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

Chapter 3 Basic Matrix Operations 247
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,
x
i
is stored in x((i−1)×incx+1).
incx < 0 x is stored backward in array x; that
is, x
i
is stored in x((i−n)×incx+1).
Use incx = 1 if the vector x is stored contiguously in
array x, that is, if x
i
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,
y
i
is stored in y((i−1)×incy+1).
incy < 0 y is stored backward in array y; that
is, y
i
is stored in y((i−n)×incy+1).
Use incy = 1 if the vector y is stored contiguously in
array y, that is, if y
i
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’