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

386 HP MLIB User’s Guide
F_SSPR2/F_DSPR2/F_CSPR2/F_ZSPR2 Symmetric rank-2 update
Name F_SSPR2/F_DSPR2/F_CSPR2/F_ZSPR2
Symmetric rank-2 update
Purpose F_xSPR2 performs the symmetric rank-2 update
where A is an n-by-n real symmetric matrix stored in packed form, α and β are
real or complex scalar, is the complex conjugate of α, x and y are real or
complex n-vectors, and x
T
and y
T
are transposes of x and y, respectively.
This F_xSPR2 interface encompasses the legacy BLAS routine SSPR2 with
added functionality for complex symmetric matrices. Refer to
“SSPR2/DSPR2/CHPR2/ZHPR2” on page 259 for a description of the HP MLIB
legacy BLAS subprograms and an illustration of the packed storage of
symmetric or Hermitian matrices.
Matrix
Storage
Because either triangle of A can be obtained from the other, you only need to
provide one triangle of A, either the upper or the lower triangle. Compared to
storing the entire matrix, you save memory by supplying that triangle stored
column-by-column in packed form in a 1-dimensional array (refer to the AP
matrix).
Usage VECLIB
INTEGER*4 INCX, INCY, N, UPLO
REAL*4 ALPHA, BETA
REAL*4 AP( * ), X( * ), Y( * )
SUBROUTINE F_SSPR2 (UPLO, N, ALPHA, X, INCX, Y, INCY, BETA, AP)
INTEGER*4 INCX, INCY, N, UPLO
REAL*8 ALPHA, BETA
REAL*8 AP( * ), X( * ), Y( * )
SUBROUTINE F_DSPR2 (UPLO, N, ALPHA, X, INCX, Y, INCY, BETA, AP)
INTEGER*4 INCX, INCY, N, UPLO
COMPLEX*8 ALPHA, BETA
COMPLEX*8 AP( * ), X( * ), Y( * )
SUBROUTINE F_CSPR2 (UPLO, N, ALPHA, X, INCX, Y, INCY, BETA, AP)
INTEGER*4 INCX, INCY, N, UPLO
COMPLEX*16 ALPHA, BETA
COMPLEX*16 AP( * ), X( * ), Y( * )
SUBROUTINE F_ZSPR2 (UPLO, N, ALPHA, X, INCX, Y, INCY, BETA, AP)
VECLIB*8
A αxy
T
αyx
T
βA with A=A
T
++←
α