/usr/share/octave/packages/control-3.0.0/lyapchol.m is in octave-control 3.0.0-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 | ## Copyright (C) 2009-2015 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] = __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);
|