solve_sylvester(a, b, q)
Computes a solution to the Sylvester matrix equation via the Bartels- Stewart algorithm. The A and B matrices first undergo Schur decompositions. The resulting matrices are used to construct an alternative Sylvester equation ( RY + YS^T = F
) where the R and S matrices are in quasi-triangular form (or, when R, S or F are complex, triangular form). The simplified equation is then solved using *TRSYL
from LAPACK directly.
Leading matrix of the Sylvester equation
Trailing matrix of the Sylvester equation
Right-hand side
If solution was not found
The solution to the Sylvester equation.
Computes a solution (X) to the Sylvester equation $AX + XB = Q$ .
Given a, b, and q solve for x:
>>> from scipy import linalg
... a = np.array([[-3, -2, 0], [-1, -1, 3], [3, -5, -1]])
... b = np.array([[1]])
... q = np.array([[1],[2],[3]])
... x = linalg.solve_sylvester(a, b, q)
... x array([[ 0.0625], [-0.5625], [ 0.6875]])
>>> np.allclose(a.dot(x) + x.dot(b), q) TrueSee :
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._solvers.solve_sylvester
scipy.linalg._solvers.solve_continuous_lyapunov
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