[Haskell-cafe] More STUArray questions

[Martin Percossi]

Hello, I am trying to write a haskell-native matrix library (providing a
similar set of functionality as gsl's matrix/eigenvector routines). I have had
a look at other attempts at matrix libraries, and have found Hal Daume's and
Alberto Ruiz's libraries to offer a good amount of functionality. There are two
major reasons for wanting to write my own library:

1. Haskell-nativeness: I have had some issues compiling and linking with gsl
libraries on 64-bit platforms. Also, it would be quite interesting to gauge
haskell's effectiveness as a scientific computing platform, in particular
making use unboxed arrays as representation.

2. Use of monads: in the afore-mentioned libraries, monads are either ignored,
or are restricted to the IO monad. I am taking a different approach, starting
my code from the ST monad, and eventually this will be generalized to work with
the IO monad.  I think the ST monad is a good monad to be able to perform
computations on matrices that update them, allowing efficient, in-place
algorithms, but it also provides the benifit of not being a one-way street like
the IO monad is. Being a relative newcomer to haskell, I would be interested to
hear any thoughts as to whether this is a good/bad idea. 

Now to my question: I would like to represent a matrix as a wrapper around a
block, which in turn is just an unboxed array. Here are the definitions for a
matrix in ST and outside of a monad, respectively:

type MBlock s = STUArray s Int Double
data MMatrix s = MMatrix Int Int (MBlock s)
type Block = UArray Int Double
data Matrix = Matrix Int Int Block

Now, I have started by providing some fairly low-level routines in the ST
monad. My problem is depressingly simple: I would like to retrieve a matrix
from the ST monad for use outside of it (in particular, to pretty-print it).
Now, this is easy for STUArrays (just use runSTUArray), but I'm not sure of how
to do it for a type that *encloses* an STUArray.

For example, here's a simple test:

runMatrix = do _A <- newListMatrix [[2, 0, 0], [0, 2, 0], [0, 0, 2]]
               _B <- newListMatrix [[1, 2, 1], [0, 1, 1], [0, 0, 1]]
               _C <- matMul _A _B
               return $ getBlock _C

main = show $ runSTUArray runMatrix

Obviously, what I get as a result of runSTUArray is a UArray, which is a pain
because I'd then have to box it "by hand" (i.e. again specifying the number of
rows and columns), instead of automatically, in order to have a Matrix again.

So what I'd like is a runSTMatrix routine, which would possibly have signature:

runSTMatrix :: ST s (Matrix s) -> Matrix

which would have semantics analogous to runSTUArray.

Does anyone have any idea of how I can write runSTMatrix?

Many thanks in advance,
Martin