[ibis-interconn] Re: Draft "pseudo-specification" for sparse matrices...
- From: "Dmitriev-Zdorov, Vladimir" <vladimir_dmitriev-zdorov@xxxxxxxxxx>
- To: <radek_biernacki@xxxxxxxxxxx>, <michael.mirmak@xxxxxxxxx>, <ibis-interconn@xxxxxxxxxxxxx>
- Date: Wed, 15 Jul 2009 12:34:39 -0600
Radek,
So here the things in the first line (1,1) (1,5) etc. serve to indicate
positions in the matrix into where we should place the numbers.
In other lines, [Implicit ...] the same things are used as names
designating the numbers that we need to put somewhere else.
I'm slightly uncomfortable with the fact that in this notation (1,1)
seems somewhat out of the row compared to other diagonal elements,
although they are all equal.
As was noted, this notation allows some freedom: we can e.g. swap (1,1)
and (5,5) and the result will not change. Is this good or bad?
Another question. We define Low or Upper for symmetrical matrix, but
symmetry in the proposed sparse sense is just a special case of data
duplication, between certain pairs of elements. Hence, for symmetric
matrices, even without mentioning 'symmetry', 'upper' or 'low' we will
not duplicate the data for sparse matrix anyway. We may however think of
saving some space when defining mapping from given entries into the
position of the final matrix. Here, we have several possibilities: (1)
list all matrix components and indicate identical [(k,m) == (m,k)], as
for general case matrix; (2) list only 'Low' or 'Upper' components, with
appropriate keyword defined earlier, or (3) list either of the (k,m) or
(m,k), but only once, with 'Symmetry' defined before. What makes more
sense?
Vladimir
[Matrix Format] Sparse
[Sparse Matrix Entries]
(1,1) (1,5) (3,1)
[Implicit Sparse Matrix Entries]
(1,1): (2,2) (3,3) (4,4)
[Implicit Sparse Matrix Entries]
(1,1): (5,5)
[Sparse Matrix Entries End]
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