Matrix-vector multiply

 

 

SSBMV/DSBMV/CHBMV/ZHBMV

 

 

of the band of A are stored in the columns of ab, and

 

 

the diagonals of the band of A are stored in the rows of

 

 

ab.

 

 

ldab

The leading dimension of array ab as declared in the

 

 

calling program unit, with ldab ≥ kd+1.

 

x

Array of length lenx = (n−1)⋅incx+1 containing the

 

 

input vector x.

 

 

incx

Increment for the array x, incx ≠ 0:

 

 

incx > 0

x is stored forward in array x; that is,

 

 

 

xi is stored in x((i−1)⋅incx+1).

 

 

incx < 0

x is stored backward in array x; that

 

 

 

is, xi is stored in x((i−n)⋅incx+1).

 

 

Use incx = 1 if the vector x is stored contiguously in

 

 

array x, that is, if xi is stored in x(i). Refer to “BLAS

 

 

Indexing Conventions” in the introduction to

 

 

Chapter 2.

 

 

beta

The scalar β.

 

 

y

Array of length leny = (n−1)⋅incy+1 containing the

 

 

n-vector y. Not used as input if beta = 0.

 

incy

Increment for the array y, incy ≠ 0:

 

 

incy > 0

y is stored forward in array y; that is,

 

 

 

yi is stored in y((i−1)⋅incy+1).

 

 

incy < 0

y is stored backward in array y; that

 

 

 

is, yi is stored in y((i−n)⋅incy+1).

 

 

Use incy = 1 if the vector y is stored contiguously in

 

 

array y, that is, if yi is stored in y(i). Refer to “BLAS

 

 

Indexing Conventions” in the introduction to

 

 

Chapter 2.

 

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’

Chapter 3 Basic Matrix Operations 247