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

Chapter 3 Basic Matrix Operations 245

Matrix-vector multiply SSBMV/DSBMV/CHBMV/ZHBMV

Upper triangular storage

The upper triangle of A is stored in an array ab with at least kd+1 = 3 rows

and 7 columns as follows:

The asterisks represent elements in the kd-by-kd triangle at the upper left

corner of ab that are not referenced. Thus, if a

is an element within the band of

the upper triangle of A, it is stored in ab(kd+1+i−j,j). Therefore, the columns of

the upper triangle of A are stored in the columns of ab, and the diagonals of the

upper triangle of A are stored in the rows of ab, with the principal diagonal in

row kd+1, the ﬁrst superdiagonal starting in the second position in row kd, and

so on.

Lower triangular storage

The lower triangle of A is stored in the array ab as follows:

The asterisks represent elements in the kd-by-kd triangle at the lower right

corner of ab that are not referenced. Thus, if a

is an element within the band of

the lower triangle of A, it is stored in ab(1+i−j,j). Therefore, the columns of the

lower triangle of A are stored in the columns of ab, and the diagonals of the

lower triangle of A are stored in the rows of ab, with the principal diagonal in

the ﬁrst row, the ﬁrst subdiagonal in the second row, and so on.

Usage VECLIB:

CHARACTER*1 uplo

INTEGER*4 n, kd, ldab, incx, incy

REAL*4 alpha, beta, ab(ldab, n), x(lenx), y(leny)

CALL SSBMV(uplo, n, kd, alpha, ab, ldab, x, incx, beta, y, incy)

CHARACTER*1 uplo

INTEGER*4 n, kd, ldab, incx, incy

REAL*8 alpha, beta, ab(ldab, n), x(lenx), y(leny)

CALL DSBMV(uplo, n, kd, alpha, ab, ldab, x, incx, beta, y, incy)

* * 13 24 35 46 57

*122334455667

11 22 33 44 55 66 77

12 23 34 45 56 67 *

13 24 35 46 57 * *