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Automatic differentiation (AD) with respect to list of matrices in Haskell
by Miguel A. Santos 08 May '16

08 May '16

I am trying to understand how can I use Numeric.AD (automatic differentiation) in Haskell. I defined a simple matrix type and a scalar function taking an array and two matrices as arguments. I want to use AD to get the gradient of the scoring function with respect to both matrices, but I'm running into compilation problems. Here is the code: ------------------------------- {-# LANGUAGE DeriveTraversable, DeriveFunctor, DeriveFoldable #-}import Numeric.AD.Mode.Reverse as Rimport Data.Traversable as Timport Data.Foldable as F --- Non-linear function on "vectors" logistic x = 1.0 / (1.0 + exp(-x) ) phi v = map logistic v phi' (x:xs) = x : (phi xs) --- dot product dot u v = foldr (+) 0 $ zipWith (*) u v --- simple matrix typedata Matrix a = M [[a]] deriving (Eq,Show,Functor,F.Foldable,T.Traversable) --- action of a matrix on a vector mv _ [] = [] mv (M []) _ = [] mv ( M m ) v = ( dot (head m) v ) : (mv (M (tail m)) v ) --- two matrices mbW1 = M $ [[1,0,0],[-1,5,1],[1,2,-3]] mbW2 = M $ [[0,0,0],[1,3,-1],[-2,4,6]] --- two different scoring functions sc1 v m = foldr (+) 0 $ (phi' . (mv m) ) v sc2 :: Floating a => [a] -> [Matrix a] -> a sc2 v [m1, m2] = foldr (+) 0 $ (phi' . (mv m2) . phi' . (mv m1) ) v strToInt = read :: String -> Double strLToIntL = map strToInt--- testing main = do putStrLn $ "mbW1:" ++ (show mbW1) putStrLn $ "mbW2:" ++ (show mbW2) rawInput <- readFile "/dev/stdin" let xin= strLToIntL $ lines rawInput putStrLn "sc xin mbW1" print $ sc1 xin mbW1 --- ok. = putStrLn "grad (sc1 xin) mbW1" print $ grad ( sc1 xin) mbW1 -- yields an error: expects xin [Reverse s Double] instead of [Double] putStrLn "grad (sc1 [3,5,7]) mbW1" print $ grad ( sc1 [3,5,7]) mbW1 --- ok. = putStrLn "sc2 xin [mbW1,mbW2]" print $ sc2 xin [mbW1, mbW2] putStrLn "grad (sc2 [3,5,7) [mbW1,mbW2]" print $ grad ( sc2 [3,5,7]) [mbW1, mbW2] --- Error: see text -------------------------------- The last line (grad on sc2) gives the following error: --------------------------------- Couldn't match type ‘Reverse s (Matrix Double)’ with ‘Matrix (Reverse s (Matrix Double))’ Expected type: [Reverse s (Matrix Double)] -> Reverse s (Matrix Double) Actual type: [Matrix (Reverse s (Matrix Double))] -> Reverse s (Matrix Double) In the first argument of ‘grad’, namely ‘(sc2 [3, 5, 7])’ In the second argument of ‘($)’, namely ‘grad (sc2 [3, 5, 7]) [mbW1, mbW2]’ --------------------------------- I don't understand where the "Matrix of Matrix" in the actual type seen comes from. I'm feeding the grad with a curried version of sc2, making it a function on a list of Matrix. Commenting out the two offending lines runs without problem, i.e., the first gradient works and is correctly calculated (I'm feeding [1,2,3] as input to the program): ------------------- mbW1:M [[1.0,0.0,0.0],[-1.0,5.0,1.0],[1.0,2.0,-3.0]] mbW2:M [[0.0,0.0,0.0],[1.0,3.0,-1.0],[-2.0,4.0,6.0]] sc1 xin mbW11232.0179800657874893 grad (sc1 [3,5,7]) mbW1 M [[3.0,5.0,7.0],[7.630996942126885e-13,1.2718328236878141e-12,1.7805659531629398e-12],[1.0057130122694228e-3,1.6761883537823711e-3,2.3466636952953197e-3]] sc2 xin [mbW1,mbW2]1.8733609463863194 ------------------- Both errors are an issue. I want to take the gradient of any such sc2 scoring function, depending on an array of matrices, evaluated at any given "point" xin. Clearly, I'm not yet understanding the AD library well enough. Any help would be appreciated. -- Public key ID: E8FE60D7 Public key server: see, e.g., hkp://keys.gnupg.net

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Infinite recursion in list comprehension
by Dushyant Juneja 06 May '16

