Documentation of zp

Global Index (short | long) | Local contents | Local Index (short | long)

Function Synopsis

[zepo,Kg]=zp(th,ku,ky,thresh)

Help text

ZP     Computes zeros, poles and static gains associated with a model

   [ZEPO,K] = zp(TH)

   For a model defined by TH (in the format described by HELP THETA)
   ZEPO is returned as the zeros and poles and K as the static gains
   of the model. The first rows in these matrices contain integers with
   information about the column in question. For the zeros and the gains
   this integer is simply the input number, while for the poles it is
   20 + the input number. The noise source e is in this context counted
   as input number 0. For multi-output models, 1000*(output # - 1) is
   added to these numbers.

   With  [ZEPO,K] = zp(TH,KU,KY) the zeros and poles associated with
   the input and output numbers given by the entries of the row vectors
   KU and KY, respectively, are computed.
   Default values: KU=[1:number of inputs], KY=[1:number of outputs].
   Noise input from source ke is counted as input # -ke.
   Input number 0 means all noise sources.
   The zeros and poles can be plotted by ZPPLOT. zpplot(zp(TH)) is a
   possible construction.
   See also th2zp.

Cross-Reference Information

Listing of function zp

function [zepo,Kg]=zp(th,ku,ky,thresh)

%   L. Ljung 10-1-86, revised 7-3-87,1-16-94.
%   Copyright (c) 1986-98 by The MathWorks, Inc.
%   $Revision: 2.3 $  $Date: 1997/12/02 03:42:17 $

% *** Set up default values ***
if nargin<4, thresh=[];end
if nargin<3, ky=[];end
if nargin<2, ku=[];end
if isempty(thresh),thresh=100000;end
if isthss(th)
    pars=th2par(th);
    if any(abs(imag(pars))>eps),cplx=1;else cplx=0;end
    if exist('ss2zp')&~cplx
       eval('[zepo,Kg]=zpss(th,ku,ky,thresh);')
    else
       eval('[zepo,Kg]=zpssnosp(th,ku,ky,thresh);')
    end
    return
end
nu=th(1,3);
if nu==0,kudef=0;else kudef=1:nu;end
if isempty(ku), ku=kudef;end
if any(ku==-1), ku(find(ku==-1))=0;end
if max(ku)>nu | min(ku)<0, error('Input indices outside # of inputs in theta')
return,end


   [a,b,c,d,f]=polyform(th);


  if length(find(ku==0))>0
       b(nu+1,1:length(c))=c;
       f(nu+1,1:length(d))=d;
  end

  [n1,nb]=size(b); [n1,nf]=size(f);

  nzp=max(nb-1,nf+length(a)-2);

 zepo=zeros(nzp+1,2*length(ku))+inf;

      cc=1;
    for k=ku
      if k<=0,k1=501;k=nu+1;else k1=k;end
      zepo(1,cc:cc+1)=[k1 20+k1];Kg(1,(cc+1)/2)=k1;
      dg=conv(a,f(k,:));
      zb=roots(b(k,:)); nzb=length(zb);
            kind=find(abs(zb)>thresh);
            if ~isempty(kind),zb(kind)=inf*ones(length(kind),1);end
      if nzb>0, zepo(2:nzb+1,cc)=zb;end
      zg=roots(dg); nzg=length(zg);
      if nzg>0, zepo(2:nzg+1,cc+1)=zg;end
      [tmp1,tmp2]=size(b(k,:));
      [md,nd] = size(dg);
      Kg(2,(cc+1)/2)=(b(k,:)*ones(tmp1,tmp2)')/(dg*ones(md,nd)');
      cc=cc+2;
    end
zepo(1,:)=sign(gett(th))*zepo(1,:);