Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / @lti / sminreal.m

diff --git a/octave_packages/control-2.3.52/@lti/sminreal.m b/octave_packages/control-2.3.52/@lti/sminreal.m
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+## Copyright (C) 2009, 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{sys} =} sminreal (@var{sys})
+## @deftypefnx {Function File} {@var{sys} =} sminreal (@var{sys}, @var{tol})
+## Perform state-space model reduction based on structure.
+## Remove states which have no influence on the input-output behaviour.
+## The physical meaning of the states is retained.
+##
+## @strong{Inputs}
+## @table @var
+## @item sys
+## State-space model.
+## @item tol
+## Optional tolerance for controllability and observability. 
+## Entries of the state-space matrices whose moduli are less or equal to @var{tol}
+## are assumed to be zero.  Default value is 0.
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item sys
+## Reduced state-space model.
+## @end table
+##
+## @seealso{minreal}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: October 2009
+## Version: 0.4
+
+function sys = sminreal (sys, tol = 0)
+
+  if (nargin > 2)            # sminreal () not possible (inside @lti)
+    print_usage ();
+  endif
+
+  if (! isa (sys, "ss"))
+    warning ("sminreal: system not in state-space form");
+    sys = ss (sys);          # needed by __sys_prune__
+  endif
+
+  if (! (is_real_scalar (tol) && tol >= 0))
+    error ("sminreal: second argument is not a valid tolerance");
+  endif
+
+  [a, b, c, d, e] = dssdata (sys, []);
+
+  a = abs (a) > tol;
+  b = abs (b) > tol;
+  c = abs (c) > tol;
+
+  if (! isempty (e))
+    e = abs (e) > tol;
+    a = a | e;
+  endif
+
+  co_idx = __controllable_states__ (a, b);
+  ob_idx = __controllable_states__ (a.', c.');
+
+  st_idx = intersect (co_idx, ob_idx);
+
+  sys = __sys_prune__ (sys, ":", ":", st_idx);
+
+endfunction
+
+
+function c_idx = __controllable_states__ (a, b)
+
+  n = rows (a);              # number of states
+  a = a & ! eye (n);         # set diagonal entries to zero
+
+  c_vec = any (b, 2);        # states directly controllable
+  c_idx = find (c_vec);      # indices of directly controllable states
+  c_idx_new = 0;             # any vector of length > 0 possible
+
+  while (all (length (c_idx) != [0, n]) && length(c_idx_new) != 0)
+
+    u_idx = find (! c_vec);  # indices of uncontrollable states
+
+    #{
+    ## debug code
+    a(u_idx, :)
+    repmat (c_vec.', length (u_idx), 1)
+    a(u_idx, :) & repmat (c_vec.', length (u_idx), 1)
+    any (a(u_idx, :) & repmat (c_vec.', length (u_idx), 1), 2)
+    find (any (a(u_idx, :) & repmat (c_vec.', length (u_idx), 1), 2))
+    #}
+
+    c_idx_new = u_idx (find (any (a(u_idx, :) & repmat (c_vec.', length (u_idx), 1), 2)));
+    c_idx = union (c_idx, c_idx_new);
+    c_vec(c_idx_new) = 1;
+
+  endwhile
+
+endfunction
+
+
+## ss: sminreal
+%!shared B, C
+%!
+%! A = ss (-2, 3, 4, 5);
+%! B = A / A;
+%! C = sminreal (B);  # no states should be removed
+%!
+%!assert (C.a, B.a);
+%!assert (C.b, B.b);
+%!assert (C.c, B.c);
+%!assert (C.d, B.d);
+
+%!shared A, B, D, E
+%!
+%! A = ss (-1, 1, 1, 0);
+%! B = ss (-2, 3, 4, 5);
+%! C = [A, B];
+%! D = sminreal (C(:, 1));
+%! E = sminreal (C(:, 2));
+%!
+%!assert (D.a, A.a);
+%!assert (D.b, A.b);
+%!assert (D.c, A.c);
+%!assert (D.d, A.d);
+%!assert (E.a, B.a);
+%!assert (E.b, B.b);
+%!assert (E.c, B.c);
+%!assert (E.d, B.d);