[OT] Use case for a 4-D matrix

[John Demme]

Tomek Sowiński wrote:

> Dnia 04-09-2010 o 08:03:12 John Demme <jdd at cs.columbia.edu> napisał(a):
> 
>> As for the graphs, I essentially take two input graphs, represented in
>> adjacency matrix form (two 2-d matrices of size n^2 each, assuming equal
>> sized graphs).  Then, I compute the Kronecker Tensor Graph Product[2],
>> which
>> creates a matrix of size n^4.  Depending on how you think about it, this
>> matrix is a simple (although large) 2-D adjacency matrix of the product
>> graph, and it can be treated as such for many operations.  It can also be
>> inspected in four dimensional space to examine the relationships between
>> possible node pairs, but I don't do this.  Frankly, it hurts my brain a
>> little bit.
> 
> Can't you compute the Kronecker product lazily? E.g. a proxy object that
> computes a value in an overloaded opIndex. Even if your algorithms inspect
> (compute) the same value several times, you may still win -- the
> bottleneck these days is memory access, not CPU cycles.

That's an interesting thought.  It'd be a bit trickier than that since I'm 
doing some post-processing on the product, but not enough to make this 
impossible.  I'll probably give this a shot if I really need to scale up -- 
it'd be difficult to fight n^4 space with more RAM... though I'd sure like 
to give it a shot :)

> 
> Fascinating stuff you're dealing with... Good luck.

Thanks

~John