The routine may be called by the names f06wcf, nagf_blas_dsfrk or its LAPACK name dsfrk.
f06wcf 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 Section 3.3.3 in the F07 Chapter Introduction.
If or if and either or then f06wcf 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 RFP representation of is normal or transposed.
The matrix is stored in normal RFP format.
The matrix is stored in transposed RFP format.
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: – Real (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 f06wcf is called.
if , ;
if , .
9: – Real (Kind=nag_wp)Input
On entry: the scalar .
10: – Real (Kind=nag_wp) arrayInput/Output
On entry: the upper or lower triangular part (as specified by uplo) of the symmetric 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.
f06wcf 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 symmetric rank- update .