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[CreaPhase.git] / octave_packages / control-2.3.52 / hsvd.m

diff --git a/octave_packages/control-2.3.52/hsvd.m b/octave_packages/control-2.3.52/hsvd.m
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+## Copyright (C) 2010, 2011   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{hsv} =} hsvd (@var{sys})
+## @deftypefnx{Function File} {@var{hsv} =} hsvd (@var{sys}, @var{"offset"}, @var{offset})
+## @deftypefnx{Function File} {@var{hsv} =} hsvd (@var{sys}, @var{"alpha"}, @var{alpha})
+## Hankel singular values of the stable part of an LTI model.  If no output arguments are
+## given, the Hankel singular values are displayed in a plot.
+##
+## @strong{Algorithm}@*
+## Uses SLICOT AB13AD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: January 2010
+## Version: 0.4
+
+function hsv_r = hsvd (sys, prop = "offset", val = 1e-8)
+
+  if (nargin != 1 && nargin != 3)
+    print_usage ();
+  endif
+
+  if (! isa (sys, "lti"))
+    error ("hsvd: first argument must be an LTI system");
+  endif
+
+  if (! is_real_scalar (val))
+    error ("hsvd: third argument must be a real scalar");
+  endif
+
+  [a, b, c, ~, ~, scaled] = ssdata (sys);
+
+  discrete = ! isct (sys);
+
+  switch (tolower (prop(1)))
+    case "o"                 # offset
+      if (discrete)
+        alpha = 1 - val;
+      else
+        alpha = - val;
+      endif
+    case "a"                 # alpha
+      alpha = val;
+    otherwise
+      error ("hsvd: second argument invalid");
+  endswitch
+  
+  [hsv, ns] = slab13ad (a, b, c, discrete, alpha, scaled);
+  
+  if (nargout)
+    hsv_r = hsv;
+  else
+    bar ((1:ns) + (rows (a) - ns), hsv);
+    title (["Hankel Singular Values of Stable Part of ", inputname(1)]);
+    xlabel ("State");
+    ylabel ("State Energy");
+    grid ("on");
+  endif
+
+endfunction
+
+
+%!shared hsv, hsv_exp
+%! a = [ -0.04165  0.0000  4.9200  -4.9200  0.0000  0.0000  0.0000
+%!       -5.2100  -12.500  0.0000   0.0000  0.0000  0.0000  0.0000
+%!        0.0000   3.3300 -3.3300   0.0000  0.0000  0.0000  0.0000
+%!        0.5450   0.0000  0.0000   0.0000 -0.5450  0.0000  0.0000
+%!        0.0000   0.0000  0.0000   4.9200 -0.04165 0.0000  4.9200
+%!        0.0000   0.0000  0.0000   0.0000 -5.2100 -12.500  0.0000
+%!        0.0000   0.0000  0.0000   0.0000  0.0000  3.3300 -3.3300];
+%!
+%! b = [  0.0000   0.0000
+%!       12.5000   0.0000
+%!        0.0000   0.0000
+%!        0.0000   0.0000
+%!        0.0000   0.0000
+%!        0.0000   12.500
+%!        0.0000   0.0000];
+%!
+%! c = [  1.0000   0.0000  0.0000   0.0000  0.0000  0.0000  0.0000
+%!        0.0000   0.0000  0.0000   1.0000  0.0000  0.0000  0.0000
+%!        0.0000   0.0000  0.0000   0.0000  1.0000  0.0000  0.0000];
+%!
+%! sys = ss (a, b, c, [], "scaled", true);
+%! hsv = hsvd (sys, "alpha", 0.0);
+%!
+%! hsv_exp = [2.5139; 2.0846; 1.9178; 0.7666; 0.5473; 0.0253; 0.0246];
+%!
+%!assert (hsv, hsv_exp, 1e-4);