scipy.linalg.

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