model_reduction(A,B,method)

function [Abar,Bbar,Q] = model_reduction(A,B,method)
%  PURPOSE: reduces dimension of the problem of finding matrices R, P,  such that AR = BRP
%
%           this problem is transformed to the problem of finding matrices
%           T, P such that Abar T = BBar T P
%           then R = Q T
%
% ---------------------------------------------------
%  USAGE: [Abar,Bbar,Q]=model_reduction(A,B,method)
%  where: 
%         A,B                       quadratic matrices, such that the
%                                   matrix pair (A,B) is regular
%         method                    method to calculate null spaces
%                                       1 - qr with pivoting
%                                       2 - svd
%
%         Abar,Bbar                 quadratic matrice forming lower dimension problem
%         Q                         matrix that determines solution to the
%                                   original problem
%
%   COMMENTS:
%
% Copyright  (c) Pawel Kowal (2006)
% All rights reserved
% LREM_SOLVE toolbox is available free for noncommercial academic use only.
% [e-mail]

[B,U,k]                         = putv(B,method);
A                               = U'*A;    
Q                               = null2(A(k+1:end,:),method);
Abar                            = A(1:k,:)*Q;      
Bbar                            = B*Q;

if size(Abar,1)~=size(Abar,2)
    error('The model is not regular');
end