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

302 HP MLIB User’s Guide
STBSV/DTBSV/CTBSV/ZTBSV Solve triangular band system
Lower triangular storage
If A is a 9-by-9 lower-triangular band matrix with bandwidth kd = 3, for
example,
the lower triangular band part of A is stored in an array ab with at least
kd+1 = 4 rows and 9 columns:
where asterisks represent elements in the kd-by-kd triangle at the lower-right
corner of ab that are not referenced. Thus, if a
ij
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.
1100000000
21220000000
313233000000
4142434400000
0525354550000
0 0 63 64 65 66 0 0 0
0 0 0 74 75 76 77 0 0
0000858687880
0000096979899
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 * * *