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

298 HP MLIB User’s Guide
STBMV/DTBMV/CTBMV/ZTBMV Matrix-vector multiply
’U’ or ’u’ A is upper triangular
trans Transposition option for A:
’N’ or ’n’ Compute x ← Ax
’T’ or ’t’ Compute x ← A
T
x
’C’ or ’c’ Compute x ← A*x
where A
T
is the transpose of A, and A* is the conjugate
transpose. In the real subprograms, ’C’ and ’c’ have the
same meaning as ’T’ and ’t’.
diag Specifies whether the matrix is unit triangular, that is,
a
ii
= 1, or not:
’N’ or ’n’ The diagonal of A is stored in the
array
’U’ or ’u’ The diagonal of A consists of unstored
ones
When diag is supplied as ’U’ or ’u’, diagonal elements of
A are not referenced, but space must be reserved for
them.
n Number of rows and columns in matrix A, n ≥ 0. If n =
0, the subprograms do not reference ab or x.
kd The number of nonzero diagonals above or below the
principal diagonal. If uplo is supplied as ’U’ or ’u’, kd
specifies the number of nonzero diagonals above the
principal diagonal. If uplo is supplied as ’L’ or ’l’, kd
specifies the number of nonzero diagonals below the
principal diagonal.
ab Array containing the n-by-n triangular band matrix A
in the compressed form described above. The columns
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).