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 function X = sylvester_nochecks(A, B, C) % Solve Sylvester equation without input checks. % % function X = sylvester_nochecks(A, B, C) % % Solves the Sylvester equation A*X + X*B = C, where A is an m-by-m matrix, % B is an n-by-n matrix, and X and C are two m-by-n matrices. % % This is a stripped-down version of Matlab's own sylvester function that % bypasses any input checks. This is significantly faster for small m and % n, which is often useful in Manopt. % % See also: sylvester lyapunov_symmetric % This file is part of Manopt: www.manopt.org. % Original author: Nicolas Boumal, July 19, 2018 % Contributors: This is a modification of Matlab's built-in sylvester. % Change log: % July 30, 2020 (NB): % Changed call from builtin('_sylvester_tri', ...) to % matlab.internal.math.sylvester_tri(...), which seems necessary for % more recent versions of Matlab. % Also had to remove the second output: the 'unique' flag. flag = 'real'; if ~isreal(A) || ~isreal(B) || ~isreal(C) flag = 'complex'; end [QA, TA] = schur(A, flag); [QB, TB] = schur(B, flag); % Solve Sylvester Equation TA*Y + Y*TB = QA'*C*QB. Y = matlab.internal.math.sylvester_tri(TA, TB, QA'*C*QB, ... 'I', 'I', 'notransp'); % Use this call instead for older versions of Matlab: % [Y, info] = builtin('_sylvester_tri', TA, TB, QA'*C*QB); X = QA*Y*QB'; end