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Today's Topics:
1. Automatic differentiation (AD) with respect to list of
matrices in Haskell (Miguel A. Santos)
2. Simple function gives UTF-8 decoding error. (Vilpesh Mistry)
3. Re: Simple function gives UTF-8 decoding error. (Imants Cekusins)
----------------------------------------------------------------------
Message: 1
Date: Sun, 8 May 2016 10:05:57 -0400
From: "Miguel A. Santos" <miguel.a.santo...@gmail.com>
To: beginners@haskell.org
Subject: [Haskell-beginners] Automatic differentiation (AD) with
respect to list of matrices in Haskell
Message-ID:
<CANmLrNymGMkC_FEOhUr0xfHYbakcK-ok9YTkuTGJWd59=jl...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
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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------------------------------
Message: 2
Date: Sun, 8 May 2016 20:37:20 +0530
From: Vilpesh Mistry <vilp...@gmail.com>
To: beginners@haskell.org
Subject: [Haskell-beginners] Simple function gives UTF-8 decoding
error.
Message-ID:
<CAH5zO6QRgkocPbEoXc_bEC14i8h7AyUWvXWf2kkJZ+h19s=k...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
Haskell version installed on my computer with OS Windows 7, 64 bit.
GHCi, version 7.8.3
My haskell script is in a file named baby.hs with following functions,
doubleMe x = x + x
doubleUs x y = x*2 + y*2
removeNonUpperCase :: [Char] -> [Char]
removeNonUpperCase st = [c | c <- st, c `?lem` ['A'..'Z']]
I get following error:-
g>:l baby
[1 of 1] Compiling Main ( baby.hs, interpreted )
baby.hs:6:42: lexical error (UTF-8 decoding error)
Failed, modules loaded: none.
I am not able to advance any further, please suggest.
--
thanks
Vilpesh
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Message: 3
Date: Sun, 8 May 2016 17:34:56 +0200
From: Imants Cekusins <ima...@gmail.com>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <beginners@haskell.org>
Subject: Re: [Haskell-beginners] Simple function gives UTF-8 decoding
error.
Message-ID:
<cap1qinzsmh-br7pptgsoewjnwoxlur9deatu6idvwcl97lh...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
? in ?lem?
?
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