naginterfaces.library.lapackeig.zupgtr

naginterfaces.library.lapackeig.zupgtr(uplo, n, ap, tau)

zupgtr generates the complex unitary matrix $Q$, which was determined by zhptrd() when reducing a Hermitian matrix to tridiagonal form.

For full information please refer to the NAG Library document for f08gt

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f08/f08gtf.html

Parameters

uplostr, length 1

This must be the same argument $uplo$ as supplied to zhptrd().

nint

$n$, the order of the matrix $Q$.

apcomplex, array-like, shape $(n\times (n+1)/2)$

Details of the vectors which define the elementary reflectors, as returned by zhptrd().

taucomplex, array-like, shape $(max(1,n-1))$

Further details of the elementary reflectors, as returned by zhptrd().

Returns

qcomplex, ndarray, shape $(n,n)$

The $n\times n$ unitary matrix $Q$.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $uplo$.

Constraint: $uplo=\text{'U'}$ or $\text{'L'}$.

(errno $-2$)

On entry, error in parameter $n$.

Constraint: $n\ge 0$.

Notes

zupgtr is intended to be used after a call to zhptrd(), which reduces a complex Hermitian matrix $A$ to real symmetric tridiagonal form $T$ by a unitary similarity transformation: $A=QT{Q}^H$. zhptrd() represents the unitary matrix $Q$ as a product of $n-1$ elementary reflectors.

This function may be used to generate $Q$ explicitly as a square matrix.

References

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