# naginterfaces.library.lapacklin.zhetri¶

naginterfaces.library.lapacklin.zhetri(uplo, n, a, ipiv)[source]

zhetri computes the inverse of a complex Hermitian indefinite matrix , where has been factorized by zhetrf().

For full information please refer to the NAG Library document for f07mw

https://www.nag.com/numeric/nl/nagdoc_29.2/flhtml/f07/f07mwf.html

Parameters
uplostr, length 1

Specifies how has been factorized.

, where is upper triangular.

, where is lower triangular.

nint

, the order of the matrix .

acomplex, array-like, shape

Details of the factorization of , as returned by zhetrf().

ipivint, array-like, shape

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

Returns
acomplex, ndarray, shape

The factorization is overwritten by the Hermitian matrix .

If , the upper triangle of is stored in the upper triangular part of the array.

If , the lower triangle of is stored in the lower triangular part of the array.

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

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

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