
Ublas : 
From: Michael Stevens (mail_at_[hidden])
Date: 20050922 14:26:35
On Donnerstag 22 September 2005 01:53, Frank Astier wrote:
> Ian 
>
> Thanks for the correction. It got rid of the bizarre effect that
> ublas seemed to always to the same amount of work, regardless of
> sparsity :)
It is not all doom and gloom! In "operation.hpp" there axpy_prod which help
considerably. Using in the test loop
axpy_prod (m, v, r1);
I get.
0.1 0.32 0.42=
0.2 0.35 0.42=
0.3 0.46 0.43=
0.4 0.56 0.42=
0.5 0.56 0.42=
0.6 0.79 0.43=
0.7 0.95 0.42=
0.8 1.07 0.42=
0.9 1.17 0.42=
and looking in more detail
0 0.02 0.49=
0.02 0.12 0.42=
0.04 0.12 0.42=
0.06 0.13 0.41=
0.08 0.12 0.42=
0.1 0.24 0.42=
0.12 0.24 0.42=
0.14 0.23 0.42=
0.16 0.23 0.42=
0.18 0.24 0.42=
0.2 0.24 0.42=
0.22 0.35 0.42=
0.24 0.34 0.42=
0.26 0.35 0.43=
0.28 0.35 0.42=
So even at 20% sparsity we are doing better. I think this is pritty good if
not glittering.
> I implemented my own sparse matrix too, optimized for multiplication
> with dense vectors (I didn't even write random access to elements, I
> don't need it!). Below 10% non zeros, I get at least 3 times better
> than the naive dense multiplication, and up to 40 times better than
> ublas on small matrix sizes (around 256x256). The matrices I handle
> don't have any structure I can take advantage of, unfortunately.
>
> I wish ublas documentation ad enough details about what to expect.
I think one could write several PhD on matrix multiplications involving sparse
matrices.
That said the normal ublas::prod is unlikely to be a good choice where sparse
matrics are involved. The are many ways the basic element access loops can be
ordered to achive a multiplication. axpy_prod use one ordering that iterates
over the matrix.
For prod to work in general expressions it uses an ordering which iterates of
the elements in the result. For sparse matrices this is bad news as we have
to do a great deal of work to find where we are in the sparse matrix.
That said I would love to see this documented further. I have some material of
my own with diagrams showing the element access paterns I could contribute.
Michael
___________________________________
Michael Stevens Systems Engineering
34128 Kassel, Germany
Phone/Fax: +49 561 5218038
Navigation Systems, Estimation and
Bayesian Filtering
http://bayesclasses.sf.net
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