/usr/share/octave/packages/control-3.0.0/ltimodels.m is in octave-control 3.0.0-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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## Copyright (C) 2009-2015 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} test ltimodels
## @deftypefnx {Function File} ltimodels
## @deftypefnx {Function File} ltimodels (@var{systype})
## Test suite and help for @acronym{LTI} models.
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: November 2009
## Version: 0.2
function ltimodels (systype = "general")
%if (nargin > 1)
print_usage ();
%endif
## TODO: write documentation
if (! ischar (systype))
error ("ltimodels: argument must be a string");
endif
systype = lower (systype);
switch (systype)
case "ss"
str = {"State Space (SS) Models"...
"-----------------------"...
""};
case "tf"
str = {"Transfer Function (TF) Models"...
"-----------------------------"...
""};
otherwise # general
str = {"Linear Time Invariant (LTI) Models"...
"----------------------------------"...
""};
endswitch
disp ("");
disp (char (str));
endfunction
## ==============================================================================
## LTI Tests
## ==============================================================================
## isct, isdt
%!shared ltisys
%! ltisys = tf (12);
%!assert (ltisys.ts, -2);
%!assert (isct (ltisys));
%!assert (isdt (ltisys));
%!shared ltisys
%! ltisys = ss (17);
%!assert (ltisys.ts, -2);
%!assert (isct (ltisys));
%!assert (isdt (ltisys));
%!shared ltisys
%! ltisys = tf (1, [1 1]);
%!assert (ltisys.ts, 0);
%!assert (isct (ltisys));
%!assert (! isdt (ltisys));
%!shared ltisys, ts
%! ts = 0.1;
%! ltisys = ss (-1, 1, 1, 0, ts);
%!assert (ltisys.ts, ts);
%!assert (! isct (ltisys));
%!assert (isdt (ltisys));
## ==============================================================================
## TF Tests
## ==============================================================================
## ==============================================================================
## SS Tests
## ==============================================================================
## staircase (SLICOT AB01OD)
%!shared Ac, Bc, Ace, Bce
%! A = [ 17.0 24.0 1.0 8.0 15.0
%! 23.0 5.0 7.0 14.0 16.0
%! 4.0 6.0 13.0 20.0 22.0
%! 10.0 12.0 19.0 21.0 3.0
%! 11.0 18.0 25.0 2.0 9.0 ];
%!
%! B = [ -1.0 -4.0
%! 4.0 9.0
%! -9.0 -16.0
%! 16.0 25.0
%! -25.0 -36.0 ];
%!
%! tol = 0;
%!
%! A = A.'; # There's a little mistake in the example
%! # program of routine AB01OD in SLICOT 5.0
%!
%! [Ac, Bc, U, ncont] = __sl_ab01od__ (A, B, tol);
%!
%! Ace = [ 12.8848 3.2345 11.8211 3.3758 -0.8982
%! 4.4741 -12.5544 5.3509 5.9403 1.4360
%! 14.4576 7.6855 23.1452 26.3872 -29.9557
%! 0.0000 1.4805 27.4668 22.6564 -0.0072
%! 0.0000 0.0000 -30.4822 0.6745 18.8680 ];
%!
%! Bce = [ 31.1199 47.6865
%! 3.2480 0.0000
%! 0.0000 0.0000
%! 0.0000 0.0000
%! 0.0000 0.0000 ];
%!
%!assert (Ac, Ace, 1e-4);
%!assert (Bc, Bce, 1e-4);
## controllability staircase form of descriptor state-space models (SLICOT TG01HD)
%!shared ac, ec, bc, cc, q, z, ncont, ac_e, ec_e, bc_e, cc_e, q_e, z_e, ncont_e
%!
%! a = [ 2 0 2 0 -1 3 1
%! 0 1 0 0 1 0 0
%! 0 0 0 1 0 0 1
%! 0 0 2 0 -1 3 1
%! 0 0 0 1 0 0 1
%! 0 1 0 0 1 0 0
%! 0 0 0 1 0 0 1 ];
%!
