schur_ordered

Returns block ordered complex Schur form of matrix \(\mathbf{A}\)

\[\begin{split}\mathbf{TAT}^H = \mathbf{A}_s = \begin{bmatrix} A_{11} & A_{12} \\ 0 & A_{22} \end{bmatrix}\end{split}\]

where \(A_{11}\in\mathbb{C}^{s\times s}\) contains the \(s\) stable eigenvalues of \(\mathbf{A}\in\mathbb{R}^{m\times m}\).

param A:

Matrix to decompose.

type A:

np.ndarray

param ct:

Continuous time system.

type ct:

bool

returns:

Tuple containing the Schur decomposition of \(\mathbf{A}\), \(\mathbf{A}_s\); the transformation \(\mathbf{T}\in\mathbb{C}^{m\times m}\); and the number of stable eigenvalues of \(\mathbf{A}\).

rtype:

tuple

Notes

This function is a wrapper of scipy.linalg.schur imposing the settings required for this application.