Numeric.AD.Internal.Reverse

Reverse-Mode Automatic Differentiation using a single Wengert list (or "tape").

This version uses Data.Reflection to find and update the tape.

This is asymptotically faster than using Reverse, which is forced to reify and topologically sort the graph, but it requires a fairly expensive rendezvous during construction when updated using multiple threads.

Documentation

data Reverse s a where

Constructors

Zero :: Reverse s a

Lift :: a -> Reverse s a

Reverse :: !Int -> a -> Reverse s a

Instances

(Reifies * s Tape, Num a, Bounded a) => Bounded (Reverse s a)

(Reifies * s Tape, Num a, Enum a) => Enum (Reverse s a)

(Reifies * s Tape, Num a, Eq a) => Eq (Reverse s a)

(Reifies * s Tape, Floating a) => Floating (Reverse s a)

(Reifies * s Tape, Fractional a) => Fractional (Reverse s a)

(Reifies * s Tape, Num a) => Num (Reverse s a)

(Reifies * s Tape, Num a, Ord a) => Ord (Reverse s a)

(Reifies * s Tape, Real a) => Real (Reverse s a)

(Reifies * s Tape, RealFloat a) => RealFloat (Reverse s a)

(Reifies * s Tape, RealFrac a) => RealFrac (Reverse s a)

Show a => Show (Reverse s a)

(Reifies * s Tape, Erf a) => Erf (Reverse s a)

(Reifies * s Tape, InvErf a) => InvErf (Reverse s a)

(Reifies * s Tape, Num a) => Mode (Reverse s a)

(Reifies * s Tape, Num a) => Jacobian (Reverse s a)

Typeable (* -> * -> *) Reverse

type Scalar (Reverse s a) = a

type D (Reverse s a) = Id a

newtype Tape

Constructors

Tape

Fields

getTape :: IORef Head

data Head

Constructors

Head !Int Cells

data Cells where

Constructors

Nil :: Cells

Unary :: !Int -> a -> Cells -> Cells

Binary :: !Int -> !Int -> a -> a -> Cells -> Cells

reifyTape :: Int -> (forall s. Reifies s Tape => Proxy s -> r) -> r

Construct a tape that starts with n variables.

partials :: forall s a. (Reifies s Tape, Num a) => Reverse s a -> [a]

Extract the partials from the current chain for a given AD variable.

partialArrayOf :: (Reifies s Tape, Num a) => Proxy s -> (Int, Int) -> Reverse s a -> Array Int a

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

partialMapOf :: (Reifies s Tape, Num a) => Proxy s -> Reverse s a -> IntMap a

Return an IntMap of sparse partials

derivativeOf :: (Reifies s Tape, Num a) => Proxy s -> Reverse s a -> a

Helper that extracts the derivative of a chain when the chain was constructed with 1 variable.

derivativeOf' :: (Reifies s Tape, Num a) => Proxy s -> Reverse s a -> (a, a)

Helper that extracts both the primal and derivative of a chain when the chain was constructed with 1 variable.

bind :: Traversable f => f a -> (f (Reverse s a), (Int, Int))

unbind :: Functor f => f (Reverse s a) -> Array Int a -> f a

unbindMap :: (Functor f, Num a) => f (Reverse s a) -> IntMap a -> f a

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

unbindMapWithDefault :: (Functor f, Num a) => b -> (a -> b -> c) -> f (Reverse s a) -> IntMap b -> f c

var :: a -> Int -> Reverse s a

varId :: Reverse s a -> Int

primal :: Num a => Reverse s a -> a