--- /dev/null
+## Copyright (C) 2010 Lukas F. Reichlin
+##
+## This file is part of LTI Syncope.
+##
+## LTI Syncope is free software: you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation, either version 3 of the License, or
+## (at your option) any later version.
+##
+## LTI Syncope is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn{Function File} {@var{u} =} lyapchol (@var{a}, @var{b})
+## @deftypefnx{Function File} {@var{u} =} lyapchol (@var{a}, @var{b}, @var{e})
+## Compute Cholesky factor of continuous-time Lyapunov equations.
+##
+## @strong{Equations}
+## @example
+## @group
+## A U' U + U' U A' + B B' = 0 (Lyapunov Equation)
+##
+## A U' U E' + E U' U A' + B B' = 0 (Generalized Lyapunov Equation)
+## @end group
+## @end example
+##
+## @strong{Algorithm}@*
+## Uses SLICOT SB03OD and SG03BD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+##
+## @seealso{lyap, dlyap, dlyapchol}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: January 2010
+## Version: 0.2.1
+
+function [u, scale] = lyapchol (a, b, e)
+
+ switch (nargin)
+ case 2
+
+ if (! is_real_square_matrix (a))
+ ## error ("lyapchol: a must be real and square");
+ error ("lyapchol: %s must be real and square", \
+ inputname (1));
+ endif
+
+ if (! is_real_matrix (b))
+ ## error ("lyapchol: b must be real")
+ error ("lyapchol: %s must be real", \
+ inputname (2))
+ endif
+
+ if (rows (a) != rows (b))
+ ## error ("lyapchol: a and b must have the same number of rows");
+ error ("lyapchol: %s and %s must have the same number of rows", \
+ inputname (1), inputname (2));
+ endif
+
+ [u, scale] = slsb03od (a.', b.', false);
+
+ ## NOTE: TRANS = 'T' not suitable because we need U' U, not U U'
+
+ case 3
+
+ if (! is_real_square_matrix (a, e))
+ ## error ("lyapchol: a, e must be real and square");
+ error ("lyapchol: %s, %s must be real and square", \
+ inputname (1), inputname (3));
+ endif
+
+ if (! is_real_matrix (b))
+ ## error ("lyapchol: b must be real");
+ error ("lyapchol: %s must be real", \
+ inputname (2));
+ endif
+
+ if (rows (b) != rows (a) || rows (e) != rows (a))
+ ## error ("lyapchol: a, b, e must have the same number of rows");
+ error ("lyapchol: %s, %s, %s must have the same number of rows", \
+ inputname (1), inputname (2), inputname (3));
+ endif
+
+ [u, scale] = slsg03bd (a.', e.', b.', false);
+
+ ## NOTE: TRANS = 'T' not suitable because we need U' U, not U U'
+
+ otherwise
+ print_usage ();
+
+ endswitch
+
+ if (scale < 1)
+ warning ("lyapchol: solution scaled by %g to prevent overflow", scale);
+ endif
+
+endfunction
+
+
+%!shared U, U_exp, X, X_exp
+%!
+%! A = [ -1.0 37.0 -12.0 -12.0
+%! -1.0 -10.0 0.0 4.0
+%! 2.0 -4.0 7.0 -6.0
+%! 2.0 2.0 7.0 -9.0 ].';
+%!
+%! B = [ 1.0 2.5 1.0 3.5
+%! 0.0 1.0 0.0 1.0
+%! -1.0 -2.5 -1.0 -1.5
+%! 1.0 2.5 4.0 -5.5
+%! -1.0 -2.5 -4.0 3.5 ].';
+%!
+%! U = lyapchol (A, B);
+%!
+%! X = U.' * U; # use lyap at home!
+%!
+%! U_exp = [ 1.0000 0.0000 0.0000 0.0000
+%! 3.0000 1.0000 0.0000 0.0000
+%! 2.0000 -1.0000 1.0000 0.0000
+%! -1.0000 1.0000 -2.0000 1.0000 ].';
+%!
+%! X_exp = [ 1.0000 3.0000 2.0000 -1.0000
+%! 3.0000 10.0000 5.0000 -2.0000
+%! 2.0000 5.0000 6.0000 -5.0000
+%! -1.0000 -2.0000 -5.0000 7.0000 ];
+%!
+%!assert (U, U_exp, 1e-4);
+%!assert (X, X_exp, 1e-4);
+
+%!shared U, U_exp, X, X_exp
+%!
+%! A = [ -1.0 3.0 -4.0
+%! 0.0 5.0 -2.0
+%! -4.0 4.0 1.0 ].';
+%!
+%! E = [ 2.0 1.0 3.0
+%! 2.0 0.0 1.0
+%! 4.0 5.0 1.0 ].';
+%!
+%! B = [ 2.0 -1.0 7.0 ].';
+%!
+%! U = lyapchol (A, B, E);
+%!
+%! U_exp = [ 1.6003 -0.4418 -0.1523
+%! 0.0000 0.6795 -0.2499
+%! 0.0000 0.0000 0.2041 ];
+%!
+%!assert (U, U_exp, 1e-4);