naginterfaces.library.lapacklin.dpotri

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

dpotri computes the inverse of a real symmetric positive definite matrix , where has been factorized by dpotrf().

For full information please refer to the NAG Library document for f07fj

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07fjf.html

Parameters
uplostr, length 1

Specifies how has been factorized.

, where is upper triangular.

, where is lower triangular.

afloat, array-like, shape

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

Returns
afloat, 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

dpotri is used to compute the inverse of a real symmetric positive definite matrix , the function must be preceded by a call to dpotrf(), 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