Documentation of ms2th

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Function Synopsis

theta=ms2th(ms,cd,parval,lambda,T)

Help text

MS2TH  Packages standard state-space parameterizations into the THETA format.
   THETA = MS2TH(MS,CD,PARVAL,LAMBDA,T)

   THETA: The resulting matrix in the THETA format (See help theta)

   MS: The model structure. Specifies which state-space matrix coeff-
   icients that are free and which are fixed (Generated by (See also)
   MODSTRUC or CANFORM)

   CD: CD='c' means a continuous-time model. CD='d' denotes a discrete
   time model (default CD='d'). For continuous time models there are
   two options: CD='czoh' (default) assumes the input to be piecewise
   constant between the samples (u(t)=u(kT) for kT<=t<kT+T)) while
   CD='cfoh' assumes the input to be piecewise linear between the
   samples (u(t) obtained by linear interpolation of the sampled values)
   (Note that, unlike 'foh' in c2dm in the CSTB, no extra delay is
   introduced in this case.)

   PARVAL: The values of the free parameters (Default zeros)
   LAMBDA: The covariance matrix of the innovations (Default Identity)
   T: The sampling interval (Default 1). For continuous time models this
   is the sampling interval of the data to be used for the fit in pem.
   See also ARX2TH, MF2TH, PEM and THETA.

Cross-Reference Information

Listing of function ms2th

function theta=ms2th(ms,cd,parval,lambda,T)

%   L. Ljung 10-2-1990,10-10-93
%   Copyright (c) 1986-98 by The MathWorks, Inc.
%   $Revision: 2.4 $  $Date: 1997/12/02 03:40:14 $

if nargin < 1
   disp('Usage: TH = MS2TH(MS)')
   disp('       TH = MS2TH(MS,CD,PARAMETERS,LAMBDA,T)')
   disp('       CD is one of ''d'', ''c'', ''czoh'', ''cfoh''.')
   return
end

if nargin<5, T=[];end
if nargin<4, lambda=[];end
if nargin<3, parval=[];end
if nargin<2, cd=[];end
if isempty(T),T=1;end
d1=sum(sum(isnan(ms))');
if isempty(parval),parval=zeros(1,d1);end
if isempty(cd), cd='d';end,cd=lower(cd);
if cd(1)~='c' & cd(1)~='d',
  error('CD must start with either ''c''(ontinuous) or ''d''(iscrete)')
end
[nx,nn]=size(ms);nyy=ms(1,nn);
if nyy<0,arx=1;else arx=0;end
[dd1,dd2]=size(parval);
if min(dd1,dd2)>1
   error('The parameters in PARVAL should be given as a row vector;')
end
if dd1>dd2,
  parval=parval.';
end

d=length(parval);
if d~=d1 & ~arx,
  error('Incorrect number of parameter values  have been specified; must be equal to the number of ''NaN'':s in the model structure.')
end

if T<0,
  error('The sampling interval T must be a positive number. Use ''c'' in the second argument to indicate continuous time model.')
end

[rarg,carg]=size(ms);
if cd(1)=='c',theta(1,2)=-abs(T);else theta(1,2)=abs(T);end
if cd(1)=='d',Tmod=-1;else Tmod=abs(T);end
theta(1,6:7)=[rarg,carg];

[a,b,c,Dd,k,x0]=ssmodx9(parval,Tmod,ms);

if ms(1,carg)>0,
   if max(abs(eig(a-k*c)))>1,disp('WARNING: Predictor unstable.'),end
end
[ny,nx]=size(c);[nx,nu]=size(b);
if isempty(lambda),lambda=eye(ny);end
theta(1,1)=det(lambda);
ti=fix(clock);
ti(1)=ti(1)/100;
theta(1,3:5)=[nu ny d];theta(2,1)=theta(1,1);
theta(2,2:6)=ti(1:5);
theta(2,7)=21;
if cd(1)=='c',
   if strcmp(cd,'cfoh')
      theta(2,8)=11;
   else
      theta(2,8)=1;
   end
else
   theta(2,8)=2;
end
if d>0,
        theta(3,1:d)=parval;
end
theta(4+d:3+d+rarg,1:carg)=ms;
theta(4+d+rarg:3+ny+d+rarg,1:ny)=lambda;