/usr/share/octave/packages/control-2.6.2/sigma.m is in octave-control 2.6.2-1build1.
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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 | ## 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} {} sigma (@var{sys})
## @deftypefnx {Function File} {} sigma (@var{sys1}, @var{sys2}, @dots{}, @var{sysN})
## @deftypefnx {Function File} {} sigma (@var{sys1}, @var{sys2}, @dots{}, @var{sysN}, @var{w})
## @deftypefnx {Function File} {} sigma (@var{sys1}, @var{'style1'}, @dots{}, @var{sysN}, @var{'styleN'})
## @deftypefnx{Function File} {[@var{sv}, @var{w}] =} sigma (@var{sys})
## @deftypefnx{Function File} {[@var{sv}, @var{w}] =} sigma (@var{sys}, @var{w})
## Singular values of frequency response. If no output arguments are given,
## the singular value plot is printed on the screen.
##
## @strong{Inputs}
## @table @var
## @item sys
## @acronym{LTI} system. Multiple inputs and/or outputs (MIMO systems) make practical sense.
## @item w
## Optional vector of frequency values. If @var{w} is not specified,
## it is calculated by the zeros and poles of the system.
## Alternatively, the cell @code{@{wmin, wmax@}} specifies a frequency range,
## where @var{wmin} and @var{wmax} denote minimum and maximum frequencies
## in rad/s.
## @item 'style'
## Line style and color, e.g. 'r' for a solid red line or '-.k' for a dash-dotted
## black line. See @command{help plot} for details.
## @end table
##
## @strong{Outputs}
## @table @var
## @item sv
## Array of singular values. For a system with m inputs and p outputs, the array sv
## has @code{min (m, p)} rows and as many columns as frequency points @code{length (w)}.
## The singular values at the frequency @code{w(k)} are given by @code{sv(:,k)}.
## @item w
## Vector of frequency values used.
## @end table
##
## @seealso{bodemag, svd}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: May 2009
## Version: 0.7
function [sv_r, w_r] = sigma (varargin)
if (nargin == 0)
print_usage ();
endif
[H, w] = __frequency_response__ (varargin, true, "std", true);
sv = cellfun (@(H) cellfun (@svd, H, "uniformoutput", false), H, "uniformoutput", false);
sv = cellfun (@(sv) horzcat (sv{:}), sv, "uniformoutput", false);
if (! nargout) # plot the information
## convert to dB for plotting
sv_db = cellfun (@(sv) 20 * log10 (sv), sv, "uniformoutput", false);
tmp = cellfun (@isa, varargin, {"lti"});
sys_idx = find (tmp);
tmp = cellfun (@ischar, varargin);
style_idx = find (tmp);
len = numel (H);
plot_args = {};
legend_args = cell (len, 1);
colororder = get (gca, "colororder");
rc = rows (colororder);
for k = 1:len
col = colororder(1+rem (k-1, rc), :);
if (k == len)
lim = nargin;
else
lim = sys_idx(k+1);
endif
style = varargin(style_idx(style_idx > sys_idx(k) & style_idx <= lim));
if (isempty (style))
plot_args = cat (2, plot_args, w(k), sv_db(k), {"-", "color", col});
else
plot_args = cat (2, plot_args, w(k), sv_db(k), style);
endif
try
legend_args{k} = inputname(sys_idx(k)); # watch out for sigma (lticell{:})
catch
legend_args{k} = "";
end_try_catch
endfor
## adjust line colors in legend
idx = horzcat (1, cellfun (@rows, sv_db)(1:end-1));
idx = cumsum (idx);
## plot results
h = semilogx (plot_args{:});
axis ("tight")
ylim (__axis_margin__ (ylim))
grid ("on")
title ("Singular Values")
xlabel ("Frequency [rad/s]")
ylabel ("Singular Values [dB]")
legend (h(idx), legend_args)
else # return values
sv_r = sv{1};
w_r = reshape (w{1}, [], 1);
endif
endfunction
%!shared sv_exp, w_exp, sv_obs, w_obs
%! A = [1, 2; 3, 4];
%! B = [5, 6; 7, 8];
%! C = [4, 3; 2, 1];
%! D = [8, 7; 6, 5];
%! w = [2, 3, 4];
%! sv_exp = [7.9176, 8.6275, 9.4393;
%! 0.6985, 0.6086, 0.5195];
%! w_exp = [2; 3; 4];
%! [sv_obs, w_obs] = sigma (ss (A, B, C, D), w);
%!assert (sv_obs, sv_exp, 1e-4);
%!assert (w_obs, w_exp, 1e-4);
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