solve_continuous_lyapunov — SciPy v1.16.0 Manual (original) (raw)

scipy.linalg.

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

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