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, 0 ≤ KU < n .

 

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

 

 

xi, i = 1,..., n, is stored in an array X() with increment

 

 

argument incx. If incx > 0 then xi is stored in

 

 

X (1 + (i - 1) x incx). If incx < 0 then xiis 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

 

 

yi, i = 1,..., n, is stored in an array Y() with increment

 

 

argument incy. If incy > 0 then yiis stored in

 

 

Y(1 + (i - 1) x incy). If incy < 0 then yi is stored in

 

 

Y(1 + (N - i) x incy). incy = 0 is an illegal value.

Output

Y

The updated Y vector replaces the input.

 

 

y ← αAx + βy

 

 

where A can be A, AT, or A*.

Chapter 3 Basic Matrix Operations 357