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

346 HP MLIB User’s Guide
F_CHER2/F_ZHER2 Hermitian rank-2 update
Name F_CHER2/F_ZHER2
Hermitian rank-2 update
Purpose F_xHER2 performs the Hermitian rank-2 update
where A is a complex Hermitian matrix, α is a complex scalar, is the complex
conjugate of α, x and y are complex n-vectors, and x* and y* are the conjugate
transposes of x and y, respectively. β is a real scalar. The routine returns
immediately if n is less than or equal to zero.
Refer to “SSYR2/DSYR2/CHER2/ZHER2” on page 279 for a description of the
equivalent HP MLIB legacy BLAS subprograms.
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, INCY, LDA, N, UPLO
REAL*4 BETA
COMPLEX*8 ALPHA, A( LDA, * ), X( * ), Y( * )
SUBROUTINE F_CHER2 (UPLO, N, ALPHA, X, INCX, Y, INCY, BETA, A,
LDA)
INTEGER*4 INCX, INCY, LDA, N, UPLO
REAL*8 BETA
COMPLEX*16 ALPHA, A( LDA, * ), X( * ), Y( * )
SUBROUTINE F_ZHER2 (UPLO, N, ALPHA, X, INCX, Y, INCY, BETA, A,
LDA)
VECLIB8
INTEGER*8 INCX, INCY, LDA, N, UPLO
REAL*4 BETA
COMPLEX*8 ALPHA, A( LDA, * ), X( * ), Y( * )
SUBROUTINE F_CHER2 (UPLO, N, ALPHA, X, INCX, Y, INCY, BETA, A,
LDA)
A αxy
∗
ayx
∗
βA with A=A
∗
++←
α