naginterfaces.library.lapacklin.dpotrf

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

dpotrf computes the Cholesky factorization of a real symmetric positive definite matrix.

For full information please refer to the NAG Library document for f07fd

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07fdf.html

Parameters
uplostr, length 1

Specifies whether the upper or lower triangular part of is stored and how is to be factorized.

The upper triangular part of is stored and is factorized as , where is upper triangular.

The lower triangular part of is stored and is factorized as , where is lower triangular.

afloat, array-like, shape

The symmetric positive definite matrix .

Returns
afloat, ndarray, shape

The upper or lower triangle of is overwritten by the Cholesky factor or as specified by .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

The leading minor of order is not positive definite and the factorization could not be completed. Hence itself is not positive definite. This may indicate an error in forming the matrix . To factorize a symmetric matrix which is not positive definite, call dsytrf() instead.

Notes

dpotrf forms the Cholesky factorization of a real symmetric positive definite matrix either as if or if , where is an upper triangular matrix and is lower triangular.

References

Demmel, J W, 1989, On floating-point errors in Cholesky, LAPACK Working Note No. 14, University of Tennessee, Knoxville, https://www.netlib.org/lapack/lawnspdf/lawn14.pdf

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore