/usr/share/octave/packages/control-2.6.2/@lti/minreal.m is in octave-control 2.6.2-1build1.
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##
## 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 @acronym{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);
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