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

Chapter 3 Basic Matrix Operations 275
Rank-1 update SSYR/DSYR/CHER/ZHER
Name SSYR/DSYR/CHER/ZHER
Rank-1 update
Purpose These subprograms compute the real symmetric or complex Hermitian rank-1
update
where A is an n-by-n real symmetric or complex Hermitian matrix, α is a real
scalar, x is a real or complex n-vector, and x* is the conjugate transpose of x.
(The conjugate transpose of a real vector is simply the transpose.)
The structure of A is indicated by the name of the subprogram used:
Refer to “F_SSYR/F_DSYR/F_CSYR/F_ZSYR” on page 392, and
“F_CHER/F_ZHER” on page 344 for equivalent BLAS Standard 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:
CHARACTER*1 uplo
INTEGER*4 n, lda, incx
REAL*4 alpha, a(lda, n), x(lenx)
CALL SSYR(uplo, n, alpha, x, incx, a, lda)
CHARACTER*1 uplo
INTEGER*4 n, lda, incx
REAL*8 alpha, a(lda, n), x(lenx)
CALL DSYR(uplo, n, alpha, x, incx, a, lda)
CHARACTER*1 uplo
INTEGER*4 n, lda, incx
REAL*4 alpha
COMPLEX*8 a(lda, n), x(lenx)
CALL CHER(uplo, n, alpha, x, incx, a, lda)
SSYR or DSYR A is a real symmetric matrix
CHER or ZHER A is a complex Hermitian matrix
A αxx*← A,+