Documentation of th2arx

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Function Synopsis

[A,B,dA,dB]=th2arx(eta)

Help text

TH2ARX converts a THETA-format model to an ARX-model.
   [A,B]=TH2ARX(TH)

   TH: The model structure defined in the THETA-format (See also TEHTA.)

   A, B : Matrices defining the ARX-structure:

          y(t) + A1 y(t-1) + .. + An y(t-n) = 
          = B0 u(t) + ..+ B1 u(t-1) + .. Bm u(t-m)

          A = [I A1 A2 .. An],  B=[B0 B1 .. Bm]


   With [A,B,dA,dB] = TH2ARX(TH), also the standard deviations
   of A and B, i.e. dA and dB are computed.

   See also ARX2TH, and ARX

Cross-Reference Information

Listing of function th2arx

function [A,B,dA,dB]=th2arx(eta)

%   L. Ljung 10-2-90,3-13-93
%   Copyright (c) 1986-98 by The MathWorks, Inc.
%   $Revision: 2.4 $  $Date: 1997/12/02 03:42:48 $

if nargin < 1
   disp('Usage: [A,B,dA,dB] = TH2ARX(TH)')
   return
end

[Ncap,nd]=getncap(eta);
if ~isthss(eta) 
   [A,B]=th2poly(eta);
   B=B(:)';
   if nargout>2,
      [par,P]=th2par(eta);eta1=eta;eta1(3,1:nd)=par+sqrt(diag(P))';
      [A1,B1]=th2poly(eta1);dA=abs(A-A1);dB=abs(B-B1);   dB=dB(:)';
   end
   return
end

tnr=eta(2,8); if tnr~=3,error('This is not an ARX-model!'),end
etapar=eta(3,1:nd);
arg=getargth(eta);
[rarg,carg]=size(arg);
as1=arg(:,1:rarg);
sumas=sum4vms(as1');
nr=find(sumas==0&~isnan(sumas));
[as,bs,cs,ds]=ssmodx9(etapar,-1,arg);
[ny,nz]=size(cs);[nx,nz]=size(as);[nz,nu]=size(bs);
if isempty(nr),na=nx/ny;else na=(nr(1)-1)/ny;end
if nu>0,nb=(nx-na*ny)/nu;else nb=0;end
A=[eye(ny) -cs(:,1:na*ny)];
if nu>0,B=[ds cs(:,na*ny+1:nx)];else B=[];end
if na==0 & ~any(isnan(arg(:,nx+nu+1:nx+nu+ny))), B=ds;end

if nargout>2
p=diag(eta(4:3+nd,1:nd));p=sqrt(p')+100*eps;
etap1=etapar+p;
[das,dbs,dcs,dds]=ssmodx9(etap1,-1,arg);
dA=abs([eye(ny) -dcs(:,1:na*ny)]-A);
if nu>0,dB=abs([dbs(1:ny,:) dcs(:,na*ny+1:nx)]-B);else dB=[];end
end