Re: About diagonal matrices

[Daniel J Sebald]

dbateman wrote:

> I consider that the fact speye(3)/0 returns a full matrix a bug unless the
> sparse_auto_mutate function is set. In fact this behavior is a hang over
> from when sparse_auto_mutate(1) was not only the default but only behavior
> and certain narrowing could be donee in the operators themselves rather than
> the narrowing function of the octave_value. I pushed a patch..
>
>
>
> octave:4> a = eye(3)/0
> a =
>
>    Inf     0     0
>      0   Inf     0
>      0     0   Inf
>
> octave:5> a = speye(3)/0
> warning: division by zero
> a =
>
> Compressed Column Sparse (rows = 3, cols = 3, nnz = 3 [33%])
> )
>
>   (1, 1) -> Inf
>   (2, 2) -> Inf
>   (3, 3) -> Inf

What does 'nnz' mean?  "something-not-zero"?  If so, then the above is wrong because any 
number divided by zero is not zero.  Hence, "nnz" should be 9, or 100%.


> octave:14> full(a)/0
> warning: division by zero
> ans =
>
>    Inf   NaN   NaN
>    NaN   Inf   NaN
>    NaN   NaN   Inf
>
> and would expect the NaN fill in even for diagonal matrices as John
> suggested and so the NaN values. The current Octave behavior is
> mathematically wrong and saying thats the answer the user expected is no
> excuse. We should bring back the NaN fill-in.

Maybe it would make more sense to define sparse matrices in terms of index sets 
(or I'll offer another REALLY creative alternative below).  Say we have 
non-intersecting sets IJ1, IJ2, IJ3, ..., IJN which are assigned numbers V0, 
V1, V2, V3, ..., VN.  Say Omega is the universe, or set of all indeces for an M 
x N matrix.  Then the assignment for sparse matrix S would be:

(i,j) in IJ1 -> S(i,j) = V1
(i,j) in IJ2 -> S(i,j) = V2
(i,j) in IJ3 -> S(i,j) = V3
...
(i,j) in IJN -> S(i,j) = VN

and finally

(i,j) in Omega-(IJ1+IJ2+IJ3+...+IJN) -> S(i,j) = V0

That last statement means that the index in question is not in any of the other 
"sparse subsets".

What that would do is allow some "default sparse value", as well as perhaps 
give a bit more compaction in the case of several repeating

Dan


PS:  One could maybe dream up a "sub-block" scheme for sparse matrices, but 
that might be a programming nightmare.