Home > documentation > qzswitch.m

qzswitch

PURPOSE ^

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

SYNOPSIS ^

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

DESCRIPTION ^

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.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [A,B,Q,Z] = qzswitch(i,A,B,Q,Z)
0002 %function [A,B,Q,Z] = qzswitch(i,A,B,Q,Z)
0003 %
0004 % Takes U.T. matrices A, B, orthonormal matrices Q,Z, interchanges
0005 % diagonal elements i and i+1 of both A and B, while maintaining
0006 % Q'AZ' and Q'BZ' unchanged.  If diagonal elements of A and B
0007 % are zero at matching positions, the returned A will have zeros at both
0008 % positions on the diagonal.  This is natural behavior if this routine is used
0009 % to drive all zeros on the diagonal of A to the lower right, but in this case
0010 % the qz transformation is not unique and it is not possible simply to switch
0011 % the positions of the diagonal elements of both A and B.
0012  realsmall=sqrt(eps)*10;
0013 %realsmall=1e-3;
0014 a = A(i,i); d = B(i,i); b = A(i,i+1); e = B(i,i+1);
0015 c = A(i+1,i+1); f = B(i+1,i+1);
0016         % A(i:i+1,i:i+1)=[a b; 0 c];
0017         % B(i:i+1,i:i+1)=[d e; 0 f];
0018 if (abs(c)<realsmall & abs(f)<realsmall)
0019     if abs(a)<realsmall
0020         % l.r. coincident 0's with u.l. of A=0; do nothing
0021         return
0022     else
0023         % l.r. coincident zeros; put 0 in u.l. of a
0024         wz=[b; -a];
0025         wz=wz/sqrt(wz'*wz);
0026         wz=[wz [wz(2)';-wz(1)'] ];
0027         xy=eye(2);
0028     end
0029 elseif (abs(a)<realsmall & abs(d)<realsmall)
0030     if abs(c)<realsmall
0031         % u.l. coincident zeros with l.r. of A=0; do nothing
0032         return
0033     else
0034         % u.l. coincident zeros; put 0 in l.r. of A
0035         wz=eye(2);
0036         xy=[c -b];
0037         xy=xy/sqrt(xy*xy');
0038         xy=[[xy(2)' -xy(1)'];xy];
0039     end
0040 else
0041     % usual case
0042     wz = [c*e-f*b, (c*d-f*a)'];
0043     xy = [(b*d-e*a)', (c*d-f*a)'];
0044     n = sqrt(wz*wz');
0045     m = sqrt(xy*xy');
0046     if m<eps*100
0047         % all elements of A and B proportional
0048         return
0049     end
0050    wz = n\wz;
0051    xy = m\xy;
0052    wz = [wz; -wz(2)', wz(1)'];
0053    xy = [xy;-xy(2)', xy(1)'];
0054 end
0055 A(i:i+1,:) = xy*A(i:i+1,:);
0056 B(i:i+1,:) = xy*B(i:i+1,:);
0057 A(:,i:i+1) = A(:,i:i+1)*wz;
0058 B(:,i:i+1) = B(:,i:i+1)*wz;
0059 Z(:,i:i+1) = Z(:,i:i+1)*wz;
0060 Q(i:i+1,:) = xy*Q(i:i+1,:);

Generated on Mon 07-Feb-2011 12:06:56 by m2html © 2005