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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:
% 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';
[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';
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