function [A,B,Q,Z] = qzswitch(i,A,B,Q,Z)



%function [A,B,Q,Z] = qzswitch(i,A,B,Q,Z)



% Written by Chris Sims


% 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.  Does nothing if ratios of diagonal elements



% in A and B at i and i+1 are the same.  Aborts if diagonal elements of



% both A and B are zero at either position.



%



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); 



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)'];



   A(i:i+1,:) = xy*A(i:i+1,:);



   B(i:i+1,:) = xy*B(i:i+1,:);



   A(:,i:i+1) = A(:,i:i+1)*wz;



   B(:,i:i+1) = B(:,i:i+1)*wz;



   Z(:,i:i+1) = Z(:,i:i+1)*wz;



   Q(i:i+1,:) = xy*Q(i:i+1,:);



end