On 10/12/2012, at 12:27 AM, srean wrote:
> I will draw your attention to what Numpy folks call broadcasting, Ufuncs and
> indexing functions
There are two separate issues in Felix: static and dynamic.
If you're in dynamic land, like NumPy, then, lacking
dependent typing, Felix would just have to do things
the same kind of way as other dynamic systems.
Eg if you're using darrays or bsarrays with dynamic
sizes in Felix.
Felix can then already do every thing NumPy can do.
For example
map f a
turns f into a "ufunc". no need for special technology.
Indexing arrays doesn't need any complex rules either:
fun (i:int) => a . (f i)
already does it. A lot of NumPy technology has to reinvent
the wheel which is stock standard in FPLs: closures,
mapping, etc.
Specific functions, eg indexing triangular matrices dynamically,
will have to await use cases (because there's too many and we
need at least one use case to test with).
> http://docs.scipy.org/doc/numpy/reference/ufuncs.html#broadcasting
>From what I can gather, a ufunc is an array functor.
In FPL that's done by map:
map f a => array a with element e replaced by f e
so basically all functions are already ufuncs. It would be
easy enough to self-map, eg get rid of the "map"
keyword. however its not clear that's desirable.
For example matrix multiplication is not an elementwise
mapping.
The broadcasting rules are problematic. For static typing,
we have embeddings, eg
double => double ^ 1 // scalar to array of one
and broadcasting is roughly extension
double ^ 1 => double ^ 20
In a static typing context all such changes should have to be
explicit. At the moment, Felix uses a coercion for shape changes.
It only allows functorially sound coercions such as:
double ^ 20 ^ 20 => double ^ (20 * 20)
// convert array of arrays to linear array with tuple index
corresponding to the usual indexing rules. Using a universal
coercion operator here is not so good, named operator
with various "danger" levels might be better. Eg changing
20 x 20 array to 10 x 10 array is nonsense but memory
safe.
> I wanted to give a few examples of how a typical multidimensional indexing
> use cases look like
>
> https://github.com/ppham/skc-python/blob/e679c20967ae97d30c38a282597f30bb2f9a92d5/skc_utils.py#L148
>
> https://github.com/alleveenstra/paithon/blob/4aa40ca4e0306fdaba3ce501f00b97fb466b3a96/collaborativefiltering.py#L61
>
> https://github.com/neurospin/nipy/blob/1989e79ba73b0a059a1601fa8a5b049496d7da31/nipy/neurospin/clustering/imm.py#L388
>
> from
> https://github.com/pmeier82/Neural-Simulation/blob/9cb4103a454d1b8a1fd9fd18c6324c7a32973170/nsim/math/math3d.py#L402
>
Cool, thanks!
My inclination for dynamics is to make the user just write out stuff
long hand and then try to simplify pieces, seeking a suitable abstraction
and DSSL. A core problem is that such abstractions are context dependent,
eg matrix multiplication is different to element wise array multiplication.
We already have actual maths for tensors, with concepts like inner
and outer products, so that kind of theory is worth supporting because
we know in advance it has great utility and should scale.
Whereas a lot of matrix operations are very specific to rank and rank 3.
For example quaternions are useful in 3d space, but the abstraction
is specific to 3d.
A high level abstraction is module theory (subsumes vector spaces).
But then you run into all sorts of things, classifying modules,
some classes lose various properties. Matrices, for example,
already lose symmetry (x * y != y * x).
--
john skaller
skal...@users.sourceforge.net
http://felix-lang.org
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