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

Chapter 3 Basic Matrix Operations 397
Triangular banded matrix-vector multiply F_STBMV/F_DTBMV/F_CTBMV/F_ZTBMV
Name F_STBMV/F_DTBMV/F_CTBMV/F_ZTBMV
Triangular banded matrix-vector multiply
Purpose F_xTBMV multiplies a vector x by a banded triangular matrix (T), its transpose
(T
T
), or its conjugate transpose (T*), and copies the resulting vector to the
vector operand x. If n is less than or equal to zero, this routine returns
immediately.
Refer to “STBMV/DTBMV/CTBMV/ZTBMV” on page 294 for a description of
the equivalent HP MLIB legacy BLAS subprograms.
Matrix
Storage
Triangular band matrices are stored in a compressed form that takes
advantage of knowing the positions of the only elements that can be nonzero.
Refer to the examples in “STBMV/DTBMV/CTBMV/ZTBMV” on page 294 for
information about the storage of triangular band matrices.
Usage VECLIB
INTEGER*4 DIAG, INCX, K, LDA, N, TRANS, UPLO
REAL*4 ALPHA
REAL*4 A( LDA, * ), X( * )
SUBROUTINE F_STBMV (UPLO, TRANS, DIAG, N, K, ALPHA, A, LDA, X,
INCX)
INTEGER*4 DIAG, INCX, K, LDA, N, TRANS, UPLO
REAL*8 ALPHA
REAL*8 A( LDA, * ), X( * )
SUBROUTINE F_DTBMV (UPLO, TRANS, DIAG, N, K, ALPHA, A, LDA,
X, INCX)
INTEGER*4 DIAG, INCX, K, LDA, N, TRANS, UPLO
COMPLEX*8 ALPHA
COMPLEX*8 A( LDA, * ), X( * )
SUBROUTINE F_CTBMV (UPLO, TRANS, DIAG, N, K, ALPHA, A, LDA,
X, INCX)
x αTx←
x αT
T
x←
x αT
∗
x←