solve_continuous_lyapunov — SciPy v1.15.2 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 \(X\).

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