HP UX Performance Tools manual 323

Matrix-vector multiply STBMV/DTBMV/CTBMV/ZTBMV

Lower triangular storage.

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

11	0	0	0	0	0	0	0	0
21	22	0	0	0	0	0	0	0
31	32	33	0	0	0	0	0	0
41	42	43	44	0	0	0	0	0
0	52	53	54	55	0	0	0	0
0	0	63	64	65	66	0	0	0
0	0	0	74	75	76	77	0	0
0	0	0	0	85	86	87	88	0
0	0	0	0	0	96	97	98	99

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

11	22	33	44	55	66	77	88	99
21	32	43	54	65	76	87	98	*
31	42	53	64	75	86	97	*	*
41	52	63	74	85	96	*	*	*

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

A, it is stored in ab(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 the first row, the first subdiagonal in the second row, and so on.

Chapter 3 Basic Matrix Operations 295