[Haskell-cafe] Automated Differentiation Type Question

[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.