Re: Applying function to vector by index

[Paul Kienzle]

On Thu, Dec 12, 2002 at 02:10:14PM -0500, Andy Adler wrote:
> On Thu, 12 Dec 2002, Paul Kienzle wrote:
> >
> > Personally I would rather not have functions spontaneously converting
> > sparse matrices to full since really small sparse matrices can form
> > really big full matrices, but I also would not want to introduce
> > needless incompatibilities.
> >
> 
> Converting to full can save memory. Consider your cos(sparse) example.
> It takes less memory to encode it as full than in a big sparse (BS)
> matrix.

There are two views of what an element-wise operation on a sparse matrix
should produce: the operation applied just to explicit values (i.e., sparse
is just a tagged vector where you can do certain operations based on the
tags like sum/min/max, as well as matrix products and decompositions), or
the operation applied to the implicit zeros as well (i.e., sparse is just
a condensed representation of a full matrix).

I can see advantages to each, and I have slight personal preference for the
first, but the second also makes sense, and since it is compatible with
matlab, I would argue for the second.  Given that, by all means, if f(0)
is not zero, then f(A) should return f(full(A)).

> 
> > BTW, I notice that
> >             sparse(1,1,0)
> > returns the following:
> >     Compressed Column Sparse (rows=1, cols=1, nnz=1)
> >       (1 , 1) -> 0
> > and
> >     [i,j,v] = spfind(sparse(1,1,0))
> > returns
> >     i = 1
> >     j = 1
> >     v = 0
> 
> I have code which goes through the matrices generated to
> remove zeros introduces this (and in other subtle) ways.
> I guess I forgot to apply it in this case.
> 
> My current opinion is that I'll try to stay Matlab compatible
> unless it is really non-sensical.

I agree doing whatever matlab does for sparse(1,1,0) makes
sense.

I prefer correctness to compatibility, though, so I would
rather have sparse(eye(2)).^(-1+1i) return [1 NaN;NaN 1]
than [1 0;0 1].

In your code this should be simple enough: if 0^x is non-zero
expand to full then do 0^x, otherwise just do 0^x on your own
vector.  Just make sure your 0^x is the same as what octave
uses for scalar 0^x so that it is consistent.

- Paul
> 
> Andy
> 
> 



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