Re: [eigen] cache-friendly matrix inverse

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

2009/5/14 Benoit Jacob <jacob.benoit.1@xxxxxxxxx>:
> Indeed, for dynamic sizes, there's no unrolling, but there's another
> issue: cache-friendliness. Gael made a very good (actually, according
> to the benchmarks on the wiki, the best all-around) cache-friendly
> matrix-vector product implementation. This becomes increasingly
> important as the matrix size increases. By contrast, our triangular
> solver does not yet have comparable optimizations (and, according to
> our benchmarks, neither do other libraries).

Actually I was wrong here. I was thinking about what Gael said the
other day on IRC,

[mer. mai 13 2009] [14:16:14] <gael__> actually, we should also
implement a cache friendly "inv(triangular) * matrix" which is
currently done one column after the other....

But what he meant was actually the case where you solve with a matrix
as the right-hand side. In this case, there is room for improvement.

But in _your_ case (i checked your benchmark code) you are only
solving with a VECTOR as right hand side.

Our triangular solver (again written by Gael) does use the
cache-friendly matrix-vector product internally, so it's already
cache-friendly in that case.

Unless Gael thinks otherwise, I'm tempted to think that there is not
much room for improvement left to improve the speed to triangular
solver in your case... and so it might be that your numbers actually
show that the matrix-vector product approach is actually faster.

Cheers,
Benoit