[Haskell-cafe] matrix computations based on the GSL

[David Roundy]

On Wed, Jun 29, 2005 at 01:38:51PM +0200, Alberto Ruiz wrote:
> Wow! It is exactly the same idea! I did not find the above message by
> Keean in my google searchs when I decided to work on this, it is very
> recent! After a quick look to the thread I wish I would have followed the
> discussions... A much more serious work was in progress. At least it was
> fun and I have learnt a lot of Haskell...

Your library is far more complete than Keean's is so far, and looks very
nice.  The one thing I'd like to see (and here I agree with Hennig) is a
distinction between matrices and tensors.  Your library is really very
tensor-based, but tensors and matrices are very different beasts.

I imagine one could take your Block, which is really a sort of generalized
tensor, and implement a Matrix type such as

data Matrix = M (Block Double)

(or perhaps for arbitrary element type) with the constructor not exported,
so that Matrices will always be guaranteed to be two-dimensional.

Then for matrices one could define * to be matrix multiplication, sqrt,
exp, cos, sin etc to be matrix functions (expm etc in octave-speak), and
then define .* and ./ to be as defined in octave.

This definition would allow considerably more type-safeness than your
current implementation (which seems scarily dynamically typed to me).
Alas, we'd still not have the truly strong typing I'd dream about where one
could define

matMul :: Int n, m, l =>  Matrix n m -> Matrix m l -> Matrix n l

which as I understand things, isn't possible in Haskell without some sort
of weird type trickery.  Of course, if you had this kind of type trickery,
you might not need to declare a separate Matrix type, since you'd be able
to represent the dimensionality of the Block in its type.

> And next I will study Keean's library.

And hopefully you and he can work together to create a great library (and
I'll be able to mooch off of whatever you create...).  :)
-- 
David Roundy
http://www.darcs.net