[Haskell-cafe] Automated Differentiation Type Question

[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 <dominic at 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.
> 
>