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

Chapter 3 Basic Matrix Operations 381
Symmetric packed matrix-vector multiply F_SSPMV/F_DSPMV/F_CSPMV/F_ZSPMV
Name F_SSPMV/F_DSPMV/F_CSPMV/F_ZSPMV
Symmetric packed matrix-vector multiply
Purpose F_xSPMV multiplies a vector x by a real or complex symmetric packed matrix
A, scales the resulting vector and adds it to the scaled vector operand y. If n is
less than or equal to zero, or if β is equal to one and α is equal to zero, this
routine returns immediately.
Refer to “SSPMV/DSPMV/CHPMV/ZHPMV” on page 249 for a description of
the equivalent HP MLIB legacy BLAS 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. Refer to
“SSPMV/DSPMV/CHPMV/ZHPMV” on page 249 for an example of packed
storage for symmetric or Hermitian matrices.
Usage VECLIB
INTEGER*4 INCX, INCY, N, UPLO
REAL*4 ALPHA, BETA
REAL*4 AP( * ), X( * ), Y( * )
SUBROUTINE F_SSPMV (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
INTEGER*4 INCX, INCY, N, UPLO
REAL*8 ALPHA, BETA
REAL*8 AP( * ), X( * ), Y( * )
SUBROUTINE F_DSPMV (UPLO, N, ALPHA, AP, X, INCX, BETA, Y,
INCY)
INTEGER*4 INCX, INCY, N, UPLO
COMPLEX*8 ALPHA, BETA
COMPLEX*8 AP( * ), X( * ), Y( * )
SUBROUTINE F_CSPMV (UPLO, N, ALPHA, AP, X, INCX, BETA, Y,
INCY)
INTEGER*4 INCX, INCY, N, UPLO
COMPLEX*16 ALPHA, BETA
COMPLEX*16 AP( * ), X( * ), Y( * )
SUBROUTINE F_ZSPMV (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
VECLIB8
y αAx βy with A=A
T
+←