conatus.contour.beyn

conatus.contour.beyn(T, region, *, poles=None, derivative=None, counted=None, control=None, residual_tol=1e-13, quadrature=32, seed=0, max_rounds=3, polish_max_iterations=20)[source]

Every eigenvalue of T(z) v = 0 in region, certified (module docstring).

T: a pair (L, M) (the pencil L + z M), a conatus.floquet.HillBlocks, or a callable z -> matrix (or scalar) with, optionally, its derivative z -> T'(z). poles: the poles of det T inside the region; required for a callable (0 when T is holomorphic there), since the count of eigenvalues is Z = N_Gamma + P. counted: a CountResult of the same T and region already computed (else count() runs, with control=). residual_tol: certification threshold of every root (declared default RESIDUAL_TOL). quadrature: Gauss-Legendre nodes per edge; seed: of the random probe block (the result is reproducible). Raises ConvergenceError when the certified roots do not account for the count after max_rounds rounds.

Parameters:

  • T (Any)

  • region (ContourBox)

  • poles (int | None)

  • derivative (Any)

  • counted (CountResult | None)

  • control (tuple[ContourBox, int] | None)

  • residual_tol (float)

  • quadrature (int)

  • seed (int)

  • max_rounds (int)

  • polish_max_iterations (int)

Return type:

BeynResult