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

Chapter 3 Basic Matrix Operations 357
General band matrix-vector multiply F_SGBMV/F_DGBMV/F_CGBMV/F_ZGBMV
KU The upper bandwidth of A, that is, the number of
nonzero diagonals above the principal diagonal in the
band, .
ALPHA The scalar ALPHA. If beta = 1 and alpha = 0, this
routine returns immediately.
A REAL or COMPLEX array, dimension (LDA, N).
LDA Leading dimension of array A. If lda < (kl + ku + 1), an
error condition is generated.
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. If beta = 1 and alpha = 0, this
routine returns immediately.
Y REAL or COMPLEX array, minimum length
(N - 1) x |incy| + 1.
INCY Increment for the array y. A vector y having component
y
i
, i = 1,..., n, is stored in an array Y() with increment
argument incy. If incy > 0 then y
i
is stored in
Y(1 + (i - 1) x incy). If incy < 0 then y
i
is stored in
Y(1 + (N - i) x |incy|). incy = 0 is an illegal value.
Output Y The updated Y vector replaces the input.
where A can be A, A
T
, or A*.
0 KU n<≤
y αAx βy+←