# naginterfaces.library.lapackeig.zhptrd¶

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

zhptrd reduces a complex Hermitian matrix to tridiagonal form, using packed storage.

For full information please refer to the NAG Library document for f08gs

https://www.nag.com/numeric/nl/nagdoc_29/flhtml/f08/f08gsf.html

Parameters
uplostr, length 1

Indicates whether the upper or lower triangular part of is stored.

The upper triangular part of is stored.

The lower triangular part of is stored.

nint

, the order of the matrix .

apcomplex, array-like, shape

The upper or lower triangle of the Hermitian matrix , packed by columns.

Returns
apcomplex, ndarray, shape

is overwritten by the tridiagonal matrix and details of the unitary matrix .

dfloat, ndarray, shape

The diagonal elements of the tridiagonal matrix .

efloat, ndarray, shape

The off-diagonal elements of the tridiagonal matrix .

taucomplex, ndarray, shape

Further details of the unitary matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

Notes

zhptrd reduces a complex Hermitian matrix , held in packed storage, to real symmetric tridiagonal form by a unitary similarity transformation: .

The matrix is not formed explicitly but is represented as a product of elementary reflectors (see the F08 Introduction for details). Functions are provided to work with in this representation (see Further Comments).

References

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