control.bdschur

control.bdschur(a, condmax=None, sort=None)[source]

Block-diagonal Schur decomposition.

Parameters

  • a ((M, M) array_like) – Real matrix to decompose

  • condmax (None or float, optional) – If None (default), use 1/sqrt(eps), which is approximately 1e8

  • sort ({None, 'continuous', 'discrete'}) – Block sorting; see below.

Returns

  • amodal ((M, M) real ndarray) – Block-diagonal Schur decomposition of a

  • tmodal ((M, M) real ndarray) – Similarity transform relating a and amodal

  • blksizes ((N,) int ndarray) – Array of Schur block sizes

Notes

If sort is None, the blocks are not sorted.

If sort is ‘continuous’, the blocks are sorted according to associated eigenvalues. The ordering is first by real part of eigenvalue, in descending order, then by absolute value of imaginary part of eigenvalue, also in decreasing order.

If sort is ‘discrete’, the blocks are sorted as for ‘continuous’, but applied to log of eigenvalues (i.e., continuous-equivalent eigenvalues).

Examples

>>> Gs = ct.tf2ss([1], [1, 3, 2])
>>> amodal, tmodal, blksizes = ct.bdschur(Gs.A)
>>> amodal                                                   
array([[-2.,  0.],
       [ 0., -1.]])