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

Chapter 3 Basic Matrix Operations 259
Rank-2 update SSPR2/DSPR2/CHPR2/ZHPR2
Name SSPR2/DSPR2/CHPR2/ZHPR2
Rank-2 update
Purpose These subprograms compute the real symmetric or complex Hermitian rank-2
update
where A is an n-by-n real symmetric or complex Hermitian matrix stored in
packed form as described in “Matrix Storage,” α is a complex scalar, is the
complex conjugate of α, x and y are real or complex n-vectors, and x* and y* are
the conjugate transposes of x and y, respectively. (The conjugate of a real scalar
is just the scalar, and 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_SSPR2/F_DSPR2/F_CSPR2/F_ZSPR2” on page 386 and
“F_CHPR2/F_ZHPR2” on page 352 for a description of the equivalent BLAS
Standard subprograms.
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.
The following examples illustrate the packed storage of symmetric or
Hermitian matrices.
SSPR2 or DSPR2 A is a real symmetric matrix
CHPR2 or ZHPR2 A is a complex Hermitian matrix
A αxy*←αyx* A,++
α