HP MLIB User's Guide Vol. 1 7th Ed.

Chapter 3 Basic Matrix Operations 289
Rank-k update SSYRK/DSYRK/CHERK/CSYRK/ZHERK/ZSYRK
Name SSYRK/DSYRK/CHERK/CSYRK/ZHERK/ZSYRK
Rank-k update
Purpose These subprograms apply a rank-k update to a real symmetric, complex
symmetric, or complex Hermitian matrix; specifically they compute
where α and β are scalars, C is an n-by-n real symmetric, complex symmetric,
or complex Hermitian matrix, and A is a matrix whose size, either n-by-k or
k-by-n, depends on which form of the update is requested. Here, A
T
and A* are
the transpose and conjugate transpose of A, respectively.
The structure of C is indicated by the name of the subprogram used:
Matrix
Storage
Because either triangle of C can be obtained from the other, these subprograms
reference and apply the update to only one triangle of C. You can supply either
the upper or the lower triangle of C, in a two-dimensional array large enough to
hold the entire matrix, and the same triangle of the updated matrix is returned
in the array. The other triangle of the array is not referenced.
Usage VECLIB:
CHARACTER*1 uplo, trans
INTEGER*4 n, k, lda, ldc
REAL*4 alpha, beta, a(lda, *), c(ldc, n)
CALL SSYRK(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
CHARACTER*1 uplo, trans
INTEGER*4 n, k, lda, ldc
REAL*8 alpha, beta, a(lda, *), c(ldc, n)
CALL DSYRK(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
CHARACTER*1 uplo, trans
INTEGER*4 n, k, lda, ldc
REAL*4 alpha, beta
COMPLEX*8 a(lda, *), c(ldc, n)
CALL CHERK(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
SSYRK or DSYRK C is a real symmetric matrix
CHERK or ZHERK C is a complex Hermitian matrix
CSYRK or ZSYRK C is a complex symmetric matrix
C αAA
T
←βC,+ C αA
T
A←βC,
C αAA*←βC,+
+
C αA* A←βC,+