function [A,B,Q,Z] = qzswitch(i,A,B,Q,Z)
%function [A,B,Q,Z] = qzswitch(i,A,B,Q,Z)
%
% Takes U.T. matrices A, B, orthonormal matrices Q,Z, interchanges
% diagonal elements i and i+1 of both A and B, while maintaining
% Q'AZ' and Q'BZ' unchanged. If diagonal elements of A and B
% are zero at matching positions, the returned A will have zeros at both
% positions on the diagonal. This is natural behavior if this routine is used
% to drive all zeros on the diagonal of A to the lower right, but in this case
% the qz transformation is not unique and it is not possible simply to switch
% the positions of the diagonal elements of both A and B.
realsmall=sqrt(eps)*10;
%realsmall=1e-3;
a = A(i,i); d = B(i,i); b = A(i,i+1); e = B(i,i+1);
c = A(i+1,i+1); f = B(i+1,i+1);
% A(i:i+1,i:i+1)=[a b; 0 c];
% B(i:i+1,i:i+1)=[d e; 0 f];
if (abs(c)