Hi Petr and Dominic, The last version of hmatrix supports integer elements and modular arithmetic, including inverting matrices: https://hackage.haskell.org/package/hmatrix-0.17.0.1/docs/Numeric-LinearAlge... This is experimental and probably not very useful for serious applications, but in any case here you can find some toy examples: http://dis.um.es/~alberto/hmatrix/finite.html Alberto On 07/01/16 08:51, Dominic Steinitz wrote:

Hi Petr,

It's not too hard to write an inverse for matrices

...

inv :: (KnownNat n, (1 <=? n) ~ 'True) => Sq n -> Sq n inv m = fromJust $ linSolve m eye But since hmatrix is LAPACK this is not going to help you with GF(2).

I wasn't aware of the 'tensor' package either but it does contain some interesting ideas and by the looks of it should be able to invert matrices even for finite fields. I'd be interested in its performance. Perhaps you could write a benchmark and I can try it with Yarr?

Probably one could improve 'tensor' by using type level literals a la the static part of hmatrix and maybe base it over Yarr for performance. I note it is GPL which I am not a great fan of and has no publicy available repository (at least I wasn't able to find one).

Good luck and please report back with anything interesting you discover on your journey.

Dominic.

On 06/01/2016 20:12, Petr Pudlák wrote:

...

Hi Dominic,

thank you for the detailed answer! I'm looking for linear algebra over finite fields (in particular GF(2)), and while hmatrix has some support, it doesn't support inverting matrices, which is something I need. So I'll need to look further. Just a moment ago I discovered the 'tensor' package, which is flexible enough to add a new representation. Currently it offers Vector, I'll try it out, and perhaps it'd be possible to include yarr too, if Vector won't perform well enough.

All the best, Petr

st 6. 1. 2016 v 10:50 odesílatel Dominic Steinitz mailto:dominic@steinitz.org> napsal:

A problem with my email prevented this making it on to the mailing list.

Hi Petr,

I am not actively developing Yarr but I would very much like to. I keep it from bit-rotting. The problem as always is finding time. On the other hand I don't think repa is very active e.g. upgrading to vector-0.11 took a while to happen although clearly more active than me on Yarr!

What I'd like is something like Python's numpy but safer and faster. If you look at the static module in the hmatrix package (https://hackage.haskell.org/package/hmatrix-0.17.0.1/docs/Numeric-LinearAlge...) you can see how type level literals can be used to prevent e.g. multiplying two inconsistent matrices together at compile time. I am sure we could do something better with either Yarr or repa (repa will currently give out of bounds errors at runtime).

For reasons I don't understand (I think a bug in Haddock) the documentation does not get generated.

There are examples of its use here: https://github.com/leventov/yarr/tree/master/tests. I wrote a blog using repa and Yarr here: https://idontgetoutmuch.wordpress.com/2013/08/06/planetary-simulation-with-e... and compare performance. You can safely ignore the theory and need only look at "Repa Implementation", "Yarr Implementation" and "Performance".

I think performance will depend on your application. I believe (but haven't confirmed) that repa will outperform Yarr on e.g grid based problems such as numerical methods for diffusions and Poisson. In the case of planets (or stars or particles) where everything is influenced by everything else then repa is a bad fit and Yarr outperforms.

If your application is linear algebra, I would think that hmatrix would have what you want or could be extended to give what you want since it is LAPACK under the covers.

I am very excited that you are interested in this area; it often feels very lonely.

Best wishes, Dominic.

On 06/01/2016 09:10, Petr Pudlák wrote: > Hi Dominic, > > what is the current state of Yarr? Is it being actively developed? Is > there some tutorial or documentation available? > > I'm deciding between repa and yarr for some linear algebra > computations. I found some references that yarr is more performant, > but I couldn't find much documentation and the hackage page [1] hasn't > indexed most modules for some reason, so there seems to be no good > place to start from. And the last commit was 9 months ago. > > [1]https://hackage.haskell.org/package/yarr > > Thank you, > Petr

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