naginterfaces.library.lapacklin.zhptri

naginterfaces.library.lapacklin.zhptri(uplo, n, ap, ipiv)[source]

zhptri computes the inverse of a complex Hermitian indefinite matrix , where has been factorized by zhptrf(), using packed storage.

For full information please refer to the NAG Library document for f07pw

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07pwf.html

Parameters
uplostr, length 1

Specifies how has been factorized.

, where is upper triangular.

, where is lower triangular.

nint

, the order of the matrix .

apcomplex, array-like, shape

The factorization of stored in packed form, as returned by zhptrf().

ipivint, array-like, shape

Details of the interchanges and the block structure of , as returned by zhptrf().

Returns
apcomplex, ndarray, shape

The factorization is overwritten by the matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

Element of the diagonal is exactly zero. is singular and the inverse of cannot be computed.

Notes

zhptri is used to compute the inverse of a complex Hermitian indefinite matrix , the function must be preceded by a call to zhptrf(), which computes the Bunch–Kaufman factorization of , using packed storage.

If , and is computed by solving for .

If , and is computed by solving for .

References

Du Croz, J J and Higham, N J, 1992, Stability of methods for matrix inversion, IMA J. Numer. Anal. (12), 1–19