06 May '16

Hi, I seem to be landing into infinite recursion when using higher order functions with list comprehension. Take this for an example. The following works well, and gives answers for numbers like 2000000 as well: primesBelowN :: Integer -> [Integer] primesBelowN n = 2:3:filter f [6*k+i | k <- [1..(n-1)`div`6], i <- [-1, 1]] where f x = foldr g True xs where g t ac = (x `rem` t /= 0) && ac xs = [5, 7..(truncate (sqrt (fromInteger x)))] However, the following never returns anything for the same number, probably due to some kind of loop malfunction: primesBelowN :: Integer -> [Integer] primesBelowN n = 2:3:filter f [6*k+i | k <- [1..(n-1)`div`6], i <- [-1, 1]] where f x = foldr g True xs where g t ac = (x `rem` t /= 0) && ac xs = [ m | m <- [5, 7, ..], m <= (truncate (sqrt (fromInteger x)))] Any ideas what might be going wrong? Thanks in advance! DJ

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Apology
by Peter McIlroy 05 May '16

05 May '16

Apologies for the two bad messages. I won't attempt responding by phone to this list anymore.

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Sieve of Aritosthenes
by Peter McIlroy 05 May '16

05 May '16

Apologies for the empty post. You might turn your attention to the following web page, which approaches the problem using recursive co-routines. Amidst a discussion of UNIX pipes, both in history and as a primitive co-routine implementation, there is a two-line Haskell program. http://www.cs.dartmouth.edu/~doug/sieve/ -----Original Message----- From: "beginners-request(a)haskell.org" <beginners-request(a)haskell.org> Sent: ‎5/‎5/‎2016 11:10 AM To: "beginners(a)haskell.org" <beginners(a)haskell.org> Subject: Beginners Digest, Vol 95, Issue 8 Send Beginners mailing list submissions to beginners(a)haskell.org To subscribe or unsubscribe via the World Wide Web, visit http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners or, via email, send a message with subject or body 'help' to beginners-request(a)haskell.org You can reach the person managing the list at beginners-owner(a)haskell.org When replying, please edit your Subject line so it is more specific than "Re: Contents of Beginners digest..." Today's Topics: 1. Re: Timed Profiling (Vale Cofer-Shabica) 2. Re: Infinite recursion in list comprehension (Silent Leaf) 3. Re: Infinite recursion in list comprehension (Silent Leaf) ---------------------------------------------------------------------- Message: 1 Date: Thu, 5 May 2016 10:38:50 -0400 From: Vale Cofer-Shabica <vale.cofershabica(a)gmail.com> To: The Haskell-Beginners Mailing List - Discussion of primarily beginner-level topics related to Haskell <beginners(a)haskell.org> Subject: Re: [Haskell-beginners] Timed Profiling Message-ID: <CAAzfV4Rse76Yw8Vq_Mqny_cFRw_9_FFcXBAAm4W+54zXWTuveQ(a)mail.gmail.com> Content-Type: text/plain; charset="utf-8" timeout(1) allows you to specify the signal(7) sent with the --signal option. It may be worth experimenting with different values. One of them might terminate the program while allowing it to clean up and generate profiling information. I don't know enough about the haskell runtime to know. -vale -- vale cofer-shabica 401.267.8253 On Wed, May 4, 2016 at 7:06 PM, Tim Perry <tim.v2.0(a)gmail.com> wrote: > I believe that timeout sends a kill signal to the process in question. I > imagine that the process is killed before the profiling information is > written and so you get an empty file. When you close the program with > alt-F4, the program gets a chance to shut down cleanly and writes on the > profiling information (.prof) > > > On Wed, May 4, 2016 at 9:11 AM, Ben Rogalski <bwrogalski(a)gmail.com> wrote: > >> I would like to generate a time and allocation profiling report after >> running my program for exactly 60 seconds (on Ubuntu Linux). >> >> I compiled with the following flags: >> >> -rtsopts -auto-all -caf-all -fforce-recomp >> >> I then ran the program: >> >> The program stops after 60 seconds, but the .prof file is empty. >> >> When I run the program without using timeout, and close it manually (Alt >> F4, it is a graphical program), the .prof file contains the information I >> would expect. >> >> _______________________________________________ >> Beginners mailing list >> Beginners(a)haskell.org >> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners >> >> > > _______________________________________________ > Beginners mailing list > Beginners(a)haskell.org > http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners > >

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Re: [Haskell-beginners] Beginners Digest, Vol 95, Issue 8
by Peter McIlroy 05 May '16

05 May '16

-----Original Message----- From: "beginners-request(a)haskell.org" <beginners-request(a)haskell.org> Sent: ‎5/‎5/‎2016 11:10 AM To: "beginners(a)haskell.org" <beginners(a)haskell.org> Subject: Beginners Digest, Vol 95, Issue 8 Send Beginners mailing list submissions to beginners(a)haskell.org To subscribe or unsubscribe via the World Wide Web, visit http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners or, via email, send a message with subject or body 'help' to beginners-request(a)haskell.org You can reach the person managing the list at beginners-owner(a)haskell.org When replying, please edit your Subject line so it is more specific than "Re: Contents of Beginners digest..." Today's Topics: 1. Re: Timed Profiling (Vale Cofer-Shabica) 2. Re: Infinite recursion in list comprehension (Silent Leaf) 3. Re: Infinite recursion in list comprehension (Silent Leaf) ---------------------------------------------------------------------- Message: 1 Date: Thu, 5 May 2016 10:38:50 -0400 From: Vale Cofer-Shabica <vale.cofershabica(a)gmail.com> To: The Haskell-Beginners Mailing List - Discussion of primarily beginner-level topics related to Haskell <beginners(a)haskell.org> Subject: Re: [Haskell-beginners] Timed Profiling Message-ID: <CAAzfV4Rse76Yw8Vq_Mqny_cFRw_9_FFcXBAAm4W+54zXWTuveQ(a)mail.gmail.com> Content-Type: text/plain; charset="utf-8" timeout(1) allows you to specify the signal(7) sent with the --signal option. It may be worth experimenting with different values. One of them might terminate the program while allowing it to clean up and generate profiling information. I don't know enough about the haskell runtime to know. -vale -- vale cofer-shabica 401.267.8253 On Wed, May 4, 2016 at 7:06 PM, Tim Perry <tim.v2.0(a)gmail.com> wrote: > I believe that timeout sends a kill signal to the process in question. I > imagine that the process is killed before the profiling information is > written and so you get an empty file. When you close the program with > alt-F4, the program gets a chance to shut down cleanly and writes on the > profiling information (.prof) > > > On Wed, May 4, 2016 at 9:11 AM, Ben Rogalski <bwrogalski(a)gmail.com> wrote: > >> I would like to generate a time and allocation profiling report after >> running my program for exactly 60 seconds (on Ubuntu Linux). >> >> I compiled with the following flags: >> >> -rtsopts -auto-all -caf-all -fforce-recomp >> >> I then ran the program: >> >> The program stops after 60 seconds, but the .prof file is empty. >> >> When I run the program without using timeout, and close it manually (Alt >> F4, it is a graphical program), the .prof file contains the information I >> would expect. >> >> _______________________________________________ >> Beginners mailing list >> Beginners(a)haskell.org >> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners >> >> > > _______________________________________________ > Beginners mailing list > Beginners(a)haskell.org > http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners > >

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Timed Profiling
by Ben Rogalski 05 May '16

05 May '16

I would like to generate a time and allocation profiling report after running my program for exactly 60 seconds (on Ubuntu Linux). I compiled with the following flags: -rtsopts -auto-all -caf-all -fforce-recomp I then ran the program: The program stops after 60 seconds, but the .prof file is empty. When I run the program without using timeout, and close it manually (Alt F4, it is a graphical program), the .prof file contains the information I would expect.

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Re: [Haskell-beginners] Double vs. Num
by Ben Rogalski 05 May '16

05 May '16

Tim and Christopher, here is my code. There is a lot of it, but I've tried to cut out the irrelevent parts. If I change the type of Transform3D.append from append :: (Floating a) => Transformer a -> Transform a -> Transformer a to append :: Transformer Double -> Transform Double -> Transformer Double The framerate goes from ~1400 fps to ~2200 fps. module Render where ... renderTree :: GLInfo -> Tree (Attribute Double) -> IO () renderTree (GLInfo names attribs uniforms) t = fst $ cFold2 f (return (),identity) t where f acc Hidden = Skip acc f (a,tr) (Transformation t) = Continue (a, append tr t) f (a,tr) (Clip b) = let (x1:.y1:._, x2:.y2:._) = extremes $ applyAABB tr b a' = do glUniform2f (uniforms M.! "maskMin") (realToFrac x1) (realToFrac y1) glUniform2f (uniforms M.! "maskMax") (realToFrac x2) (realToFrac y2) in Continue (a >> a', tr) f (a,tr) (Texture _ (x1:.y1:.x2:.y2:._)) = let a' = do glUniform1i (uniforms M.! "texSampler") 0 glUniform4f (uniforms M.! "uvCoords") (realToFrac x1) (realToFrac y1) (realToFrac x2) (realToFrac y2) glUniformMatrix4fv' (uniforms M.! "mvp") 1 (fromBool False) (map realToFrac $ transformerToList tr) glDrawElements gl_TRIANGLES (fromIntegral $ attribs M.! "iboLenSquare") gl_UNSIGNED_INT nullPtr in Continue (a >> a', tr) f acc _ = Continue acc ... module Transform3D where ... data Transform a = RotationZ a | Scale (Vec3 a) | Translation (Vec3 a) deriving (Eq, Read, Show) newtype Transformer a = Transformer (Vec4 (Vec4 a)) append :: (Floating a) => Transformer a -> Transform a -> Transformer a append (Transformer m) t = Transformer $ m #*# toMatrix t identity :: (Num a) => Transformer a identity = Transformer identityMatrix toMatrix :: (Floating a) => Transform a -> Vec4 (Vec4 a) toMatrix (RotationZ z) = rotationZMatrix z toMatrix (Scale (x:.y:.z:._)) = scaleMatrix x y z toMatrix (Translation (x:.y:.z:._)) = translationMatrix x y z identityMatrix :: (Num a) => Vec4 (Vec4 a) identityMatrix = (1:.0:.0:.0:.Nil):. (0:.1:.0:.0:.Nil):. (0:.0:.1:.0:.Nil):. (0:.0:.0:.1:.Nil):.Nil rotationZMatrix :: (Floating a) => a -> Vec4 (Vec4 a) rotationZMatrix a = let c = cos a s = sin a in (c:.(-s):.0:.0:.Nil):. (s:.c:.0:.0:.Nil):. (0:.0:.1:.0:.Nil):. (0:.0:.0:.1:.Nil):.Nil scaleMatrix :: (Num a) => a -> a -> a -> Vec4 (Vec4 a) scaleMatrix x y z = (x:.0:.0:.0:.Nil):. (0:.y:.0:.0:.Nil):. (0:.0:.z:.0:.Nil):. (0:.0:.0:.1:.Nil):.Nil translationMatrix :: (Num a) => a -> a -> a -> Vec4 (Vec4 a) translationMatrix x y z = (1:.0:.0:.x:.Nil):. (0:.1:.0:.y:.Nil):. (0:.0:.1:.z:.Nil):. (0:.0:.0:.1:.Nil):.Nil ... module Vector where ... infixr 5 :. --data Cons u t = (:.) t (u t) deriving (Eq, Read, Show) data Cons u t = (:.) ! t ! (u t) deriving (Eq, Read, Show) data Nil t = Nil deriving (Eq, Read, Show) ... (|*#) :: (Num t, Vector w, Vector u) => w t -> w (u t) -> u t (|*#) v m = (transpose m) #*| v (#*#) :: (Num t, Vector u, Vector v, Vector w) => u (v t) -> v (w t) -> u (w t) (#*#) x y = transpose $ fmap (x #*|) (transpose y) dot :: (Num t, Vector v) => v t -> v t -> t dot xs ys = sum ((*) <$> xs <*> ys) ...

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Double vs. Num
by Ben Rogalski 04 May '16

04 May '16

I have found that using the type Double in a type signature causes my program to run much faster than if I use a type variable with a Num constraint. Is this common, and if so, why is explicitly using Double faster?

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CAF taking all the memory
by Mahdi 03 May '16

03 May '16

Hello there, I’m pretty new to Haskell and I’m trying to write a Neural Network in Haskell for educational purposes. So, I have my neural network working, it can learn XOR in 500 iterations, but the thing is, if I increase the iterations to something like 5 milion times, the process just drains my RAM until either it’s killed or the OS drowns. Here is the code: [0] I searched online and tried to get information on why this is happening, I profiled the memory usage and found that the memory is taken by CAF, searching online, it seems like an optimization done by compiler to reduce runtime computations. Here is the profile: [1] I searched online on how to prevent this from happening, couldn’t find anything helpful. I found this [2] and tried the workaround, but it didn’t work. Is there any way to solve this problem? Because when I’m moving to more complex problems, I have to train with much more iterations, and it just doesn’t work. [0] https://github.com/mdibaiee/biscuit/blob/master/src/examples/xor.hs [1] https://gist.github.com/mdibaiee/95878469a80f1c448b8cf0762178720e [2] http://stackoverflow.com/questions/6090932/how-to-make-a-caf-not-a-caf-in-h… Thank you, – Mahdi

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ByteString unfold that can fail
by John Ky 03 May '16

03 May '16

Hello, Does anyone know of anything like Data.ByteString.unfoldr, except that it can fail with a return value? Cheers, -John

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