What you need to know to use these subprograms

Table 4-12 JAD Format Matrix

11 12 0 14

51 52 0 54

21 22 0 0

0 0 33 34

0 0 0 44

And the JAD representation of the row-permuted matrix could be given by:

Table 4-13 JAD Row-Permuted Matrix

val=

11

51

21

33

44

12

52

22

34

14

54

indx=

1

1

1

3

4

2

2

2

4

4

4

pntr=

1

6

10

12

 

 

 

 

 

 

 

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

 

 

 

 

11

21

0

0

51

 

21

22

32

42

0

 

0

32

33

0

0

 

0

42

0

44

54

 

51

0

0

54

55

The lower triangular part of this matrix could be represented in SKY format as:

Chapter 4 Sparse BLAS Operations 431