This module provides reverse-mode Automatic Differentiation implementation using linear time topological sorting after the fact.
For this form of reverse-mode AD we use
StableName to recover
sharing information from the tape to avoid combinatorial explosion, and thus
run asymptotically faster than it could without such sharing information, but the use
of side-effects contained herein is benign.
- newtype Kahn a = Kahn (Tape a (Kahn a))
- data Tape a t
- partials :: forall a. Num a => AD Kahn a -> [(Int, a)]
- partialArray :: Num a => (Int, Int) -> AD Kahn a -> Array Int a
- partialMap :: Num a => AD Kahn a -> IntMap a
- derivative :: Num a => AD Kahn a -> a
- derivative' :: Num a => AD Kahn a -> (a, a)
- vgrad :: Grad i o o' a => i -> o
- vgrad' :: Grad i o o' a => i -> o'
- class Num a => Grad i o o' a | i -> a o o', o -> a i o', o' -> a i o where
Kahn is a
Mode using reverse-mode automatic differentiation that provides fast
grad2 and a fast
jacobian when you have a significantly smaller number of outputs than inputs.
Tape records the information needed back propagate from the output to each input during reverse
This returns a list of contributions to the partials. The variable ids returned in the list are likely not unique!