Hi All
I get the impression that Kronecker products are becoming more and more
popular in Machine Learning research. However, people only seem to be
using Kronecker products as part of their derivations, while the actual
programs don't use them. I don't really like this, as the resulting code
is often hard to follow.
The reason why people don't use Kronecker products in their code is that
the resulting matrices often are huge when you are working on real world
problems. So, I'm thinking: why not just have Kronecker products as a
special type of matrix, just like we have for diagonal matrices?
The attached code is a simple m-file implementation of such a class
('kronprod'). It implements the following functions (besides trivial
stuff like 'size', 'numel', 'display', ...):
ctranspose
transpose
uplus
uminus
rank
trace
det
mtimes
mldivide
mpower
inv
eig
svd
This is just a prototype, but it seems to work quite well (it has no
error checking, documentation or fancy stuff like that, though). As an
example, I can do
A = rand (200, 300);
B = rand (400, 500);
v1 = rand (rows (A)*rows (B), 1);
tic, r1 = kronprod (A, B) \ v1; toc
which gives me
Elapsed time is 0.601284 seconds.
If I use the current 'kron' function
tic, r2 = kron (A, B) \ v1; toc
I instead get
error: memory exhausted or requested size too large for range of
Octave's index type -- trying to return to prompt
In general, the code is quite simple as it is just an application of
properties of Kronecker products.
My question is then: is it worth the effort of trying to integrate this
properly into Octave (which would require putting corresponding C++ code
in 'liboctave') or should I just finish the class and stuff it in the
'linalg' package?
Søren