pymor.algorithms.sylvester
¶
Module Contents¶
Functions¶
Solve Sylvester equation by Schur decomposition. |
- pymor.algorithms.sylvester.solve_sylv_schur(A, Ar, E=None, Er=None, B=None, Br=None, C=None, Cr=None)[source]¶
Solve Sylvester equation by Schur decomposition.
Solves Sylvester equation
\[A V E_r^T + E V A_r^T + B B_r^T = 0\]or
\[A^T W E_r + E^T W A_r + C^T C_r = 0\]or both using (generalized) Schur decomposition (Algorithms 3 and 4 in [BKohlerS11]), if the necessary parameters are given.
Parameters
- A
Real
Operator
.- Ar
Real
Operator
. It is converted into aNumPy array
usingto_matrix
.- E
Real
Operator
orNone
(then assumed to be the identity).- Er
Real
Operator
orNone
(then assumed to be the identity). It is converted into aNumPy array
usingto_matrix
.- B
Real
Operator
orNone
.- Br
Real
Operator
orNone
. It is assumed thatBr.range.from_numpy
is implemented.- C
Real
Operator
orNone
.- Cr
Real
Operator
orNone
. It is assumed thatCr.source.from_numpy
is implemented.
Returns
- V
Returned if
B
andBr
are given,VectorArray
fromA.source
.- W
Returned if
C
andCr
are given,VectorArray
fromA.source
.
Raises
- ValueError
If
V
andW
cannot be returned.