%! e = [ 0 0 1 0 0 0 0
%! 0 0 0 0 0 1 0
%! 0 0 0 0 0 0 1
%! 0 0 0 0 0 0 1
%! 0 0 0 1 0 0 0
%! 0 0 1 0 -1 0 0
%! 1 3 0 2 0 0 0 ];
%!
%! b = [ 2 1 0
%! 0 0 0
%! 0 0 0
%! 0 0 0
%! 0 0 0
%! 0 0 0
%! 1 2 3 ];
%!
%! c = [ 1 0 0 1 0 0 1
%! 0 -1 1 0 -1 1 0 ];
%!
%! tol = 0;
%!
%! [ac, ec, bc, cc, q, z, ncont] = __sl_tg01hd__ (a, e, b, c, tol);
%!
%! ncont_e = 3;
%!
%! ac_e = [ 0.0000 0.0000 0.0000 0.0000 -1.2627 0.4334 0.4666
%! 0.0000 2.0000 0.0000 -3.7417 -0.8520 0.2924 -0.4342
%! 0.0000 0.0000 1.7862 0.3780 -0.2651 -0.7723 0.0000
%! 0.0000 0.0000 0.0000 3.7417 0.8520 -0.2924 0.4342
%! 0.0000 0.0000 0.0000 0.0000 -1.5540 0.5334 0.5742
%! 0.0000 0.0000 0.0000 0.0000 -0.6533 0.2242 0.2414
%! 0.0000 0.0000 0.0000 0.0000 -0.5892 0.2022 0.2177 ];
%!
%! ec_e = [ -1.8325 1.0000 2.3752 0.0000 -0.8214 0.2819 1.8016
%! 0.4887 0.0000 0.3770 -0.5345 0.1874 0.5461 0.0000
%! -0.1728 0.0000 -0.1333 -1.1339 0.1325 0.3861 0.0000
%! 0.0000 0.0000 0.0000 0.0000 0.8520 -0.2924 0.4342
%! 0.0000 0.0000 0.0000 0.0000 -1.0260 -0.1496 0.0000
%! 0.0000 0.0000 0.0000 0.0000 0.0000 1.1937 0.0000
%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 ];
%!
%! bc_e = [ 1.0000 2.0000 3.0000
%! 2.0000 1.0000 0.0000
%! 0.0000 0.0000 0.0000
%! 0.0000 0.0000 0.0000
%! 0.0000 0.0000 0.0000
%! 0.0000 0.0000 0.0000
%! 0.0000 0.0000 0.0000 ];
%!
%! cc_e = [ 0.0000 1.0000 0.0000 0.0000 -1.2627 0.4334 0.4666
%! 0.3665 0.0000 -0.9803 -1.6036 0.1874 0.5461 0.0000 ];
%!
%! q_e = [ 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000
%! 0.0000 0.0000 0.7071 0.0000 0.2740 -0.6519 0.0000
%! 0.0000 0.0000 0.0000 0.0000 0.8304 0.3491 -0.4342
%! 0.0000 0.0000 0.0000 -1.0000 0.0000 0.0000 0.0000
%! 0.0000 0.0000 0.0000 0.0000 0.4003 0.1683 0.9008
%! 0.0000 0.0000 0.7071 0.0000 -0.2740 0.6519 0.0000
%! 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ];
%!
%! z_e = [ 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000
%! -0.6108 0.0000 0.7917 0.0000 0.0000 0.0000 0.0000
%! 0.4887 0.0000 0.3770 -0.5345 0.1874 0.5461 0.0000
%! 0.0000 0.0000 0.0000 0.0000 -0.4107 0.1410 0.9008
%! 0.6108 0.0000 0.4713 0.2673 -0.1874 -0.5461 0.0000
%! -0.1222 0.0000 -0.0943 -0.8018 -0.1874 -0.5461 0.0000
%! 0.0000 0.0000 0.0000 0.0000 -0.8520 0.2924 -0.4342 ];
%!
