Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/control-2.3.52/@lti/mtimes.m b/octave_packages/control-2.3.52/@lti/mtimes.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 -*-
+## Matrix multiplication of LTI objects.  If necessary, object conversion
+## is done by sys_group.  Used by Octave for "sys1 * sys2".
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: September 2009
+## Version: 0.2
+
+function sys = mtimes (sys2, sys1)
+
+  if (nargin != 2)  # prevent sys = mtimes (sys1, sys2, sys3, ...)
+    error ("lti: mtimes: this is a binary operator");
+  endif
+
+  [p1, m1] = size (sys1);
+  [p2, m2] = size (sys2);
+
+  if (m2 != p1)
+    error ("lti: mtimes: system dimensions incompatible: (%dx%d) * (%dx%d)",
+            p2, m2, p1, m1);
+  endif
+
+  M22 = zeros (m2, p2);
+  M21 = eye (m2, p1);
+  M12 = zeros (m1, p2);
+  M11 = zeros (m1, p1);
+
+  M = [M22, M21;
+       M12, M11];
+
+  out_idx = 1 : p2;
+  in_idx = m2 + (1 : m1);
+
+  sys = __sys_group__ (sys2, sys1);
+  sys = __sys_connect__ (sys, M);
+  sys = __sys_prune__ (sys, out_idx, in_idx);
+
+endfunction
+
+
+## Alternative code: consistency vs. compatibility
+#{
+  M11 = zeros (m1, p1);
+  M12 = zeros (m1, p2);
+  M21 = eye (m2, p1);
+  M22 = zeros (m2, p2);
+  
+
+  M = [M11, M12;
+       M21, M22];
+
+  out_idx = p1 + (1 : p2);
+  in_idx = 1 : m1;
+
+  sys = __sys_group__ (sys1, sys2);
+#}
+## Don't forget to adapt @tf/__sys_connect__.m draft code
+
+
+## mtimes
+%!shared sysmat, sysmat_exp
+%! sys1 = ss ([0, 1; -3, -2], [0; 1], [-5, 1], [2]);
+%! sys2 = ss ([-10], [1], [-40], [5]);
+%! sys3 = sys2 * sys1;
+%! [A, B, C, D] = ssdata (sys3);
+%! sysmat = [A, B; C, D];
+%! A_exp = [ -10   -5    1
+%!             0    0    1
+%!             0   -3   -2 ];
+%! B_exp = [   2
+%!             0
+%!             1 ];
+%! C_exp = [ -40  -25    5 ];
+%! D_exp = [  10 ];
+%! sysmat_exp = [A_exp, B_exp; C_exp, D_exp];
+%!assert (sysmat, sysmat_exp)
+
+
+## Cascade inter-connection of two systems in state-space form
+## Test from SLICOT AB05MD
+## TODO: order of united state vector: consistency vs. compatibility?
+#%!shared M, Me
+#%! A1 = [ 1.0   0.0  -1.0
+#%!        0.0  -1.0   1.0
+#%!        1.0   1.0   2.0 ];
+#%!
+#%! B1 = [ 1.0   1.0   0.0
+#%!        2.0   0.0   1.0 ].';
+#%!
+#%! C1 = [ 3.0  -2.0   1.0
+#%!        0.0   1.0   0.0 ];
+#%!
+#%! D1 = [ 1.0   0.0
+#%!        0.0   1.0 ];
+#%!
+#%! A2 = [-3.0   0.0   0.0
+#%!        1.0   0.0   1.0
+#%!        0.0  -1.0   2.0 ];
+#%!
+#%! B2 = [ 0.0  -1.0   0.0
+#%!        1.0   0.0   2.0 ].';
+#%!
+#%! C2 = [ 1.0   1.0   0.0
+#%!        1.0   1.0  -1.0 ];
+#%!
+#%! D2 = [ 1.0   1.0
+#%!        0.0   1.0 ];
+#%!
+#%! sys1 = ss (A1, B1, C1, D1);
+#%! sys2 = ss (A2, B2, C2, D2);
+#%! sys = sys2 * sys1;
+#%! [A, B, C, D] = ssdata (sys);
+#%! M = [A, B; C, D];
+#%!
+#%! Ae = [ 1.0000   0.0000  -1.0000   0.0000   0.0000   0.0000
+#%!        0.0000  -1.0000   1.0000   0.0000   0.0000   0.0000
+#%!        1.0000   1.0000   2.0000   0.0000   0.0000   0.0000
+#%!        0.0000   1.0000   0.0000  -3.0000   0.0000   0.0000
+#%!       -3.0000   2.0000  -1.0000   1.0000   0.0000   1.0000
+#%!        0.0000   2.0000   0.0000   0.0000  -1.0000   2.0000 ];
+#%!
+#%! Be = [ 1.0000   2.0000
+#%!        1.0000   0.0000
+#%!        0.0000   1.0000
+#%!        0.0000   1.0000
+#%!       -1.0000   0.0000
+#%!        0.0000   2.0000 ];
+#%!
+#%! Ce = [ 3.0000  -1.0000   1.0000   1.0000   1.0000   0.0000
+#%!        0.0000   1.0000   0.0000   1.0000   1.0000  -1.0000 ];
+#%!
+#%! De = [ 1.0000   1.0000
+#%!        0.0000   1.0000 ];
+#%!
+#%! Me = [Ae, Be; Ce, De];
+#%!
+#%!assert (M, Me, 1e-4);