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

Chapter 3 Basic Matrix Operations 253
Matrix-vector multiply SSPMV/DSPMV/CHPMV/ZHPMV
Output y The updated y vector replaces the input.
Notes These subprograms conform to specifications of the Level 2 BLAS.
If an error in the arguments is detected, the subprograms call error handler
XERBLA, which writes an error message onto the standard error file and
terminates execution. The standard version of XERBLA (refer to the end of this
chapter) can be replaced with a user-supplied version to change the error
procedure. Error conditions are:
uplo ≠ ’L’ or ’l’ or ’U’ or ’u’
n < 0
incx = 0
incy = 0
Actual character arguments in a subroutine call may be longer than the
corresponding dummy arguments. Therefore, readability of the CALL
statement may be improved by coding the uplo argument as ’LOWER’ for ’L’ or
’UPPER’ for ’U’. Refer to “Example 2.”
Example 1 Form the REAL*4 matrix-vector product y = Ax, where A is a 9-by-9 real
symmetric matrix whose upper triangle is stored in packed form in an array AP
of dimension 55, x is a real vector 9 elements long stored in an array X of
dimension 10, and y is a real vector 9 elements long stored in an array Y, also of
dimension 10.
CHARACTER*1 UPLO
INTEGER*4 N,INCX,INCY
REAL*4 ALPHA,BETA,AP(55),X(10),Y(10)
UPLO = ’U’
N = 9
ALPHA = 1.0
BETA = 0.0
INCX = 1
INCY = 1
CALL SSPMV (UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
Example 2 Form the COMPLEX*8 matrix-vector product , where ρ is a
complex scalar, A is a 9-by-9 complex Hermitian matrix whose lower triangle is
stored in packed form in an array AP of dimension 55, x is a complex vector 9
elements long stored in an array X of dimension 10, and y is a complex vector 9
elements long stored in an array Y, also of dimension 10.
INTEGER*4 N
COMPLEX*8 RHO,AP(55),X(10),Y(10)
N = 9
CALL CHPMV (’LOWER’,N,-RHO,AP,X,1,(0.5E0,0.0E0),Y,1)
y
1
2
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y ρAx–=