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

344 HP MLIB User’s Guide
F_CHER/F_ZHER Hermitian rank-1 update
Name F_CHER/F_ZHER
Hermitian rank-1 update
Purpose F_xHER performs the Hermitian rank-1 update
where A is an n-by-n complex Hermitian matrix, α is a real scalar, x is a
complex n-vector, and x* is the conjugate transpose of x. The routine returns
immediately if n is less than or equal to zero.
Refer to “SSYR/DSYR/CHER/ZHER” on page 275 for a description of the HP
MLIB legacy BLAS subprogram for rank-1 update.
Matrix
Storage
Because either triangle of A can be obtained from the other, these subprograms
reference and apply the update to only one triangle of A. You can supply either
the upper or the lower triangle of A, 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
INTEGER*4 INCX, LDA, N, UPLO
REAL*4 ALPHA, BETA
COMPLEX*8 A( LDA, * ), X( * )
SUBROUTINE F_CHER (UPLO, N, ALPHA, X, INCX, BETA, A, LDA)
INTEGER*4 INCX, LDA, N, UPLO
REAL*8 ALPHA, BETA
COMPLEX*16 A( LDA, * ), X( * )
SUBROUTINE F_ZHER (UPLO, N, ALPHA, X, INCX, BETA, A, LDA)
VECLIB8
INTEGER*8 INCX, LDA, N, UPLO
REAL*4 ALPHA, BETA
COMPLEX*8 A( LDA, * ), X( * )
SUBROUTINE F_CHER (UPLO, N, ALPHA, X, INCX, BETA, A, LDA)
INTEGER*8 INCX, LDA, N, UPLO
REAL*8 ALPHA, BETA
COMPLEX*16 A( LDA, * ), X( * )
SUBROUTINE F_ZHER (UPLO, N, ALPHA, X, INCX, BETA, A, LDA)
Input UPLO Specifies whether a triangular matrix is upper or lower
triangular. Use either BLAS_UPPER or BLAS_LOWER.
A αxx
∗
βA
∗
with A=A
∗
+←