naginterfaces.library.blas.dsfrk

naginterfaces.library.blas.dsfrk(transr, uplo, trans, k, alpha, a, beta, c)[source]

dsfrk performs one of the symmetric rank- update operations

where is a real matrix, is an real symmetric matrix stored in Rectangular Full Packed (RFP) format, and and are real scalars.

For full information please refer to the NAG Library document for f06wc

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f06/f06wcf.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 in RFP format.

The upper triangular part of is stored in RFP format.

The lower triangular part of is stored in RFP format.

transstr, length 1

Specifies the operation to be performed.

.

.

kint

, the number of columns of if , or the number of rows of if .

alphafloat

The scalar .

afloat, array-like, shape

Note: the required extent for this argument in dimension 1 is determined as follows: if : ; if : ; otherwise: .

Note: the required extent for this argument in dimension 2 is determined as follows: if : ; if : ; otherwise: .

The matrix ; is if , or if . If , is not referenced.

betafloat

The scalar .

cfloat, array-like, shape

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

Returns
cfloat, ndarray, shape

The updated matrix , that is its upper or lower triangular part stored in RFP format.

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: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

dsfrk performs one of the symmetric rank- update operations

where is a real matrix, is an real symmetric matrix stored in Rectangular Full Packed (RFP) format, and and are real scalars. The RFP storage format is described in the F07 Introduction.

If or if and either or then dsfrk returns immediately. If and either or then is set to the zero matrix.

References

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)