ad- Automatic Differentiation

PortabilityGHC only
Safe HaskellNone



Dense Forward AD. Useful when the result involves the majority of the input elements. Do not use for hessian and beyond, since they only contain a small number of unique nth derivatives -- (n + k - 1) choose k for functions of k inputs rather than the k^n that would be generated by using Dense, not to mention the redundant intermediate derivatives that would be calculated over and over during that process!

Assumes all instances of f have the same number of elements.

NB: We don't need the full power of Traversable here, we could get by with a notion of zippable that can plug in 0's for the missing entries. This might allow for gradients where f has exponentials like ((->) a)


data Dense f a s Source


Lift !a 
Dense !a (f a) 


(Traversable f, Num a, Bounded a) => Bounded (Dense f a s) 
(Traversable f, Num a, Enum a) => Enum (Dense f a s) 
(Traversable f, Num a, Eq a) => Eq (Dense f a s) 
(Traversable f, Floating a) => Floating (Dense f a s) 
(Traversable f, Fractional a) => Fractional (Dense f a s) 
(Traversable f, Num a) => Num (Dense f a s) 
(Traversable f, Num a, Ord a) => Ord (Dense f a s) 
(Traversable f, Real a) => Real (Dense f a s) 
(Traversable f, RealFloat a) => RealFloat (Dense f a s) 
(Traversable f, RealFrac a) => RealFrac (Dense f a s) 
Show a => Show (Dense f a s) 
(Traversable f, Erf a) => Erf (Dense f a s) 
(Traversable f, InvErf a) => InvErf (Dense f a s) 
(Num a, Traversable f) => Mode (Dense f a s) 
(Traversable f, Num a) => Jacobian (Dense f a s) 

ds :: f a -> Dense f a s -> f aSource

ds' :: Num a => f a -> Dense f a s -> (a, f a)Source

vars :: (Traversable f, Num a) => f a -> f (Dense f a s)Source

apply :: (Traversable f, Num a) => (f (Dense f a s) -> b) -> f a -> bSource