solve_continuous_lyapunov#
- scipy.linalg.solve_continuous_lyapunov(a, q)[source]#
- Solves the continuous Lyapunov equation \(AX + XA^H = Q\). - Uses the Bartels-Stewart algorithm to find \(X\). - The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details. - Parameters:
- aarray_like
- A square matrix 
- qarray_like
- Right-hand side square matrix 
 
- Returns:
- xndarray
- Solution to the continuous Lyapunov equation 
 
 - See also - solve_discrete_lyapunov
- computes the solution to the discrete-time Lyapunov equation 
- solve_sylvester
- computes the solution to the Sylvester equation 
 - Notes - The continuous Lyapunov equation is a special form of the Sylvester equation, hence this solver relies on LAPACK routine ?TRSYL. - Added in version 0.11.0. - Examples - Given a and q solve for x: - >>> import numpy as np >>> from scipy import linalg >>> a = np.array([[-3, -2, 0], [-1, -1, 0], [0, -5, -1]]) >>> b = np.array([2, 4, -1]) >>> q = np.eye(3) >>> x = linalg.solve_continuous_lyapunov(a, q) >>> x array([[ -0.75 , 0.875 , -3.75 ], [ 0.875 , -1.375 , 5.3125], [ -3.75 , 5.3125, -27.0625]]) >>> np.allclose(a.dot(x) + x.dot(a.T), q) True