Skip to content
Permalink
master
Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
Go to file
 
 
Cannot retrieve contributors at this time
function X = lyapunov_symmetric_eig(V, lambda, C, tol)
% Solves AX + XA = C when A = A', as a pseudo-inverse, given eig(A).
%
% function X = lyapunov_symmetric_eig(V, lambda, C)
% function X = lyapunov_symmetric_eig(V, lambda, C, tol)
%
% Same as lyapunov_symmetric(A, C, [tol]), where A is symmetric, its
% eigenvalue decomposition [V, lambda] = eig(A, 'vector') is provided as
% input directly, and C is a single matrix of the same size as A.
%
% See also: lyapunov_symmetric sylvester lyap sylvester_nocheck
% This file is part of Manopt: www.manopt.org.
% Original author: Nicolas Boumal, Aug. 31, 2018.
% Contributors:
% Change log:
% AX + XA = C is equivalent to DY + YD = M with
% Y = V'XV, M = V'CV and D = diag(lambda).
M = V'*C*V;
% W(i, j) = lambda(i) + lambda(j)
W = bsxfun(@plus, lambda, lambda');
% Normally, the solution Y is simply this:
Y = M ./ W;
% But this may involve divisions by (almost) 0 in certain places.
% Thus, we go for a pseudo-inverse.
absW = abs(W);
if ~exist('tol', 'var') || isempty(tol)
tol = numel(C)*eps(max(absW(:))); % similar to pinv tolerance
end
Y(absW <= tol) = 0;
% Undo the change of variable
X = V*Y*V';
end