[Haskell-cafe] Re: Patrick Perry's BLAS package
Patrick Perry
patperry at stanford.edu
Fri Jun 6 14:56:00 EDT 2008
Wow, thanks for noticing, Alberto! For anyone interested, I put up a
formal announcement describing the bindings a little bit here:
http://quantile95.com/
I just registered the domain yesterday, so it may take a few days to
resolve the DNS magic. Here's the text of the announcement:
I’m really happy that people seem to be interested in the library.
Alberto, in particular, is the primary author of hmatrix, another
haskell linear algebra library (which I stole a few ideas from), so if
he endorses it, that means a lot to me.
So, Yet Another Linear Algebra Library? I’ve already mentioned
hmatrix. There’s also another one called HBlas. Why would anyone want
a third? Here are my reasons:
* Support for both immutable and mutable types. Haskell tries to make
you use immutable types as much as possible, and indeed there is a
very good reason for this, but sometimes you have a 100MB matrix, and
it just isn’t very practical to make a copy of it every time you
modify it. hmatrix only supports immutable types, and HBlas only
supports mutable ones. I wanted both.
* Access control via phantom types. When you have immutable and
mutable types, it’s very annoying to have separate functions for each
type. Do I want to have to call “numCols” for immutable matrices and
“getNumCols” for mutable ones, even though both functions are pure,
and both do exactly the same thing? No. If I want to add an immutable
matrix to a mutable one, to I want to first call “unsafeThaw” on the
immutable one to cast it to be mutable? No. With the phantom type
trick, you can get around this insanity. Jane Street Capital has a
very good description of how this works.
* Phantom types for matrix and vector shapes. This is a trick I
learned from darcs. It means that the compiler can catch many
dimension-mismatch mistakes. So, for instance, a function like
foo :: (BLAS1 e) =>
Matrix (m,n) e -> Matrix (n,k) e -> Int -> Vector m e
foo a b i = let x = row b i in a <*> x
will not type-check. (”<*>” is the function to multiply a matrix by a
vector. Everything is ok if you replace “row” by “col”.) This feature
has caught a few bugs in my code.
* Taking the conjugate transpose (”herm”) of a matrix is an O(1)
operation. This is similar to hmatrix, where taking the transpose is
O(1). As BLAS and LAPACK (mostly) support this, it makes no sense to
copy a matrix just to work with the conjugate transpose. Why conjugate
transpose instead of just transpose? Because the former is a far more
common operation. This is why the “‘” operator in MATLAB is conjugate
transpose. The drawback for this feature is that BLAS and LAPACK do
not support it everywhere. In particular, QR decomposition with
pivoting is going to be a huge pain in the ass to support for herm-ed
matrices.
* Support for triangular and hermitian views of matrices. This is a
feature of BLAS that no one seems to support (not even MATLAB). In
addition to the “Matrix” type, there are “Tri Matrix” and “Herm
Matrix” types that only refer to the upper- or lower-triangular part
of the matrix.
Hopefully the features above are compelling enough to make people want
to use the library. These bindings have been a lot of work. For me to
come up with the feature list above, I’ve already gone through a few
iterations of dramatic re-writes (hence the version number). Of
course, I always welcome suggestions for how to make it better.
What’s next? In the immediate future, I plan to add banded matrices.
I’ve already written a good chunk of code for this, but it isn’t very
well tested, so I decided to leave it out of the release. I’m also
going to add permutation matrices. I don’t have plans to add support
for packed triangular matrices, but if someone else wanted to do that,
I would be happy to include it. The same goes for symmetric complex
matrices.
LAPACK support is on the horizon, but that may take awhile. Also, I
probably won’t do more than SVD, QR, and Cholesky, since those are all
I need. Expect a preliminary announcement by the end of the summer.
This work would not have been possible without looking at the other
excellent linear algebra libraries out there. In particular the GNU
Scientific Library was the basis for much of the design. I also drew
inspiration from hmatrix and the haskell array libraries.
Please let me know if you have any success in using the library, and
if you have any suggestions for how to make it better.
Patrick
On Jun 6, 2008, at 5:36 AM, Alberto Ruiz wrote:
> Hello all,
>
> I have just noticed that yesterday this fantastic package has been
> uploaded to hackage:
>
> http://hackage.haskell.org/cgi-bin/hackage-scripts/package/blas-0.4
>
> We finally have a high quality library for numeric linear algebra.
> This is very good news for the Haskell community.
>
> Patrick, many thanks for your excellent work. Do you have similar
> plans for LAPACK?
>
> Alberto
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