%!assert (ac, ac_e, 1e-4);
%!assert (ec, ec_e, 1e-4);
%!assert (bc, bc_e, 1e-4);
%!assert (cc, cc_e, 1e-4);
%!assert (q, q_e, 1e-4);
%!assert (z, z_e, 1e-4);
%!assert (ncont, ncont_e);
## observability staircase form of descriptor state-space models (SLICOT TG01ID)
%!shared ao, eo, bo, co, q, z, nobsv, ao_e, eo_e, bo_e, co_e, q_e, z_e, nobsv_e
%!
%! a = [ 2 0 0 0 0 0 0
%! 0 1 0 0 0 1 0
%! 2 0 0 2 0 0 0
%! 0 0 1 0 1 0 1
%! -1 1 0 -1 0 1 0
%! 3 0 0 3 0 0 0
%! 1 0 1 1 1 0 1 ];
%!
%! e = [ 0 0 0 0 0 0 1
%! 0 0 0 0 0 0 3
%! 1 0 0 0 0 1 0
%! 0 0 0 0 1 0 2
%! 0 0 0 0 0 -1 0
%! 0 1 0 0 0 0 0
%! 0 0 1 1 0 0 0 ];
%!
%! b = [ 1 0
%! 0 -1
%! 0 1
%! 1 0
%! 0 -1
%! 0 1
%! 1 0 ];
%!
%! c = [ 2 0 0 0 0 0 1
%! 1 0 0 0 0 0 2
%! 0 0 0 0 0 0 3 ];
%!
%! tol = 0;
%!
%! [ao, eo, bo, co, q, z, nobsv] = __sl_tg01id__ (a, e, b, c, tol);
%!
%! nobsv_e = 3;
%!
%! ao_e = [ 0.2177 0.2414 0.5742 0.4342 0.0000 -0.4342 0.4666
%! 0.2022 0.2242 0.5334 -0.2924 -0.7723 0.2924 0.4334
%! -0.5892 -0.6533 -1.5540 0.8520 -0.2651 -0.8520 -1.2627
%! 0.0000 0.0000 0.0000 3.7417 0.3780 -3.7417 0.0000
%! 0.0000 0.0000 0.0000 0.0000 1.7862 0.0000 0.0000
%! 0.0000 0.0000 0.0000 0.0000 0.0000 2.0000 0.0000
%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ];
%!
%! eo_e = [ 1.0000 0.0000 0.0000 0.4342 0.0000 0.0000 1.8016
%! 0.0000 1.1937 -0.1496 -0.2924 0.3861 0.5461 0.2819
%! 0.0000 0.0000 -1.0260 0.8520 0.1325 0.1874 -0.8214
%! 0.0000 0.0000 0.0000 0.0000 -1.1339 -0.5345 0.0000
%! 0.0000 0.0000 0.0000 0.0000 -0.1333 0.3770 2.3752
%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
%! 0.0000 0.0000 0.0000 0.0000 -0.1728 0.4887 -1.8325 ];
%!
%! bo_e = [ 0.4666 0.0000
%! 0.4334 0.5461
%! -1.2627 0.1874
%! 0.0000 -1.6036
%! 0.0000 -0.9803
%! 1.0000 0.0000
%! 0.0000 0.3665 ];
%!
%! co_e = [ 0.0000 0.0000 0.0000 0.0000 0.0000 2.0000 1.0000
%! 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 2.0000
%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3.0000 ];
%!
%! q_e = [ 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000
%! 0.0000 0.0000 0.0000 0.0000 0.7917 0.0000 -0.6108
%! 0.0000 0.5461 0.1874 -0.5345 0.3770 0.0000 0.4887
%! 0.9008 0.1410 -0.4107 0.0000 0.0000 0.0000 0.0000
%! 0.0000 -0.5461 -0.1874 0.2673 0.4713 0.0000 0.6108
%! 0.0000 -0.5461 -0.1874 -0.8018 -0.0943 0.0000 -0.1222
%! -0.4342 0.2924 -0.8520 0.0000 0.0000 0.0000 0.0000 ];
%!
