[Haskell-cafe] Automated Differentiation Type Question

2013-04-23 Thread Dominic Steinitz 
Can anyone tell me why I get a type error with testGrad2? What are my options? 
Clearly I would like to be able find the gradient of my cost function for 
different sets of observations.

Thanks, Dominic.

 {-# LANGUAGE NoMonomorphismRestriction #-}
 
 import Numeric.AD
 
 default()
 
 costFn :: Floating a = [a] - [[a]] - [a] - a
 costFn ys xss thetas = (/ (2*m)) $ sum $ map (^ (2 :: Int)) $
zipWith (\y xs - costFnAux y xs thetas) ys xss
   where
 m = fromIntegral $ length xss
 costFnAux :: Floating a = a - [a] - [a] - a
 costFnAux y xs thetas = y - head thetas - sum (zipWith (*) xs (tail 
 thetas))
 
 ys :: Floating a = [a]
 ys = [1.0, 2.0, 3.0]
 
 xss :: Floating a = [[a]]
 xss = [[1.0], [2.0], [3.0]]
 
 thetas :: Floating a = [a]
 thetas = [0.0, 1.0]
 
 test :: Floating a = a
 test = costFn ys xss thetas
 
 testGrad0 = grad (costFn ys xss)
 
 testGrad1 :: Floating a = [a] - [[a]] - [a] - [a]
 testGrad1 ys xss = grad (costFn (undefined :: Floating a = [a]) (undefined 
 :: Floating a = [[a]]))
 
 testGrad2 :: Floating a = [a] - [[a]] - [a] - [a]
 testGrad2 ys xss = grad (costFn ys xss)

 [1 of 1] Compiling Main ( 
 /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs, interpreted )
 
 /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:33:
 Could not deduce (a ~ ad-3.4:Numeric.AD.Internal.Types.AD s a)
 from the context (Floating a)
   bound by the type signature for
  testGrad2 :: Floating a = [a] - [[a]] - [a] - [a]
   at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14-53
 or from (Numeric.AD.Internal.Classes.Mode s)
   bound by a type expected by the context:
  Numeric.AD.Internal.Classes.Mode s =
  [ad-3.4:Numeric.AD.Internal.Types.AD s a]
  - ad-3.4:Numeric.AD.Internal.Types.AD s a
   at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:20-39
   `a' is a rigid type variable bound by
   the type signature for
 testGrad2 :: Floating a = [a] - [[a]] - [a] - [a]
   at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14
 Expected type: [ad-3.4:Numeric.AD.Internal.Types.AD s a]
   Actual type: [a]
 In the first argument of `costFn', namely `ys'
 In the first argument of `grad', namely `(costFn ys xss)'
 In the expression: grad (costFn ys xss)
 
 /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:36:
 Could not deduce (a ~ ad-3.4:Numeric.AD.Internal.Types.AD s a)
 from the context (Floating a)
   bound by the type signature for
  testGrad2 :: Floating a = [a] - [[a]] - [a] - [a]
   at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14-53
 or from (Numeric.AD.Internal.Classes.Mode s)
   bound by a type expected by the context:
  Numeric.AD.Internal.Classes.Mode s =
  [ad-3.4:Numeric.AD.Internal.Types.AD s a]
  - ad-3.4:Numeric.AD.Internal.Types.AD s a
   at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:20-39
   `a' is a rigid type variable bound by
   the type signature for
 testGrad2 :: Floating a = [a] - [[a]] - [a] - [a]
   at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14
 Expected type: [[ad-3.4:Numeric.AD.Internal.Types.AD s a]]
   Actual type: [[a]]
 In the second argument of `costFn', namely `xss'
 In the first argument of `grad', namely `(costFn ys xss)'
 In the expression: grad (costFn ys xss)
 Failed, modules loaded: none.



