The routine may be called by the names f06wqf, nagf_blas_zhfrk or its LAPACK name zhfrk.
f06wqf 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 Section 3.3.3 in the F07 Chapter Introduction.
If or if and either or then f06wqf returns immediately. If and either or then is set to the zero matrix.
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. Software37, 2
1: – Character(1)Input
On entry: 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.
2: – Character(1)Input
On entry: 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.
3: – Character(1)Input
On entry: specifies the operation to be performed.
4: – IntegerInput
On entry: , the order of the matrix .
5: – IntegerInput
On entry: , the number of columns of if , or the number of rows of if .
6: – Real (Kind=nag_wp)Input
On entry: the scalar .
7: – Complex (Kind=nag_wp) arrayInput
Note: the second dimension of the array a
must be at least
if and at least if .
On entry: the matrix ; is if , or if . If , a is not referenced.
8: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06wqf is called.
if , ;
if , .
9: – Real (Kind=nag_wp)Input
On entry: the scalar .
10: – Complex (Kind=nag_wp) arrayInput/Output
On entry: the upper or lower triangular part (as specified by uplo) of the Hermitian matrix , stored in RFP format (as specified by transr). The storage format is described in detail in Section 3.3.3 in the F07 Chapter Introduction.
On exit: the updated matrix , that is its upper or lower triangular part stored in RFP format.
6Error Indicators and Warnings
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f06wqf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
This example reads in the lower triangular part of a symmetric matrix which it converts to RFP format. It also reads in , and a matrix and then performs the Hermitian rank- update .