Campus Livre
ordqz
Reorders the eigenvalues in a QZ factorization.
Category: Mathematics > Linear Algebra
Syntax
[AS, BS, QS, ZS] = ordqz(AA, BB, Q, Z, select)Reorders (AA, BB) so that the eigenvalues chosen by select come first.
Description
The QZ algorithm triangularizes a matrix pair (A, B); the generalized eigenvalues are the ratios of diagonal entries AA(k,k)/BB(k,k). ordqz swaps diagonal entries so that a chosen group, such as the stable eigenvalues in the left half plane, is gathered at the top. This is needed to split a problem into stable and unstable subsystems.
Input arguments
AA, BB, Q, Z- Outputs of
qz: triangular pair and the transformations. select- A logical vector marking eigenvalues to move to the top left, or a keyword such as
'lhp','rhp','udi'or'udo'.
Output arguments
AS, BS- Reordered triangular pair.
QS, ZS- Updated transformation matrices.
Example
Moving the left half plane eigenvalue first
A = [1 2; 0 -3];
B = eye(2);
[AA, BB, Q, Z] = qz(A, B);
[AS, BS, QS, ZS] = ordqz(AA, BB, Q, Z, 'lhp');
disp(diag(AS) ./ diag(BS))Output
-3.0000
1.0000