function [A,B,Q,Z] = PI_qzdiv(stake,A,B,Q,Z)
%function [A,B,Q,Z] = PI_qzdiv(stake,A,B,Q,Z)
%
% Takes U.T. matrices A, B, orthonormal matrices Q,Z, rearranges them
% so that all cases of abs(B(i,i)/A(i,i))>stake are in lower right
% corner, while preserving U.T. and orthonormal properties and Q'AZ' and
% Q'BZ'.

% Original file downloaded from:
% http://sims.princeton.edu/yftp/gensys/mfiles/qzdiv.m

% Copyright © 1993-2007 Christopher Sims
% Copyright © 2008-2024 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare.  If not, see <https://www.gnu.org/licenses/>.

[n, ~] = size(A);
root = abs([diag(A) diag(B)]);
root(:,1) = root(:,1)-(root(:,1)<1.e-13).*(root(:,1)+root(:,2));
root(:,2) = root(:,2)./root(:,1);
for i = n:-1:1
    m=0;
    for j=i:-1:1
        if (root(j,2) > stake || root(j,2) < -.1)
            m=j;
            break
        end
    end
    if (m==0)
        return
    end
    for k=m:1:i-1
        [A, B, Q, Z] = PI_qzswitch(k,A,B,Q,Z);
        tmp = root(k,2);
        root(k,2) = root(k+1,2);
        root(k+1,2) = tmp;
    end
end
