MATLAB Function Reference |
Reorder eigenvalues in QZ factorization
Syntax
[AAS,BBS,QS,ZS] = ordqz(AA,BB,Q,Z,select) [...] = ordqz(AA,BB,Q,Z,keyword) [...] = ordqz(AA,BB,Q,Z,clusters)
Description
[AAS,BBS,QS,ZS] = ordqz(AA,BB,Q,Z,select)
reorders the QZ factorizations Q*A*Z = AA
and Q*B*Z = BB
produced by the qz
function for a matrix pair (A,B)
. It returns the reordered pair (AAS,BBS)
and the cumulative orthogonal transformations QS
and ZS
such that QS*A*ZS = AAS
and QS*B*ZS = BBS
. In this reordering, the selected cluster of eigenvalues appears in the leading (upper left) diagonal blocks of the quasitriangular pair (AAS,BBS)
, and the corresponding invariant subspace is spanned by the leading columns of ZS
. The logical vector select
specifies the selected cluster as E(select)
where E
is the vector of eigenvalues as they appear along the diagonal of AA-*BB
.
Note
To extract E from AA and BB , use ordeig(BB) , instead of eig . This ensures that the eigenvalues in E occur in the same order as they appear on the diagonal of AA-*BB .
|
[...] = ordqz(AA,BB,Q,Z,keyword)
sets the selected cluster to include all eigenvalues in the region specified by keyword
:
keyword |
Selected Region |
'lhp' |
Left-half plane (real(E) < 0 ) |
'rhp' |
Right-half plane (real(E) > 0 ) |
'udi' |
Interior of unit disk (abs(E) < 1 ) |
'udo' |
Exterior of unit disk (abs(E) > 1 ) |
[...] = ordqz(AA,BB,Q,Z,clusters)
reorders multiple clusters at once. Given a vector clusters
of cluster indices commensurate with E = ordeig(AA,BB)
, such that all eigenvalues with the same clusters
value form one cluster, ordqz
sorts the specified clusters in descending order along the diagonal of (AAS,BBS)
. The cluster with highest index appears in the upper left corner.
Algorithm
For full matrices AA
and BB
, qz
uses the LAPACK routines listed in the following table.
AA and BB Real |
AA or BB Complex |
|
A and B double |
DTGSEN |
ZTGSEN |
A or B single |
STGSEN |
CTGSEN |
See Also
orderfields | ordschur |
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