naginterfaces.library.lapacklin.dpftrf

naginterfaces.library.lapacklin.dpftrf(transr, uplo, n, ar)[source]

dpftrf computes the Cholesky factorization of a real symmetric positive definite matrix stored in Rectangular Full Packed (RFP) format.

For full information please refer to the NAG Library document for f07wd

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07wdf.html

Parameters
transrstr, length 1

Specifies whether the RFP representation of is normal or transposed.

The matrix is stored in normal RFP format.

The matrix is stored in transposed RFP format.

uplostr, length 1

Specifies whether the upper or lower triangular part of is stored.

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.

nint

, the order of the matrix .

arfloat, array-like, shape

The upper or lower triangular part (as specified by ) of the symmetric matrix , in either normal or transposed RFP format (as specified by ). The storage format is described in detail in the F07 Introduction.

Returns
arfloat, ndarray, shape

If no exception or warning is raised, the factor or from the Cholesky factorization or , in the same storage format as .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

Warns
NagAlgorithmicWarning
(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 . There is no function specifically designed to factorize a symmetric matrix stored in RFP format which is not positive definite; the matrix must be treated as a full symmetric matrix, by calling dsytrf().

Notes

dpftrf forms the Cholesky factorization of a real symmetric positive definite matrix either as if or if , where is an upper triangular matrix and is a lower triangular, stored in RFP format. The RFP storage format is described in the F07 Introduction.

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

Gustavson, F G, Waśniewski, J, Dongarra, J J and Langou, J, 2010, Rectangular full packed format for Cholesky’s algorithm: factorization, solution, and inversion, ACM Trans. Math. Software (37, 2)