64 lines
1.9 KiB
Matlab
64 lines
1.9 KiB
Matlab
% from Chris Sims web site
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% http://eco-072399b.princeton.edu/yftp/gensys/mfiles/QZSWITCH.M
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%
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function [A,B,Q,Z] = qzswitch(i,A,B,Q,Z)
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%function [A,B,Q,Z] = qzswitch(i,A,B,Q,Z)
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%
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% Takes U.T. matrices A, B, orthonormal matrices Q,Z, interchanges
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% diagonal elements i and i+1 of both A and B, while maintaining
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% Q'AZ' and Q'BZ' unchanged. If diagonal elements of A and B
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% are zero at matching positions, the returned A will have zeros at both
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% positions on the diagonal. This is natural behavior if this routine is used
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% to drive all zeros on the diagonal of A to the lower right, but in this case
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% the qz transformation is not unique and it is not possible simply to switch
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% the positions of the diagonal elements of both A and B.
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realsmall=sqrt(eps)*10;
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%realsmall=1e-3;
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a = A(i,i); d = B(i,i); b = A(i,i+1); e = B(i,i+1);
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c = A(i+1,i+1); f = B(i+1,i+1);
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% A(i:i+1,i:i+1)=[a b; 0 c];
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% B(i:i+1,i:i+1)=[d e; 0 f];
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if (abs(c)<realsmall & abs(f)<realsmall)
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if abs(a)<realsmall
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% l.r. coincident 0's with u.l. of A=0; do nothing
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return
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else
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% l.r. coincident zeros; put 0 in u.l. of a
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wz=[b; -a];
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wz=wz/sqrt(wz'*wz);
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wz=[wz [wz(2)';-wz(1)'] ];
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xy=eye(2);
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end
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elseif (abs(a)<realsmall & abs(d)<realsmall)
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if abs(c)<realsmall
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% u.l. coincident zeros with l.r. of A=0; do nothing
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return
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else
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% u.l. coincident zeros; put 0 in l.r. of A
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wz=eye(2);
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xy=[c -b];
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xy=xy/sqrt(xy*xy');
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xy=[[xy(2)' -xy(1)'];xy];
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end
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else
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% usual case
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wz = [c*e-f*b, (c*d-f*a)'];
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xy = [(b*d-e*a)', (c*d-f*a)'];
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n = sqrt(wz*wz');
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m = sqrt(xy*xy');
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if m<eps*100
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% all elements of A and B proportional
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return
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end
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wz = n\wz;
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xy = m\xy;
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wz = [wz; -wz(2)', wz(1)'];
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xy = [xy;-xy(2)', xy(1)'];
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end
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A(i:i+1,:) = xy*A(i:i+1,:);
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B(i:i+1,:) = xy*B(i:i+1,:);
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A(:,i:i+1) = A(:,i:i+1)*wz;
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B(:,i:i+1) = B(:,i:i+1)*wz;
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Z(:,i:i+1) = Z(:,i:i+1)*wz;
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Q(i:i+1,:) = xy*Q(i:i+1,:); |