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

Chapter 4 Sparse BLAS Operations 431
What you need to know to use these subprograms
Table 4-12 JAD Format Matrix
And the JAD representation of the row-permuted matrix could be given by:
Table 4-13 JAD Row-Permuted Matrix
SKY- (Triangular) Skyline. The Skyline format can be used to represent
square triangular matrices. Two arrays are required for the SKY
representation:
• val(*) - Scalar array of length pntr(m+1)-1 (see below for pntr( )) containing
all the nonzero entries, and maybe some zero entries of A. A must be a
square triangular matrix (m=k). val( ) is row oriented if A is a lower
triangular matrix, and column oriented if A is an upper triangular matrix.
All entries from the first nonzero entry through the diagonal entry of a row
(column) are stored.
• pntr(*) - Integer array of length m+1 (A lower triangular) or k+1 (A upper
triangular) such that pntr(i) and pntr(i+1)-1, respectively, point to the
location in val( ) of the first entry and last entry of the skyline profile in row
(column) i. In any case, the last entry is the diagonal entry.
Consider, for example, the symmetric 5 x 5 matrix:
Table 4-14 5 x 5 Matrix
The lower triangular part of this matrix could be represented in SKY format as:
11 12 0 14
51 52 0 54
21 22 0 0
0 0 33 34
00044
val= 11 51 21 33 44 12 52 22 34 14 54
indx= 11134222444
pntr= 1 6 10 12
11 21 0 0 51
21 22 32 42 0
03233 0 0
0 42 0 44 54
51 0 0 54 55