HP UX Performance Tools manual 331

Solve triangular band system STBSV/DTBSV/CTBSV/ZTBSV

Upper triangular storage

If A is a 9-by-9 upper-triangular band matrix with bandwidth kd = 3, for example,

11	12	13	14	0	0	0	0	0
0	22	23	24	25	0	0	0	0
0	0	33	34	35	36	0	0	0
0	0	0	44	45	46	47	0	0
0	0	0	0	55	56	57	58	0
0	0	0	0	0	66	67	68	69
0	0	0	0	0	0	77	78	79
0	0	0	0	0	0	0	88	89
0	0	0	0	0	0	0	0	99

the upper triangular band part of A is stored in an array ab with at least kd+1 = 4 rows and 9 columns:

*	*	*	14	25	36	47	58	69
*	*	13	24	35	46	57	68	79
*	12	23	34	45	56	67	78	89
11	22	33	44	55	66	77	88	99

where asterisks represent elements in the kd-by-kdtriangle at the upper-left corner of ab that are not referenced. Thus, if aij is an element within the band of

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

Usage	VECLIB:
	CHARACTER*1	uplo, trans, diag
	INTEGER*4	n, kd, ldab, incx
	REAL*4	ab(ldab, n), x(lenx)

CALL STBSV(uplo, trans, diag, n, kd, ab, ldab, x, incx)

CHARACTER*1	uplo, trans, diag
INTEGER*4	n, kd, ldab, incx
REAL*8	ab(ldab, n), x(lenx)

CALL DTBSV(uplo, trans, diag, n, kd, ab, ldab, x, incx)

Chapter 3 Basic Matrix Operations 303