Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/control-2.3.52/@lti/inv.m b/octave_packages/control-2.3.52/@lti/inv.m
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+## Copyright (C) 2009, 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 -*-
+## Inversion of LTI objects.
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: October 2009
+## Version: 0.2
+
+function retsys = inv (sys)
+
+  if (nargin != 1)  # prevent sys = inv (sys1, sys2, sys3, ...)
+    error ("lti: inv: this is an unary operator");
+  endif
+
+  [p, m] = size (sys);
+
+  if (p != m)
+    error ("lti: inv: system must be square");
+  endif
+
+  retsys = __sys_inverse__ (sys);
+
+  ## TODO: handle i/o names
+
+endfunction
+
+
+## inverse of state-space models
+## test from SLICOT AB07ND
+## result differs intentionally from a commercial
+## implementation of an octave-like language
+%!shared M, Me
+%! A = [ 1.0   2.0   0.0
+%!       4.0  -1.0   0.0
+%!       0.0   0.0   1.0 ];
+%!
+%! B = [ 1.0   0.0
+%!       0.0   1.0
+%!       1.0   0.0 ];
+%!
+%! C = [ 0.0   1.0  -1.0
+%!       0.0   0.0   1.0 ];
+%!
+%! D = [ 4.0   0.0
+%!       0.0   1.0 ];
+%!
+%! sys = ss (A, B, C, D);
+%! sysinv = inv (sys);
+%! [Ai, Bi, Ci, Di] = ssdata (sysinv);
+%! M = [Ai, Bi; Ci, Di];
+%!
+%! Ae = [ 1.0000   1.7500   0.2500
+%!        4.0000  -1.0000  -1.0000
+%!        0.0000  -0.2500   1.2500 ];
+%!
+%! Be = [-0.2500   0.0000
+%!        0.0000  -1.0000
+%!       -0.2500   0.0000 ];
+%!
+%! Ce = [ 0.0000   0.2500  -0.2500
+%!        0.0000   0.0000   1.0000 ];
+%!
+%! De = [ 0.2500   0.0000
+%!        0.0000   1.0000 ];
+%!
+%! Me = [Ae, Be; Ce, De];  # Me = [Ae, -Be; -Ce, De];
+%!
+%!assert (M, Me, 1e-4);