naginterfaces.library.lapackeig.ztrexc

naginterfaces.library.lapackeig.ztrexc(compq, t, q, ifst, ilst)

ztrexc reorders the Schur factorization of a complex general matrix.

For full information please refer to the NAG Library document for f08qt

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f08/f08qtf.html

Parameters

compqstr, length 1

Indicates whether the matrix $Q$ of Schur vectors is to be updated.

$compq=\text{'V'}$

The matrix $Q$ of Schur vectors is updated.

$compq=\text{'N'}$

No Schur vectors are updated.

tcomplex, array-like, shape $(n,n)$

The $n\times n$ upper triangular matrix $T$, as returned by zhseqr().

qcomplex, array-like, shape $(:,:)$

Note: the required extent for this argument in dimension 1 is determined as follows: if $compq=\text{'V'}$: $n$; if $compq=\text{'N'}$: $1$; otherwise: $0$.

Note: the required extent for this argument in dimension 2 is determined as follows: if $compq=\text{'V'}$: $n$; if $compq=\text{'N'}$: $1$; otherwise: $0$.

If $compq=\text{'V'}$, $q$ must contain the $n\times n$ unitary matrix $Q$ of Schur vectors.

ifstint

$ifst$ and $ilst$ must specify the reordering of the diagonal elements of $T$. The element with row index $ifst$ is moved to row $ilst$ by a sequence of exchanges between adjacent elements.

ilstint

$ifst$ and $ilst$ must specify the reordering of the diagonal elements of $T$. The element with row index $ifst$ is moved to row $ilst$ by a sequence of exchanges between adjacent elements.

Returns

tcomplex, ndarray, shape $(n,n)$

$t$ is overwritten by the updated matrix $\tilde{T}$.

qcomplex, ndarray, shape $(:,:)$

If $compq=\text{'V'}$, $q$ contains the updated matrix of Schur vectors.

If $compq=\text{'N'}$, $q$ is not referenced.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $compq$.

Constraint: $compq=\text{'V'}$ or $\text{'N'}$.

(errno $-2$)

On entry, error in parameter $\text{n}$.

Constraint: $n\ge 0$.

(errno $-7$)

On entry, error in parameter $ifst$.

Constraint: $1\le ifst\le n$.

(errno $-8$)

On entry, error in parameter $ilst$.

Constraint: $1\le ilst\le n$.

Notes

ztrexc reorders the Schur factorization of a complex general matrix $A=QT{Q}^H$, so that the diagonal element of $T$ with row index $ifst$ is moved to row $ilst$.

The reordered Schur form $\tilde{T}$ is computed by a unitary similarity transformation: $\tilde{T}=Z^{H}TZ$. Optionally the updated matrix $\tilde{Q}$ of Schur vectors is computed as $\tilde{Q}=QZ$, giving $A=\tilde{Q}\tilde{T}{\tilde{Q}}^H$.

References

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore