the 3 flavored scaffold repositories demo this technique: https://github.com/complyue/hadui/blob/master/README.md#quick-start
Suppose a 2d array initialisation whereby each entry depends on the entries immediately above the current entry and to the left and above and to the left. That can naturally be computed in parallel by traversing along the diagonals. Example:
1 2 3
4 5 6
7 8 9You start with 1, then compute 4 and 2 in parallel then 7 5 3 in parallel then 8 6 in parallel then 9 in parallel
Im having trouble coming up with a way to do this with arrayfire/repa/massiv
@chessai Doing so in a reusable (general multidimensional) fashion is certainly non trivial, but for a specific case like a 2D array it is not too hard to do with massiv, but not straightforward either. Let me think about it for a moment and I'll try to come up with an example for you.
By the way, here is a paper that describes the method I want to implement (at least variation of it): https://dl.acm.org/citation.cfm?id=1708052&dl=ACM&coll=DL
@chessai Here is almost something what you were looking for, in fact it is a bit better. Cause you don't want to schedule individual elements to be computed in parallel, but rather chunks of the diagonals. This won't matter for small arrays, but for bigger ones I suspect there will be difference. Anyways, here it is:
waterfallCreate ::
(Mutable r Ix2 a, PrimMonad m, MonadUnliftIO m, MonadThrow m)
=> Sz2
-> (Maybe a -> Maybe a -> a)
-> (a -> a -> a)
-> m (Array r Ix2 a)
waterfallCreate sz@(Sz2 m n) g f =
createArray_ Par sz $ \scheduler marr -> do
forM_ (0 ..: m) $ \i -> writeM marr (i :. 0) . g Nothing =<< A.read marr (i - 1 :. 0)
-- ^ fill left edge
forM_ (1 ..: n) $ \j -> do
writeM marr (0 :. j) . (`g` Nothing) =<< A.read marr (0 :. j - 1)
-- ^ fill the top edge
let jIter = rangeStepSize Seq j (-1) (Sz (min (m - 1) j))
iforSchedulerM_ scheduler jIter $ \i' -> writeF marr (i' + 1)
forM_ (2 ..: m) $ \i -> do
let jIter = rangeStepSize Seq (n - 1) (-1) (Sz (min (n - 1) (m - i)))
iforSchedulerM_ scheduler jIter $ \i' -> writeF marr (i' + i)
where
writeF marr i j = do
left <- readM marr (i :. j - 1)
top <- readM marr (i - 1 :. j)
writeM marr (i :. j) $ f left top
{-# INLINE writeF #-}
{-# INLINE waterfallCreate #-}
The reason for two functions
g and f instead of one, because it will be more performant if you supply separate functions: one that produces elements for the borders and another one for the inside, this way function f always knows that it will get the neighbors it needs and doesn't have to check for that edge case. Here is a cool part, because you know that the whole array will be filled up, and since f and g are pure, we are guaranteed that the whole waterfallCreate is pure, so we can safely wrap it in unsafePerformIO. More over the interior read and write functions, are guaranteed not to be out of bounds, so once you are done with all the testing you can improve the performance even further by switching to unsafe* functions:
waterfallCreate ::
Mutable r Ix2 a => Sz2 -> (Maybe a -> Maybe a -> a) -> (a -> a -> a) -> Array r Ix2 a
waterfallCreate sz@(Sz2 m n) g f =
unsafePerformIO $
createArray_ Par sz $ \scheduler marr -> do
void $ write marr (0 :. 0) $ g Nothing Nothing
forM_ (1 ..: m) $ \i ->
unsafeWrite marr (i :. 0) . g Nothing . Just =<< unsafeRead marr (i - 1 :. 0)
forM_ (1 ..: n) $ \j -> do
unsafeWrite marr (0 :. j) . (`g` Nothing) . Just =<< unsafeRead marr (0 :. j - 1)
let jIter = rangeStepSize Seq j (-1) (Sz (min (m - 1) j))
iforSchedulerM_ scheduler jIter $ \i' -> writeF marr (i' + 1)
forM_ (2 ..: m) $ \i -> do
let jIter = rangeStepSize Seq (n - 1) (-1) (Sz (min (n - 1) (m - i)))
iforSchedulerM_ scheduler jIter $ \i' -> writeF marr (i' + i)
where
writeF marr i j = do
left <- unsafeRead marr (i :. j - 1)
top <- unsafeRead marr (i - 1 :. j)
unsafeWrite marr (i :. j) $ f left top
{-# INLINE writeF #-}
{-# INLINE waterfallCreate #-}
Couple examples won't hurt:
λ> g mx my = maybe (fromMaybe 0 my) (+1) mx
λ> waterfallCreate (Sz2 4 6) g (+) :: Array P Ix2 Int
Array P Par (Sz (4 :. 6))
[ [ 0, 1, 2, 3, 4, 5 ]
, [ 0, 1, 3, 6, 10, 15 ]
, [ 0, 1, 4, 10, 20, 35 ]
, [ 0, 1, 5, 15, 35, 70 ]
]
λ> waterfallCreate (Sz2 6 4) g (+) :: Array P Ix2 Int
Array P Par (Sz (6 :. 4))
[ [ 0, 1, 2, 3 ]
, [ 0, 1, 3, 6 ]
, [ 0, 1, 4, 10 ]
, [ 0, 1, 5, 15 ]
, [ 0, 1, 6, 21 ]
, [ 0, 1, 7, 28 ]
]To sum it up:
- Not sure about
arrayfire, but I kow for a certain you can't do that inrepa - Small mistake in what you said, you can't compute 9 in parallel, since it depends on 8 and 6
8 6 in parallel then 9 in parallel
- For parallelization it is always better to schedule bigger tasks, rather than a bunch of small ones, that is why splitting loading of diagonals in chunks with
iforSchedulerM_is better. That being said, if you still feel like you want to load each element in parallel, you can easily do that by switching to manually doingscheduleWork_per each element:iforM_ jIter $ \i' -> scheduleWork_ scheduler $ writeF marr (i' + 1) - Another optimization I want to do, once I get to actually adding that to
massivis try to perform loading in blocks, rather than strips of diagonals, just cause it is better for cache locality and will be faster, but that is a totally separate story ;)
@YPares If you are talking about things like
pseq or parMap then I've never seen them being faster than massiv arrays. But most importantly, with lists you will likely end up dealing with boxed values, so you'll end up with terrible performance. I personally would advise against your suggested approach, but I'd love to see being proven wrong ;)
@lehins Oh no I'm not saying that'd be faster :) Probably yours will be, but if it's a matter of just initializing the array (and not processing an existing one) maybe this wouldn't have been much of a factor. Yeah, thinking about that I wouldn't have used
pseq anyway, probably. More likely brutal IO loops with async to init in place the array, and that's close to what you proposed.
Using
async would be slower too, it would introduce much more overhead than the solution above. Using a single Scheduler for loading the full array we ensure that there are only as many threads as there are cores at any time and only two MVars will be created for the whole operation. While with async you spawn 3 threads and 1 MVar each time you call concurrently!
So if you were to load a 100x100 array you'd end up creating 3 threads per element which would result in staggering 30000 threads
green threads are cheap, but not that cheap ;)
@/all is anyone interested in taking over
xeno( https://github.com/ocramz/xeno/ )? I don't have time to maintain it anymore and it needs some maintenance love.
@unhammer ?
@r_mohan_twitter take a look at the monad-bayes library
@r_mohan_twitter , we wrote a little intro about it here in case that you are interested:
https://www.tweag.io/posts/2019-09-20-monad-bayes-1.html
https://www.tweag.io/posts/2019-11-08-monad-bayes-2.html
otherwise these papers give a good overview of what it's doing:
https://dl.acm.org/citation.cfm?id=3236778
http://mlg.eng.cam.ac.uk/pub/pdf/SciGhaGor15.pdf
on probabilistic programming - i'm curious what people w/ more of a PL / FP background think of "Functional Tensors for Probabilistic Programming" https://arxiv.org/pdf/1910.10775.pdf
(wouldn't recommend this for day-to-day practical modeling yet, this is still pretty research-y for now)
@austinvhuang I actually read it some days ago. I very much agree with treating quantities as terms of some abstract syntax rather than constants. This is similar to how "push arrays" are implemented, and in fact deferring computation as long as possible to perfom symbolic simplifications is a very good idea
btw are tou going to PROBPROG in April?
*you
feedback would be nice
Hi, it's been a while (studies and stuff). I'm still motivated tho! I am currently looking at http://www.datahaskell.org/, so I have a few questions:
- who maintains it ?
- is it still updated ?
And more general questions : is there a general roadmap, a "place" where people here would like to take Data Haskell to ?
Sorry if those topics have been discussed many times already, but I believe that as time goes by it can be clearer and change
as for the roadmap .. everyone has different ideas on how that should look like.
what advantages does monad-bayes have over more traditional probablistic programming library such as say pymc3
I am just an occasional user but I find Monad Bayes quite comfortable to use. Here are three things that come to my mind at the moment, compared to pymc3:
- it integrates with standard Haskell syntax, you can sample from standard datatypes, functions and use do notation to combine those operations. With pymc3 you have to deal with theano tensors etc ...
- Haskell syntax make the code really concise. It really looks almost like what you would write with standard math notation in an article.
- Monad Bayes provides an abstraction on top of different inference representations and you can build new ones out of these basic building blocks. For example, mcmc requires a different representation of a prob distribution (in terms of accumulated log likelihood of the samples) than sequential monte carlo, or inverse sampling (cumulative distribution function) or a particle filter. Checkout table 1 in https://pdfs.semanticscholar.org/76ad/0090bf4a076391fe2cc6d6029f79ebc66308.pdf . AFAIK in pymc3 you basically chose a configurable out-of-the box sampler and than run it.