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eta=mvarx(z,nn,maxsize,Tsamp);
MVARX Estimates (multivariate) ARX-models
Auxiliary routine to ARX
TH = mvarx(Z,[NA NB NK])
Z: The output-input data Z = [Y U] with the outputs Y
and the inputs U arranged in column vectors
[NA NB NK]: defines the model structure as follows:
NA: an ny|ny matrix whose i-j entry is the order of the
polynomial (in the delay operator) that relates the
j:th output to the i:th output
NB: an ny|nu matrix whose i-j entry is the order of the
polynomial that related the j:th input to the i:th output
NK: an ny|nu matrix whose i-j entry is the delay from
the j:th input to the i:th output
(ny: the number of outputs, nu: the number of inputs)
Each row of [NA NB NK] is thus consistent with the way
single output ARX structures is defined (See Help ARX)
TH: the resulting model, given in the THETA-format (see HELP THETA)
With TH=mvarx(Z,[NA NB NK],MAXSIZE,T) some additional
options can be achieved. See HELP AUXVAR for details
| This function calls | This function is called by |
|---|---|
function eta=mvarx(z,nn,maxsize,Tsamp);
%
% L. Ljung 10-2-90
% Copyright (c) 1986-98 by The MathWorks, Inc.
% $Revision: 3.3 $ $Date: 1997/12/02 03:42:38 $
[nnr,nnc]=size(nn);
ny=nnr;nu=(nnc-ny)/2;
[Ncap,nz]=size(z);
if nz>Ncap,error(' Data should be organized in column vectors!'),return,end
if nz~=(nu+ny),
disp(' Incorrect number of orders specified!'),
disp('For an AR-model nn=na'),
disp('For an ARX-model, nn=[na nb nk]'),
error('see above'),return
end
na=nn(:,1:ny);
if nu>0,nb=nn(:,ny+1:ny+nu);else nb=zeros(ny,1);end
if nu>0,nk=nn(:,ny+nu+1:nnc);else nk=zeros(ny,1);end
nma=max(max(na)');nbkm=max(max(nb+nk)')-1;nkm=min(min(nk)');
nd=sum(sum(na)')+sum(sum(nb)');
n=nma*ny+(nbkm-nkm+1)*nu;
% *** Set up default values **
maxsdef=idmsize(Ncap,nd);
if nargin<4, Tsamp=1;end
if nargin<3, maxsize=maxsdef;end
if isempty(Tsamp),Tsamp=1;end,if Tsamp<0,Tsamp=1;end % Changed T to Tsamp, JNL 9/19/91
if isempty(maxsize),maxsize=maxsdef;end,if maxsize<0, maxsize=maxsdef; end
% *** construct regression matrix ***
nmax=max([nma nbkm]');
M=floor(maxsize/n);
R=zeros(n);F=zeros(n,ny);
for k=nmax:M:Ncap
if min(Ncap,k+M)<k+1,ntz=0;else ntz=1;end
if ntz,jj=(k+1:min(Ncap,k+M));phi=zeros(length(jj),n);end
for kl=1:nma,
if ntz,
phi(:,(kl-1)*ny+1:kl*ny)=z(jj-kl,1:ny);
end
end
ss=nma*ny;
for kl=nkm:nbkm,
if ntz
phi(:,ss+(kl-nkm)*nu+1:ss+(kl-nkm+1)*nu)=z(jj-kl,ny+1:nz);
end
end
if ntz,R=R+phi'*phi; F=F+phi'*z(jj,1:ny);end
end
%
% *** compute loss functions ***
%
par=[];parb=[];p11=[];p12=[];p22=[];lamm=[];
for outp=1:ny
rowind=[];
for kk=1:ny
rowind=[rowind kk:ny:ny*na(outp,kk)];
end
for kk=1:nu
baslev=nma*ny+(nk(outp,kk)-nkm)*nu;
rowind=[rowind baslev+kk:nu:baslev+nu*nb(outp,kk)];
end
rowind=sort(rowind);
if Ncap>M,
th=R(rowind,rowind)\F(rowind,outp);
else
th=phi(:,rowind)\z(jj,outp);
end
pth=inv(R(rowind,rowind));
LAM=(z(nmax+1:Ncap,outp)'*z(nmax+1:Ncap,outp)-F(rowind,outp)'*pth*...
F(rowind,outp))/(Ncap-nmax);
pth=LAM*pth;
lamm=[[lamm,zeros(length(lamm),1)];[zeros(1,length(lamm)),LAM]];
k00=sum((nk(outp,:)==0).*(nb(outp,:)>0));
naux=sum(na(outp,:));
ind1=1:naux;ind2=naux+k00+1:length(th);ind3=naux+1:naux+k00;
par=[par th(ind1).' th(ind2).'];parb=[parb th(ind3).'];
[sp11,ssp11]=size(p11);lni=length(ind1)+length(ind2);
p11=[[p11,zeros(sp11,lni)];[zeros(lni,sp11),...
[[pth(ind1,ind1),pth(ind1,ind2)];...
[pth(ind2,ind1),pth(ind2,ind2)]]]];
[sp12,ssp12]=size(p12);
[sp22,ssp22]=size(p22);
p12=[[p12,zeros(sp11,length(ind3))];[zeros(lni,ssp12),...
[pth(ind1,ind3);pth(ind2,ind3)]]];
p22=[[p22,zeros(sp22,length(ind3))];...
[zeros(length(ind3),ssp22),pth(ind3,ind3)]];
end
eta=mketaarx(nn,[par parb],lamm,Tsamp);
eta(2,7)=31;e=pe(z,eta); lamm=e'*e/(Ncap-nmax);
pvar=[[p11,p12];[p12',p22]];
d=length([par parb]);
eta(4:3+d,1:d)=pvar;rarg=eta(1,6);
eta(4+d+rarg:3+ny+d+rarg,1:ny)=lamm;eta(1,1)=det(lamm);
eta(2,1)=eta(1,1)*(1+nd/Ncap)/(1-nd/Ncap);