/usr/share/octave/packages/control-2.6.2/lyapchol.m is in octave-control 2.6.2-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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##
## 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] = __sl_sb03od__ (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] = __sl_sg03bd__ (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);
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