naginterfaces.library.blas.zhfrk

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

zhfrk performs one of the Hermitian rank- update operations

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

For full information please refer to the NAG Library document for f06wq

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/f06/f06wqf.html

Parameters
transrstr, length 1

Specifies whether the normal RFP representation of or its conjugate transpose is stored.

The matrix is stored in normal RFP format.

The conjugate transpose of the RFP representation of the matrix is stored.

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 .

acomplex, 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 .

ccomplex, array-like, shape

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

Returns
ccomplex, 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.

zhfrk performs one of the Hermitian rank- update operations

where is a complex matrix, is an complex Hermitian 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 zhfrk 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)