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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA -
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
function [nt,dt,rk]=trzeros(Sl)
//Transmission zeros of Sl = nt./dt
// Syntax : [nt,dt]=trzeros(Sl)
//!
[LHS,RHS]=argn(0);
sltyp=typeof(Sl)
if sltyp == "polynomial" then
D=Sl;
[m,n]=size(D);
if m<>n then
error(msprintf(gettext("%s: Wrong size for input argument #%d: Square matrix expected.\n"),"trzeros",1));
return;
end
chis=det(D);nt=roots(chis);dt=ones(nt);
if LHS==1 then
nt=nt./dt;dt=[];rk=[];
end
return;
end
if sltyp == "rational" then
if size(Sl)==1 then
nt=roots(Sl("num"));dt=[];rk=1;
return;
end
Sl=tf2ss(Sl);
end
if typeof(Sl)<>"state-space" then
error(msprintf(gettext("%s: Wrong type for input argument #%d: A linear dynamical system or a polynomial expected.\n"),"trzeros",1))
end
//Sl=minss(Sl);
[A,B,C,D]=Sl(2:5);
if type(D)==2 then
[m,n]=size(D);
if m<>n then
error(msprintf(gettext("%s: Wrong size for input argument #%d: Square system expected.\n"),"trzeros",1));
end
chis=det(systmat(Sl));nt=roots(chis);dt=ones(nt);
if LHS==1 then nt=nt./dt;dt=[];rk=[];end
return;
end
if size(A,"*")==0 then
if type(D)==1 then nt=[];dt=[];return;end;
if type(D)==2 then
[m,n]=size(D);
if m<>n then
error(msprintf(gettext("%s: Wrong size for input argument #%d: Square system expected.\n"),"trzeros",1));
end
chis=det(D);nt=roots(chis);dt=ones(nt);
if LHS==1 then nt=nt./dt;dt=[];rk=[];end
return;
end;
end;
[ld,kd]=size(D);
if norm(D,1)<sqrt(%eps)|ld==kd then
[nt,dt,rk]=tr_zer(A,B,C,D);
if norm(dt,1) > 1.d-10 then
if LHS==1 then nt=nt./dt;dt=[];rk=[];end
return;
end
end
if ld < kd & norm(D*pinv(D)-eye(),1)< 1.d-10
//nt=spec(A-B*pinv(D)*C);dt=ones(nt);
[nt,dt]=tr_zer(A,B,C,D);
rk=ld;
if LHS==1 then nt=nt./dt;end;
return;
end
if ld > kd & norm(pinv(D)*D-eye(),1)< 1.d-10
//nt=spec(A-B*pinv(D)*C);dt=ones(nt);
[nt,dt]=tr_zer(A,B,C,D);
rk=kd;
if norm(dt,1) > 1.d-10 then
if LHS==1 then nt=nt./dt;dt=[];rk=[];end;return;
end
end
//warning('Trzeros:non-square system with D non zero and not full')
//By kronecker form
s=poly(0,"s");
syst_matrix=systmat(Sl); //form system matrix
[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(syst_matrix);
ix=Qd(1)+Qd(2)+1:Qd(1)+Qd(2)+Qd(3);
iy=Zd(1)+Zd(2)+1:Zd(1)+Zd(2)+Zd(3);
finitepencil=Q(ix,:)*syst_matrix*Z(:,iy);
[E,A]=pen2ea(finitepencil);
[nt,dt]=spec(A,E);rk=[];
if LHS==1 then nt=nt./dt;dt=[];rk=[];end;
endfunction
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