--- /dev/null
+## 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} =} minreal (@var{sys})
+## @deftypefnx {Function File} {@var{sys} =} minreal (@var{sys}, @var{tol})
+## Minimal realization or zero-pole cancellation of LTI models.
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: October 2009
+## Version: 0.3
+
+function sys = minreal (sys, tol = "def")
+
+ if (nargin > 2) # nargin == 0 not possible because minreal is inside @lti
+ print_usage ();
+ endif
+
+ if (! is_real_scalar (tol) && tol != "def")
+ error ("minreal: second argument must be a real scalar");
+ endif
+
+ sys = __minreal__ (sys, tol);
+
+endfunction
+
+
+## ss: minreal (SLICOT TB01PD)
+%!shared C, D
+%!
+%! A = ss (-2, 3, 4, 5);
+%! B = A / A;
+%! C = minreal (B, 1e-15);
+%! D = ss (1);
+%!
+%!assert (C.a, D.a);
+%!assert (C.b, D.b);
+%!assert (C.c, D.c);
+%!assert (C.d, D.d);
+
+%!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
+%! 1.0 ];
+%!
+%! C = [ 0.0 1.0 -1.0
+%! 0.0 0.0 1.0 ];
+%!
+%! D = zeros (2, 1);
+%!
+%! sys = ss (A, B, C, D, "scaled", true);
+%! sysmin = minreal (sys, 0.0);
+%! [Ar, Br, Cr, Dr] = ssdata (sysmin);
+%! M = [Ar, Br; Cr, Dr];
+%!
+%! Ae = [ 1.0000 -1.4142 1.4142
+%! -2.8284 0.0000 1.0000
+%! 2.8284 1.0000 0.0000 ];
+%!
+%! Be = [-1.0000
+%! 0.7071
+%! 0.7071 ];
+%!
+%! Ce = [ 0.0000 0.0000 -1.4142
+%! 0.0000 0.7071 0.7071 ];
+%!
+%! De = zeros (2, 1);
+%!
+%! Me = [Ae, Be; Ce, De];
+%!
+%!assert (M, Me, 1e-4);
+
+
+## dss: minreal (SLICOT TG01JD)
+## FIXME: Test fails with larger ldwork in sltg01jd.cc
+%!shared Ar, Br, Cr, Dr, Er, Ae, Be, Ce, De, Ee
+%! A = [ -2 -3 0 0 0 0 0 0 0
+%! 1 0 0 0 0 0 0 0 0
+%! 0 0 -2 -3 0 0 0 0 0
+%! 0 0 1 0 0 0 0 0 0
+%! 0 0 0 0 1 0 0 0 0
+%! 0 0 0 0 0 1 0 0 0
+%! 0 0 0 0 0 0 1 0 0
+%! 0 0 0 0 0 0 0 1 0
+%! 0 0 0 0 0 0 0 0 1 ];
+%!
+%! E = [ 1 0 0 0 0 0 0 0 0
+%! 0 1 0 0 0 0 0 0 0
+%! 0 0 1 0 0 0 0 0 0
+%! 0 0 0 1 0 0 0 0 0
+%! 0 0 0 0 0 0 0 0 0
+%! 0 0 0 0 1 0 0 0 0
+%! 0 0 0 0 0 0 0 0 0
+%! 0 0 0 0 0 0 1 0 0
+%! 0 0 0 0 0 0 0 1 0 ];
+%!
+%! B = [ 1 0
+%! 0 0
+%! 0 1
+%! 0 0
+%! -1 0
+%! 0 0
+%! 0 -1
+%! 0 0
+%! 0 0 ];
+%!
+%! C = [ 1 0 1 -3 0 1 0 2 0
+%! 0 1 1 3 0 1 0 0 1 ];
+%!
+%! D = zeros (2, 2);
+%!
+%! sys = dss (A, B, C, D, E, "scaled", true);
+%! sysmin = minreal (sys, 0.0);
+%! [Ar, Br, Cr, Dr, Er] = dssdata (sysmin);
+%!
+%! Ae = [ 1.0000 -0.0393 -0.0980 -0.1066 0.0781 -0.2330 0.0777
+%! 0.0000 1.0312 0.2717 0.2609 -0.1533 0.6758 -0.3553
+%! 0.0000 0.0000 1.3887 0.6699 -0.4281 1.6389 -0.7615
+%! 0.0000 0.0000 0.0000 -1.2147 0.2423 -0.9792 0.4788
+%! 0.0000 0.0000 0.0000 0.0000 -1.0545 0.5035 -0.2788
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 1.6355 -0.4323
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 ];
+%!
+%! Ee = [ 0.4100 0.2590 0.5080 -0.3109 0.0705 0.1429 -0.1477
+%! -0.7629 -0.3464 0.0992 -0.3007 0.0619 0.2483 -0.0152
+%! 0.1120 -0.2124 -0.4184 -0.1288 0.0569 -0.4213 -0.6182
+%! 0.0000 0.1122 -0.0039 0.2771 -0.0758 0.0975 0.3923
+%! 0.0000 0.0000 0.3708 -0.4290 0.1006 0.1402 -0.2699
+%! 0.0000 0.0000 0.0000 0.0000 0.9458 -0.2211 0.2378
+%! 0.0000 0.0000 0.0000 0.5711 0.2648 0.5948 -0.5000 ];
+%!
+%! Be = [ -0.5597 0.2363
+%! -0.4843 -0.0498
+%! -0.4727 -0.1491
+%! 0.1802 1.1574
+%! 0.5995 0.1556
+%! -0.1729 -0.3999
+%! 0.0000 0.2500 ];
+%!
+%! Ce = [ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 4.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 3.1524 -1.7500 ];
+%!
+%! De = zeros (2, 2);
+%!
+%!assert (Ar, Ae, 1e-4);
+%!assert (Br, Be, 1e-4);
+%!assert (Cr, Ce, 1e-4);
+%!assert (Dr, De, 1e-4);
+%!assert (Er, Ee, 1e-4);
+
+
+## tf: minreal
+%!shared a, b, c, d
+%! s = tf ("s");
+%! G1 = (s+1)*s*5/(s+1)/(s^2+s+1);
+%! G2 = tf ([1, 1, 1], [2, 2, 2]);
+%! G1min = minreal (G1);
+%! G2min = minreal (G2);
+%! a = G1min.num{1, 1};
+%! b = G1min.den{1, 1};
+%! c = G2min.num{1, 1};
+%! d = G2min.den{1, 1};
+%!assert (a, [5, 0], 1e-4);
+%!assert (b, [1, 1, 1], 1e-4);
+%!assert (c, 0.5, 1e-4);
+%!assert (d, 1, 1e-4);
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff