bundles / scipy latest / scipy / linalg / _solvers / solve_continuous_lyapunov
function
scipy.linalg._solvers:solve_continuous_lyapunov
source: build-install/usr/lib/python3.14/site-packages/scipy/linalg/_solvers.py:116
Signature
def solve_continuous_lyapunov(a, q)Summary
Solves the continuous Lyapunov equation .
Extended Summary
Uses the Bartels-Stewart algorithm to find .
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 linalg_batch for details. The NEP 5 signature of this function is (i,i),(i,i)->(i,i).
Parameters
a: array_likeA square matrix
q: array_likeRight-hand side square matrix
Returns
x: ndarraySolution 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.
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, 5.313],
[ -3.75 , 5.313, -27.063]])
np.allclose(a.dot(x) + x.dot(a.T), q)
✓True
See also
- solve_discrete_lyapunov
computes the solution to the discrete-time Lyapunov equation
- solve_sylvester
computes the solution to the Sylvester equation
Aliases
scipy.linalg.solve_continuous_lyapunov