Re: [Haskell-beginners] Automatic Differentiation

jacobian :: (Traversable https://hackage.haskell.org/package/base-4.9.0.0/docs/Data-Traversable.html#... f, Functor https://hackage.haskell.org/package/base-4.9.0.0/docs/Data-Functor.html#t:Fu... g, Num https://hackage.haskell.org/package/base-4.9.0.0/docs/Prelude.html#t:Num a) => (forall s. Reifies https://hackage.haskell.org/package/reflection-2.1.2/docs/Data-Reflection.ht... s Tape https://hackage.haskell.org/package/ad-4.3.2.1/docs/Numeric-AD-Internal-Reve... => f (Reverse https://hackage.haskell.org/package/ad-4.3.2.1/docs/Numeric-AD-Mode-Reverse.... s a) -> g (Reverse https://hackage.haskell.org/package/ad-4.3.2.1/docs/Numeric-AD-Mode-Reverse.... s a)) -> f a -> g (f a) Thanks a lot for your help Jonas BÉAL On 17 August 2016 at 10:40, Jonas Béal wrote:

Hello,

I have some questions about the Automatic Differentiation package in Haskell (https://hackage.haskell.org/package/ad-4.3.2.1/docs/Numeric -AD.html) I need to compute the jacobian with that method and I have a type problem, here a simplified example in order to focus on the error:

According to documentation I need to write "*jacobian function values*". So I built the input *function. *Please notice this is important for me that my function may depend on an external parameter (named factor here) testFunctionForJacobian :: Fractional a => a -> [a] -> [a] testFunctionForJacobian factor inputs = [(sum inputs) * factor]

Then, using *jacobian* function of Numeric.AD in terminal, as a test, it works perfectly

...

jacobian (testFunctionForJacobian 2) [1,2] < [[2.0,2.0]]

No apparent type problem here

...

:t (testFunctionForJacobian 2) (testFunctionForJacobian 2) :: Fractional a => [a] -> [a]

But, I would like to insert that in a bigger function computing the jacobian testJacobian :: Fractional a => a -> [a] -> [[a]] testJacobian factor inputs = jacobian (testFunctionForJacobian factor) inputs

This time it generates an error message about *factor* Couldn't match expected type ‘Numeric.AD.Internal.Reverse.Reverse http://numeric.ad.internal.reverse.reverse/ s a’ with actual type ‘a’ ‘a’ is a rigid type variable bound by the type signature for testJacobian :: Fractional a => a -> [a] -> [[a]] s a’

All in all, my type seems implicitly correct in the terminal example but I did not manage to write it explicitly in my function.

Here the *jacobian* function signature to help you answer me:

-- Jonas Béal

-- Jonas Béal R&D Scientist Intern jonas.beal@novadiscovery.com Novadiscovery The Effect Model Co. www.novadiscovery.com +33 9 72 53 13 00 Bioparc Laënnec, 60 avenue Rockefeller, 69008 Lyon -- *This message is intended only for the personal and confidential use of the designated recipient(s) named above. If you are not the intended recipient of this message you are hereby notified that any review, dissemination, distribution or copying of this message is strictly prohibited. Email transmission cannot be guaranteed to be secure or error-free. Therefore, we do not represent that this information is complete or accurate and it should not be relied upon as such. All information is subject to change without notice.*