Numeric.AD.Internal.Reverse

Reverse-Mode Automatic Differentiation implementation details

For reverse mode AD we use System.Mem.StableName.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.

Documentation

newtype Reverse a

Reverse is a Mode using reverse-mode automatic differentiation that provides fast diffFU, diff2FU, grad, grad2 and a fast jacobian when you have a significantly smaller number of outputs than inputs.

Constructors

Reverse (Tape a (Reverse a))

Instances

Typeable1 Reverse

Lifted Reverse => Jacobian Reverse

Primal Reverse

Lifted Reverse => Mode Reverse

Lifted Reverse

Var Reverse

Show a => Show (Reverse a)

MuRef (Reverse a)

Var (AD Reverse)

data Tape a t

A Tape records the information needed back propagate from the output to each input during Reverse Mode AD.

Constructors

Lift a

Var a !Int

Binary a a a t t

Unary a a t

Instances

Typeable2 Tape

(Data a, Data t) => Data (Tape a t)

(Show a, Show t) => Show (Tape a t)

partials :: Num a => AD Reverse a -> [(Int, a)]

This returns a list of contributions to the partials. The variable ids returned in the list are likely not unique!

partialArray :: Num a => (Int, Int) -> AD Reverse a -> Array Int a

Return an Array of partials given bounds for the variable IDs.

partialMap :: Num a => AD Reverse a -> IntMap a

Return an IntMap of sparse partials

derivative :: Num a => AD Reverse a -> a

derivative' :: Num a => AD Reverse a -> (a, a)

class Primal v => Var v where

Used to mark variables for inspection during the reverse pass

Methods

var :: a -> Int -> v a

varId :: v a -> Int

Instances

Var Reverse

Var (AD Reverse)

bind :: (Traversable f, Var v) => f a -> (f (v a), (Int, Int))

unbind :: (Functor f, Var v) => f (v a) -> Array Int a -> f a

unbindMap :: (Functor f, Var v, Num a) => f (v a) -> IntMap a -> f a

unbindWith :: (Functor f, Var v, Num a) => (a -> b -> c) -> f (v a) -> Array Int b -> f c

unbindMapWithDefault :: (Functor f, Var v, Num a) => b -> (a -> b -> c) -> f (v a) -> IntMap b -> f c