%! z_e = [ 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000
%! 0.0000 -0.6519 0.2740 0.0000 0.7071 0.0000 0.0000
%! -0.4342 0.3491 0.8304 0.0000 0.0000 0.0000 0.0000
%! 0.0000 0.0000 0.0000 -1.0000 0.0000 0.0000 0.0000
%! 0.9008 0.1683 0.4003 0.0000 0.0000 0.0000 0.0000
%! 0.0000 0.6519 -0.2740 0.0000 0.7071 0.0000 0.0000
%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 ];
%!
%!assert (ao, ao_e, 1e-4);
%!assert (eo, eo_e, 1e-4);
%!assert (bo, bo_e, 1e-4);
%!assert (co, co_e, 1e-4);
%!assert (q, q_e, 1e-4);
%!assert (z, z_e, 1e-4);
%!assert (nobsv, nobsv_e);
## ss2tf conversion by Slicot TB04BD
## Test provided by Slicot
%!shared NUM, DEN, NUMe, DENe
%! A = [ -1.0 0.0 0.0
%! 0.0 -2.0 0.0
%! 0.0 0.0 -3.0 ];
%!
%! B = [ 0.0 1.0 -1.0
%! 1.0 1.0 0.0 ].';
%!
%! C = [ 0.0 1.0 1.0
%! 1.0 1.0 1.0 ];
%!
%! D = [ 1.0 0.0
%! 0.0 1.0 ];
%!
%! [NUM, DEN] = tfdata (ss (A, B, C, D));
%!
%! NUMe = {[1, 5, 7], [1]; [1], [1, 5, 5]};
%!
%! DENe = {[1, 5, 6], [1, 2]; [1, 5, 6], [1, 3, 2]};
%!
%!assert (NUM, NUMe, 1e-4);
%!assert (DEN, DENe, 1e-4);
## ss2tf conversion by Slicot TB04BD
## Trivial test
%!shared NUM, DEN, NUMe, DENe
%! A = [ 0 ];
%!
%! B = [ 1 ];
%!
%! C = [ 1 ];
%!
%! D = [ 0 ];
%!
%! [NUM, DEN] = tfdata (ss (A, B, C, D));
%!
%! NUMe = {[1]};
%!
%! DENe = {[1, 0]};
%!
%!assert (NUM, NUMe, 1e-4);
%!assert (DEN, DENe, 1e-4);
## transfer function to state-space conversion
## test from SLICOT TD04AD
%!shared Mo, Me
%! INDEX = [ 3 3 ];
%!
%! DCOEFF = [ 1.0 6.0 11.0 6.0
%! 1.0 6.0 11.0 6.0 ];
%!
%! UCOEFF = zeros (2, 2, 4);
%!
%! u11 = [ 1.0 6.0 12.0 7.0 ];
%! u12 = [ 0.0 1.0 4.0 3.0 ];
%! u21 = [ 0.0 0.0 1.0 1.0 ];
%! u22 = [ 1.0 8.0 20.0 15.0 ];
%!
%! UCOEFF(1,1,:) = u11;
%! UCOEFF(1,2,:) = u12;
%! UCOEFF(2,1,:) = u21;
%! UCOEFF(2,2,:) = u22;
%!
%! [Ao, Bo, Co, Do] = __sl_td04ad__ (UCOEFF, DCOEFF, INDEX, 0);
%!
%! Ae = [ 0.5000 -0.8028 0.9387
%! 4.4047 -2.3380 2.5076
%! -5.5541 1.6872 -4.1620 ];
%!
%! Be = [ -0.2000 -1.2500
%! 0.0000 -0.6097
%! 0.0000 2.2217 ];
%!
%! Ce = [ 0.0000 -0.8679 0.2119
%! 0.0000 0.0000 0.9002 ];
%!
%! De = [ 1.0000 0.0000
%! 0.0000 1.0000 ];
%!
%! Mo = [Ao, Bo; Co, Do];
%! Me = [Ae, Be; Ce, De];
%!
%!assert (Mo, Me, 1e-4);
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