[RR,PP,SS1,SS2,QQ1,QQ2]=state_set(R,P,S1,S2,Q1,Q2,K)

function [RR,PP,SS1,SS2,QQ1,QQ2]=state_set(R,P,S1,S2,Q1,Q2,K)
%  PURPOSE: set chosen variables as state variables in a model in the
%           state-space form
%
%               y_t     = R u_t + S_1 epsilon_t + S_2 omega_t                                
%               u_t     = P u_t + Q_1 epsilon_t + Q_2 omega_t
%
%           where epsilon_t, omega_t are i.i.d. random variable with zero mean
%           y_t is a vector of endogenous variables, and u_t is a vector of
%           state variables
%
%           This model is transformed to the model
%
%               y_t     = RR v_t + SS_1 epsilon_t + SS_2 omega_t
%               v_t     = PP v_t + QQ_1 epsilon_t + QQ_2 omega_t
%
%           where v_t = [x_t, w_t]', dim(x_t) + dim(w_t) = dim(u_t)
%           and 
%
%               x_t     = K y_t
%           
% ---------------------------------------------------
%  USAGE: [RR,PP,SS1,SS2,QQ1,QQ2] = state_set(R,P,S1,S2,Q1,Q2,K)
%  where: 
%         R,P,S1,S2,Q1,Q2           matrices representing the model,
%         K                         a matrix determining selected state
%                                   variables

%         RR,PP,SS1,SS2,QQ1,QQ2     matrices representing the transformed
%                                   model
%
%   COMMENTS:
%
% Copyright  (c) Pawel Kowal (2006)
% All rights reserved
% LREM_SOLVE toolbox is available free for noncommercial academic use only.
% [e-mail]

%checks whether selected variables may be chosen as state variables
info                    = state_check(K,R);
if info==0
    error('selected variables may not be chosen as state variables');
end

[U,S,V]                 = svd(K*R);
n                       = size(S,1);
S                       = S(:,1:n);
SS                      = diag(diag(S).^-1);

P                       = V'*P*V;
P11                     = P(1:n,1:n);
P12                     = P(1:n,n+1:end);
P21                     = P(n+1:end,1:n);
P22                     = P(n+1:end,n+1:end);

PP                      =[U*S*P11*SS*U' U*S*P12;P21*SS*U' P22];
QQ1                     =[U*S*Q1(1:n,:);Q1(n+1:end,:)];
QQ2                     =[U*S*Q2(1:n,:);Q2(n+1:end,:)];
RR                      =R*[V(:,1:n)*SS*U' V(:,n+1:end)];
SS1                     =S1;
SS2                     =S2;