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

306 HP MLIB User’s Guide
STBSV/DTBSV/CTBSV/ZTBSV Solve triangular band system
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
right-hand-side n-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.
Output x The solution vector of the triangular band system
replaces the input.
Notes These subprograms conform to specifications of the Level 2 BLAS.
The subprograms do not check for singularity of matrix A. A is singular if diag
= ’N’ or ’n’ and some a
ii
= 0. This condition causes a division by zero to occur.
Therefore, the program must detect singularity and take appropriate action to
avoid a problem before calling any of these subprograms.
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.