conatus.contour.count

conatus.contour.count(T, region, *, poles=None, derivative=None, control=None, phase_step=0.7853981633974483, initial_points=16, max_evaluations=20000)[source]

Number of eigenvalues of T(z) in region (a conatus.contour.box()) by the argument principle, certified as an integer (module docstring).

T: a pair (L, M) for the pencil L + z M, a conatus.floquet.HillBlocks, or a callable z -> matrix (or scalar). poles: poles of det T inside the region, for a callable (0 if T is holomorphic there; a pencil and a linear Hill operator have none by construction); without it the result gives the winding Z - P and count=None. control=(box2, n): count box2 first and refuse unless it holds n (a box whose count is known checks the operator and the walk). phase_step, initial_points, max_evaluations: the walk (declared defaults PHASE_STEP_MAX, INITIAL_POINTS, MAX_EVALUATIONS). Raises ConvergenceError when the walk cannot be completed (an eigenvalue on the boundary, a discontinuous determinant) or does not close on an integer.

Parameters:

  • T (Any)

  • region (ContourBox)

  • poles (int | None)

  • derivative (Any)

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

  • phase_step (float)

  • initial_points (int)

  • max_evaluations (int)

Return type:

CountResult