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Re: [Haskell-cafe] Automated Differentiation Type Question

2013-04-23 Thread Dominic Steinitz 
Answering my own question, what I needed was:

testGrad2 :: (Fractional a, Num a) =
 (forall s . Mode s = [AD s a]) -
 (forall s . Mode s = [[AD s a]]) -
 [a] - [a]
testGrad2 ys xss = grad (costFn ys xss)


On 23 Apr 2013, at 10:44, Dominic Steinitz domi...@steinitz.org wrote:

 Can anyone tell me why I get a type error with testGrad2? What are my 
 options? Clearly I would like to be able find the gradient of my cost 
 function for different sets of observations.
 
 Thanks, Dominic.
 
 {-# LANGUAGE NoMonomorphismRestriction #-}
 
 import Numeric.AD
 
 default()
 
 costFn :: Floating a = [a] - [[a]] - [a] - a
 costFn ys xss thetas = (/ (2*m)) $ sum $ map (^ (2 :: Int)) $
   zipWith (\y xs - costFnAux y xs thetas) ys xss
  where
m = fromIntegral $ length xss
costFnAux :: Floating a = a - [a] - [a] - a
costFnAux y xs thetas = y - head thetas - sum (zipWith (*) xs (tail 
 thetas))
 
 ys :: Floating a = [a]
 ys = [1.0, 2.0, 3.0]
 
 xss :: Floating a = [[a]]
 xss = [[1.0], [2.0], [3.0]]
 
 thetas :: Floating a = [a]
 thetas = [0.0, 1.0]
 
 test :: Floating a = a
 test = costFn ys xss thetas
 
 testGrad0 = grad (costFn ys xss)
 
 testGrad1 :: Floating a = [a] - [[a]] - [a] - [a]
 testGrad1 ys xss = grad (costFn (undefined :: Floating a = [a]) (undefined 
 :: Floating a = [[a]]))
 
 testGrad2 :: Floating a = [a] - [[a]] - [a] - [a]
 testGrad2 ys xss = grad (costFn ys xss)
 
 [1 of 1] Compiling Main ( 
 /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs, interpreted )
 
 /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:33:
Could not deduce (a ~ ad-3.4:Numeric.AD.Internal.Types.AD s a)
from the context (Floating a)
  bound by the type signature for
 testGrad2 :: Floating a = [a] - [[a]] - [a] - [a]
  at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14-53
or from (Numeric.AD.Internal.Classes.Mode s)
  bound by a type expected by the context:
 Numeric.AD.Internal.Classes.Mode s =
 [ad-3.4:Numeric.AD.Internal.Types.AD s a]
 - ad-3.4:Numeric.AD.Internal.Types.AD s a
  at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:20-39
  `a' is a rigid type variable bound by
  the type signature for
testGrad2 :: Floating a = [a] - [[a]] - [a] - [a]
  at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14
Expected type: [ad-3.4:Numeric.AD.Internal.Types.AD s a]
  Actual type: [a]
In the first argument of `costFn', namely `ys'
In the first argument of `grad', namely `(costFn ys xss)'
In the expression: grad (costFn ys xss)
 
 /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:36:
Could not deduce (a ~ ad-3.4:Numeric.AD.Internal.Types.AD s a)
from the context (Floating a)
  bound by the type signature for
 testGrad2 :: Floating a = [a] - [[a]] - [a] - [a]
  at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14-53
or from (Numeric.AD.Internal.Classes.Mode s)
  bound by a type expected by the context:
 Numeric.AD.Internal.Classes.Mode s =
 [ad-3.4:Numeric.AD.Internal.Types.AD s a]
 - ad-3.4:Numeric.AD.Internal.Types.AD s a
  at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:20-39
  `a' is a rigid type variable bound by
  the type signature for
testGrad2 :: Floating a = [a] - [[a]] - [a] - [a]
  at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14
Expected type: [[ad-3.4:Numeric.AD.Internal.Types.AD s a]]
  Actual type: [[a]]
In the second argument of `costFn', namely `xss'
In the first argument of `grad', namely `(costFn ys xss)'
In the expression: grad (costFn ys xss)
 Failed, modules loaded: none.
 
 


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