# naginterfaces.library.lapackeig.zupgtr¶

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

zupgtr generates the complex unitary matrix , 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://www.nag.com/numeric/nl/nagdoc_29/flhtml/f08/f08gtf.html

Parameters
uplostr, length 1

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

nint

, the order of the matrix .

apcomplex, array-like, shape

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

taucomplex, array-like, shape

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

Returns
qcomplex, ndarray, shape

The unitary matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

Notes

zupgtr is intended to be used after a call to zhptrd(), which reduces a complex Hermitian matrix to real symmetric tridiagonal form by a unitary similarity transformation: . zhptrd() represents the unitary matrix as a product of elementary reflectors.

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

References

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