# ordqz

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-λ*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-λ*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.

## See Also

#### Introduced before R2006a

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