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

Chapter 3 Basic Matrix Operations 385
Symmetric packed rank-1 update F_SSPR/F_DSPR/F_CSPR/F_ZSPR
INTEGER*8 INCX, N, UPLO
REAL*8 ALPHA, BETA, AP( * ), X( * )
SUBROUTINE F_DSPR (UPLO, N, ALPHA, X, INCX, BETA, AP)
INTEGER*8 INCX, N, UPLO
COMPLEX*8 ALPHA, BETA, AP( * ), X( * )
SUBROUTINE F_CSPR (UPLO, N, ALPHA, X, INCX, BETA, AP)
INTEGER*8 INCX, N, UPLO
COMPLEX*16 ALPHA, BETA, AP( * ), X( * )
SUBROUTINE F_ZSPR (UPLO, N, ALPHA, X, INCX, BETA, AP)
Input UPLO Specifies whether a triangular matrix is upper or lower
triangular. Use either BLAS_UPPER or BLAS_LOWER.
N Number of elements of vector x.
ALPHA The scalar ALPHA.
X REAL or COMPLEX array, minimum length
(N - 1) x |incx| + 1.
INCX Increment for the array x. A vector x having component
x
i
, i = 1,..., n, is stored in an array X() with increment
argument incx. If incx > 0 then x
i
is stored in
X (1 + (i - 1) x incx). If incx < 0 then x
i
is stored in
X (1 + (N - i) x |incx|). incx = 0 is an illegal value.
BETA The scalar BETA.
AP Array containing the upper or lower triangle, as
specified by uplo of an n-by-n real symmetric or
complex Hermitian matrix A, stored by columns in
packed form.
Output AP The upper or lower triangle of the updated A matrix, as
specified by uplo, replaces the input.
A αxx
T
βA with A=A
T
+←