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## Copyright (C) 1996, 2000, 2005, 2007
## Auburn University. All rights reserved.
##
##
## This program 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.
##
## This program 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 this program; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} zgreduce (@var{sys}, @var{meps})
## Implementation of procedure REDUCE in (Emami-Naeini and Van Dooren,
## Automatica, # 1982).
## @end deftypefn
function retsys = zgreduce (Asys, meps)
if (nargin != 2)
print_usage ();
endif
## SYS_INTERNAL accesses members of system data structure
is_digital (Asys); # make sure it's pure digital/continuous
exit_1 = 0; # exit_1 = 1 or 2 on exit of loop
if (Asys.n + Asys.nz == 0)
exit_1 = 2; # there are no finite zeros
endif
while (! exit_1)
[Q, R, Pi] = qr (Asys.d); # compress rows of D
Asys.d = Q'*Asys.d;
Asys.c = Q'*Asys.c;
## check row norms of Asys.d
[sig, tau] = zgrownorm (Asys.d, meps);
## disp("=======================================")
## disp(["zgreduce: meps=",num2str(meps), ", sig=",num2str(sig), ...
## ", tau=",num2str(tau)])
## sysout(Asys)
if (tau == 0)
exit_1 = 1; # exit_1 - reduction complete and correct
else
Cb = Db = [];
if (sig)
Cb = Asys.c(1:sig,:);
Db = Asys.d(1:sig,:);
endif
Ct = Asys.c(sig+(1:tau),:);
## compress columns of Ct
[pp, nn] = size (Ct);
rvec = nn:-1:1;
[V, Sj, Pi] = qr (Ct');
V = V(:,rvec);
[rho, gnu] = zgrownorm (Sj, meps);
## disp(["zgreduce: rho=",num2str(rho),", gnu=",num2str(gnu)])
## Cb
## Db
## Ct
## Sj'
if (rho == 0)
exit_1 = 1; # exit_1 - reduction complete and correct
elseif (gnu == 0)
exit_1 = 2; # there are no zeros at all
else
mu = rho + sig;
## update system with Q
M = [Asys.a, Asys.b ];
[nn, mm] = size (Asys.b);
pp = rows(Asys.d);
Vm =[V, zeros(nn,mm); zeros(mm,nn), eye(mm)];
if (sig)
M = [M; Cb, Db];
Vs =[V', zeros(nn,sig); zeros(sig,nn), eye(sig)];
else
Vs = V';
endif
## disp("zgreduce: before transform: M=");
## M
## Vs
## Vm
M = Vs*M*Vm;
## disp("zgreduce: after transform: M=");
## M
## disp("debugging code:")
## Mtmp = [Asys.a Asys.b; Asys.c Asys.d]
## Vl = [V', zeros(nn,mm); zeros(mm,nn),Q]
## Vr =[V,zeros(nn,mm) ; zeros(mm,nn), eye(mm)];
## Mtmpf = Vl*Mtmp*Vr
idx = 1:gnu;
jdx = nn + (1:mm);
sdx = gnu + (1:mu);
Asys.a = M(idx,idx);
Asys.b = M(idx,jdx);
Asys.c = M(sdx,idx);
Asys.d = M(sdx,jdx);
## disp(["zgreduce: resulting system: nn =",num2str(nn)," mu=",num2str(mu)])
## sysout(Asys)
## idx
## jdx
## sdx
endif
endif
endwhile
## disp(["zgreduce: while loop done: exit_1=",num2str(exit_1)]);
if (exit_1 == 2)
## there are no zeros at all!
Asys.a = Asys.b = Asys.c = [];
endif
## update dimensions
if (is_digital (Asys))
Asys.nz = rows (Asys.a);
else
Asys.n = rows (Asys.a);
endif
retsys = Asys;
endfunction
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