/usr/share/octave/packages/control-3.0.0/covar.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 | ## 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{p}, @var{q}] =} covar (@var{sys}, @var{w})
## Return the steady-state covariance.
##
## @strong{Inputs}
## @table @var
## @item sys
## @acronym{LTI} model.
## @item w
## Intensity of Gaussian white noise inputs which drive @var{sys}.
## @end table
##
## @strong{Outputs}
## @table @var
## @item p
## Output covariance.
## @item q
## State covariance.
## @end table
##
## @seealso{lyap, dlyap}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: January 2010
## Version: 0.1
function [p, q] = covar (sys, w)
if (nargin != 2)
print_usage ();
endif
if (! isa (sys, "lti"))
error ("covar: first argument must be an LTI model");
endif
if (! isstable (sys))
error ("covar: system must be stable");
endif
[a, b, c, d] = ssdata (sys);
if (isct (sys))
if (any (d(:)))
error ("covar: system is not strictly proper");
endif
q = lyap (a, b*w*b.');
p = c*q*c.';
else
q = dlyap (a, b*w*b.');
p = c*q*c.' + d*w*d.';
endif
endfunction
## continuous-time
%!shared p, q, p_exp, q_exp
%! sys = ss (-1, 1, 1, 0);
%! [p, q] = covar (sys, 5);
%! p_exp = 2.5000;
%! q_exp = 2.5000;
%!assert (p, p_exp, 1e-4);
%!assert (q, q_exp, 1e-4);
## discrete-time
%!shared p, q, p_exp, q_exp
%! sys = ss ([-0.2, -0.5; 1, 0], [2; 0], [1, 0.5], [0], 0.1);
%! [p, q] = covar (sys, 5);
%! p_exp = 30.3167;
%! q_exp = [27.1493, -3.6199; -3.6199, 27.1493];
%!assert (p, p_exp, 1e-4);
%!assert (q, q_exp, 1e-4);
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