qttools.lyapunov

source package qttools.lyapunov

Classes

• LyapunovSolver — Solver interface for the discrete-time Lyapunov equation.

• LyapunovMemoizer — Memoization class to reuse the result of an Lyapunov evaluation.

• Doubling — A solver for the Lyapunov equation using iterative doubling.

• Spectral — A solver for the Lyapunov equation by using the matrix spectrum.

source class LyapunovSolver()

Bases : ABC

Solver interface for the discrete-time Lyapunov equation.

The discrete-time Lyapunov equation is defined as:

\[ X - A X A^H = Q \]

source class LyapunovMemoizer(lyapunov_solver: LyapunovSolver, num_ref_iterations: int = 3, memoize_rel_tol: float = 0.2, memoize_abs_tol: float = 1e-06, warning_threshold: float = 1e-05, reduce_sparsity: bool = True, memoizing_mode: str = 'auto')

Memoization class to reuse the result of an Lyapunov evaluation.

Initializes the memoizer.

Parameters

• lyapunov_solver : LyapunovSolver — The Lyapunov solver to wrap.

• num_ref_iterations : int, optional — The number of refinement iterations to do.

• memoize_rel_tol : float, optional — The required relative accuracy to only memoize.

• memoize_abs_tol : float, optional — The required absolute accuracy to only memoize. If either of the tolerances is met, the result is memoized.

• warning_threshold : float, optional — The threshold for the relative recursion error to issue a warning.

• reduce_sparsity : bool, optional — Whether to reduce the sparsity of the system matrix. If sparsity of any obc is changed during runtime, then the cache needs to be invalidated.

• memoizing_mode : str, optional — Possible modes are:

  • 'auto': (default) automatically decide whether to memoize or recompute based on the recursion error.
  • 'force': always memoize
  • 'force-after-first': always memoize after the first call
  • 'off': never memoize

source class Doubling(max_iterations: int = 10, convergence_rel_tol: float = 1e-05, convergence_abs_tol: float = 1e-08, reduce_sparsity: bool = True)

Bases : LyapunovSolver

A solver for the Lyapunov equation using iterative doubling.

Initializes the solver.

Parameters

• max_iterations : int, optional — The maximum number of iterations to perform.

• convergence_rel_tol : float, optional — The required relative accuracy for convergence.

• convergence_abs_tol : float, optional — The required absolute accuracy for convergence. Either convergence_rel_tol or convergence_abs_tol must be satisfied.

• reduce_sparsity : bool, optional — Whether to reduce the sparsity of the system matrix

source class Spectral(num_ref_iterations: int = 3, warning_threshold: float = 0.1, eig_compute_location: str = 'numpy', reduce_sparsity: bool = True, use_pinned_memory: bool = True)

Bases : LyapunovSolver

A solver for the Lyapunov equation by using the matrix spectrum.

Initializes the spectral Lyapunov solver.

Parameters

• num_ref_iterations : int, optional — The number of refinement iterations to perform.

• warning_threshold : float, optional — The threshold for the relative recursion error to issue a warning.

• eig_compute_location : str, optional — The location where to compute the eigenvalues and eigenvectors. Can be either "numpy" or "cupy". Only relevant if cupy is used.

• reduce_sparsity : bool, optional — Whether to reduce the sparsity of the system matrix.

• use_pinned_memory : bool, optional — Whether to use pinnend memory if cupy is used. Default is True.