naginterfaces.library.lapacklin.zpptri

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

zpptri computes the inverse of a complex Hermitian positive definite matrix , where has been factorized by zpptrf(), using packed storage.

For full information please refer to the NAG Library document for f07gw

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07gwf.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 Cholesky factor of stored in packed form, as returned by zpptrf().

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 )

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

Notes

zpptri is used to compute the inverse of a complex Hermitian positive definite matrix , the function must be preceded by a call to zpptrf(), which computes the Cholesky factorization of , using packed storage.

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