Copyright | (c) Edward Kmett 2010-2014 |
---|---|
License | BSD3 |
Maintainer | ekmett@gmail.com |
Stability | experimental |
Portability | GHC only |
Safe Haskell | None |
Language | Haskell2010 |
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 n
th derivatives --
(n + k - 1)
for functions of choose
kk
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)
Documentation
(Traversable f, Num a, Bounded a) => Bounded (Dense f a) | |
(Traversable f, Num a, Enum a) => Enum (Dense f a) | |
(Traversable f, Num a, Eq a) => Eq (Dense f a) | |
(Traversable f, Floating a) => Floating (Dense f a) | |
(Traversable f, Fractional a) => Fractional (Dense f a) | |
(Traversable f, Num a) => Num (Dense f a) | |
(Traversable f, Num a, Ord a) => Ord (Dense f a) | |
(Traversable f, Real a) => Real (Dense f a) | |
(Traversable f, RealFloat a) => RealFloat (Dense f a) | |
(Traversable f, RealFrac a) => RealFrac (Dense f a) | |
Show a => Show (Dense f a) | |
(Traversable f, Erf a) => Erf (Dense f a) | |
(Traversable f, InvErf a) => InvErf (Dense f a) | |
(Num a, Traversable f) => Mode (Dense f a) | |
(Traversable f, Num a) => Jacobian (Dense f a) | |
type Scalar (Dense f a) = a | |
type D (Dense f a) = Id a |
vars :: (Traversable f, Num a) => f a -> f (Dense f a) Source
apply :: (Traversable f, Num a) => (f (Dense f a) -> b) -> f a -> b Source