% DEC2MAT   Extract matrix variable value from vector of decision variables
%
%   X = DEC2MAT(LMISYS,DECVARS,XID) returns the value of the matrix 
%   variable with identifier XID (see LMIVAR) given the LMI system 
%   description LMISYS and the vector DECVARS of decision variable values.
%   This command is useful to convert the output of LMI solvers back into
%   individual matrix variables.
%
%   See also  MAT2DEC, DECINFO, DECNBR, LMIVAR.

% Authors: P. Gahinet and A. Nemirovski 3/95
% Copyright 1995-2004 The MathWorks, Inc.
%       $Revision: 1.1.6.1 $

function X=dec2mat(LMIsys,decvars,k);


if nargin ~= 3,
  error('usage: X = dec2mat(LMISYS,decvars,k)');
elseif size(LMIsys,1)<10 | size(LMIsys,2)>1,
  error('LMISYS is an incomplete LMI system description');
elseif any(LMIsys(1:8)<0),
  error('LMISYS is not an LMI description');
end



decvars=decvars(:);
decn=decnbr(LMIsys);
if length(decvars)~=decn,
  error(sprintf('DECVARS must be a vector of length %d',decn));
end


[LMI_set,LMI_var]=lmiunpck(LMIsys);

if isempty(LMI_var),
  error('No matrix variable description in LMISYS');
elseif isempty(k),
  error('K must be nonempty');
elseif k<=0 | k>max(LMI_var(1,:)),
  error('K is out of range');
end


varrec=LMI_var(:,find(LMI_var(1,:)==k));
type=varrec(2);
base=varrec(3); last=varrec(4);
row=varrec(5);   col=varrec(6);

lfreev=length(decvars);


if type==1,

  if base>=lfreev | last>lfreev,
     error('Length of DECVARS too short!');
  end

  nblocks=varrec(7);
  struct=varrec(8:7+2*nblocks);
  decvars=decvars(base+1:last);
  first=1; X=[];

  for k=1:nblocks,
     siz=struct(2*k-1);
     if struct(2*k)==0,		% scalar block
	X=mdiag(X,decvars(first)*eye(siz,siz));
	first=first+1;
     elseif struct(2*k)==1,     % full symmetric bloc
	nvar=siz*(siz+1)/2;
	X=mdiag(X,ve2ma(decvars(first+(0:nvar-1)),1));
	first=first+nvar;
     else                       % zero block
        X=mdiag(X,zeros(siz));
     end
  end

elseif type==2,		% rectangular

  if base>=lfreev | last>lfreev,
     error('Length of DECVARS too short!');
  end

  X=ve2ma(decvars(base+(1:row*col)),2,[row,col]);

else			% special

  struct=varrec(7:6+row*col);

  if ~isempty(find(struct>lfreev)),
     error('Length of DECVARS too short!');
  end

  decvars=[0 ; decvars];
  X=decvars(abs(struct)+ones(size(struct)));
  X=ve2ma(sign(struct).*X,2,[row,col]);

end