/usr/share/octave/packages/control-2.6.2/@lti/norm.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.
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 | ## Copyright (C) 2009-2014 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{gain} =} norm (@var{sys}, @var{2})
## @deftypefnx {Function File} {[@var{gain}, @var{wpeak}] =} norm (@var{sys}, @var{inf})
## @deftypefnx {Function File} {[@var{gain}, @var{wpeak}] =} norm (@var{sys}, @var{inf}, @var{tol})
## Return H-2 or L-inf norm of @acronym{LTI} model.
##
## @strong{Algorithm}@*
## Uses SLICOT AB13BD and AB13DD by courtesy of
## @uref{http://www.slicot.org, NICONET e.V.}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: November 2009
## Version: 0.5
function [gain, varargout] = norm (sys, ntype = "2", tol = 0.01)
if (nargin > 3) # norm () is caught by built-in function
print_usage ();
endif
if (is_real_scalar (ntype))
if (ntype == 2)
ntype = "2";
elseif (isinf (ntype))
ntype = "inf";
else
error ("lti: norm: invalid norm type");
endif
elseif (ischar (ntype))
ntype = lower (ntype);
else
error ("lti: norm: invalid norm type");
endif
switch (ntype)
case "2"
gain = h2norm (sys);
case "inf"
[gain, varargout{1}] = linfnorm (sys, tol);
otherwise
error ("lti: norm: invalid norm type");
endswitch
endfunction
function gain = h2norm (sys)
if (isstable (sys))
[a, b, c, d] = ssdata (sys);
discrete = ! isct (sys);
if (! discrete && any (d(:))) # continuous and non-zero feedthrough
gain = inf;
else
gain = __sl_ab13bd__ (a, b, c, d, discrete);
endif
else
gain = inf;
endif
endfunction
function [gain, wpeak] = linfnorm (sys, tol = 0.01)
[a, b, c, d, e, tsam, scaled] = dssdata (sys, []);
discrete = ! isct (sys);
tol = max (tol, 100*eps);
if (isempty (e))
[fpeak, gpeak] = __sl_ab13dd__ (a, a, b, c, d, discrete, false, tol, scaled); # TODO: avoid dummy argument
else
if (rcond (e) < eps)
gain = inf;
wpeak = inf;
return;
else
[fpeak, gpeak] = __sl_ab13dd__ (a, e, b, c, d, discrete, true, tol, scaled);
endif
endif
if (fpeak(2) > 0)
if (discrete)
wpeak = fpeak(1) / abs (tsam); # tsam could be -1
else
wpeak = fpeak(1);
endif
else
wpeak = inf;
endif
if (gpeak(2) > 0)
gain = gpeak(1);
else
gain = inf;
endif
endfunction
## norm ct
%!shared H2, Hinf
%! sys = ss (-1, 1, 1, 0);
%! H2 = norm (sys, 2);
%! Hinf = norm (sys, inf);
%!assert (H2, 0.7071, 1.5e-5);
%!assert (Hinf, 1, 5e-4);
## norm dt
%!shared H2, Hinf
%! a = [ 2.417 -1.002 0.5488
%! 2 0 0
%! 0 0.5 0 ];
%! b = [ 1
%! 0
%! 0 ];
%! c = [-0.424 0.436 -0.4552 ];
%! d = [ 1 ];
%! sys = ss (a, b, c, d, 0.1);
%! H2 = norm (sys, 2);
%! Hinf = norm (sys, inf);
%!assert (H2, 1.2527, 1.5e-5);
%!assert (Hinf, 2.7, 0.1);
|