function [S,T,Q,Z] = qzswitch(i,S,T,Q,Z)

%
% Written by Chris Sims
% Takes U.T. matrices S, T, orthonormal matrices Q,Z, interchanges
% diagonal elements i and i+1 of both S and T, while maintaining
% Q'SZ' and Q'TZ' unchanged.  Does nothing if ratios of diagonal elements
% in S and T at i and i+1 are the same.  Aborts if diagonal elements of
% both S and T are zero at either position.
%

a = S(i,i); d = T(i,i); b = S(i,i+1); e = T(i,i+1);
c = S(i+1,i+1); f = T(i+1,i+1); 
wz = [c*e-f*b, (c*d-f*a)'];
xy = [(b*d-e*a)', (c*d-f*a)'];
n = sqrt(wz*wz');
m = sqrt(xy*xy');

if n == 0
   return
else
   wz = n\wz;
   xy = m\xy;
   wz = [wz; -wz(2)', wz(1)'];
   xy = [xy;-xy(2)', xy(1)'];
   S(i:i+1,:) = xy*S(i:i+1,:);
   T(i:i+1,:) = xy*T(i:i+1,:);
   S(:,i:i+1) = S(:,i:i+1)*wz;
   T(:,i:i+1) = T(:,i:i+1)*wz;
   Z(:,i:i+1) = Z(:,i:i+1)*wz;
   Q(i:i+1,:) = xy*Q(i:i+1,:);
end