[Jprogramming] Re: Symmetric inner and outer products

[Henry Rich]

I agree completely about +/ .* .   With work expected
on numerics, it would be a bad idea to proliferate
special cases.  (I had said I would vote against that).

But Mark also netioned improving %., which was what I
was thinking of approvingly.  I had the idea that,
depending on the implementation, the test might not
require much code.  After looking at some reference
books I no longer believe this.

Henry Rich

> -----Original Message-----
> From: programming-bounces at jsoftware.com 
> [mailto:programming-bounces at jsoftware.com] On Behalf Of Roger Hui
> Sent: Saturday, September 02, 2006 5:40 PM
> To: Programming forum
> Subject: Re: RE: [Jprogramming] Re: Symmetric inner and outer products
> 
> So we agree that the important consideration is
> whether the special code is worthwhile, not that
> the checking can be done in O(n^2) time.
> 
> For the checking and for the special code for 
> symmetric matrices, you get a speed-up by a factor
> which is at most 2.  The code for +/ .* would be at
> least doubled in size, which means when it comes 
> time to have really special code, exploiting SSE or
> multi core or whatever, the amount of code to be
> changed is doubled.
> 
> On the other hand, consider putting effort into 
> improving +/ .* on sparse matrices.  There, the 
> speed-up can be from O(n^3) to O(n^2), and the 
> factor can be as large as you like.  You can do 
> products on matrices whose dense representations 
> wouldn't even fit in 32-bit space.
> 
> 
> 
> ----- Original Message -----
> From: Henry Rich <HenryHRich at nc.rr.com>
> Date: Saturday, September 2, 2006 11:45 am
> Subject: RE: [Jprogramming] Re: Symmetric inner and outer products
> 
> > The checking for identity is only O(n^2) if the result is
> > true - usually it's O(1) approximately.
> > 
> > The question is, is it worth the coding effort?  Symmetric
> > matrices are so common - more likely than not, in my work -
> > that Mark's suggestion has merit.
> 
> 
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