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 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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