naginterfaces.library.lapacklin.zpotri

naginterfaces.library.lapacklin.zpotri(uplo, a)[source]

zpotri computes the inverse of a complex Hermitian positive definite matrix , where has been factorized by zpotrf().

For full information please refer to the NAG Library document for f07fw

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07fwf.html

Parameters
uplostr, length 1

Specifies how has been factorized.

, where is upper triangular.

, where is lower triangular.

acomplex, array-like, shape

The upper triangular matrix if or the lower triangular matrix if , as returned by zpotrf().

Returns
acomplex, ndarray, shape

is overwritten by the upper triangle of if ; is overwritten by the lower triangle of if .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

Diagonal element of the Cholesky factor is zero; the Cholesky factor is singular and the inverse of cannot be computed.

Notes

zpotri is used to compute the inverse of a complex Hermitian positive definite matrix , the function must be preceded by a call to zpotrf(), which computes the Cholesky factorization of .

If , and is computed by first inverting and then forming .

If , and is computed by first inverting and then forming .

References

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