if the system is stable, False otherwise.

Return type:

bool

property eigenvalues: Tuple[ndarray, ndarray, ndarray]

Get the eigenvalues.

Returns:

Stable eigenvalues, unstable eigenvalues, and center eigenvalues.

Return type:

Tuple[np.ndarray, np.ndarray, np.ndarray]

property eigenvectors: Tuple[ndarray, ndarray, ndarray]

Get the eigenvectors.

Returns:

Stable eigenvectors, unstable eigenvectors, and center eigenvectors.

Return type:

Tuple[np.ndarray, np.ndarray, np.ndarray]

get_real_eigenvectors(vectors, values)[source]

Get the real eigenvectors.

Parameters:

  • vectors (np.ndarray) – Eigenvectors.

  • values (np.ndarray) – Eigenvalues.

Returns:

Real eigenvalues and eigenvectors.

Return type:

Tuple[np.ndarray, np.ndarray]

Raises:

ValueError – If the eigenvalues are not real.