[OT] Use case for a 4-D matrix

[BCS]

Hello Tomek,

> Dnia 04-09-2010 o 08:03:12 John Demme <jdd at cs.columbia.edu>
> napisal(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.
> 

If enough elements from the 4d matrix are accessed, in the wrong order, then 
the cache effects of doing it lazily might kill it. I'd guess that highly 
optimized code for doing the pre-compute version exists already.
 
> Fascinating stuff you're dealing with... Good luck.
> 
> Tomek
> 
-- 
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