Numeric.AD.Internal.Chain

Reverse-Mode Automatic Differentiation using a single 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.

Documentation

data Chain s a where

Constructors

Zero :: Chain s a

Lift :: a -> Chain s a

Chain :: !Int -> a -> Chain s a

Instances

Typeable2 Chain

(Mode (Chain s), Mode (D (Chain s)), Reifies s Tape, Lifted (Chain s)) => Jacobian (Chain s)

Primal (Chain s)

(Reifies s Tape, Lifted (Chain s)) => Mode (Chain s)

Reifies s Tape => Lifted (Chain s)

Primal (Chain s) => Var (Chain s)

Show a => Show (Chain s 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) => AD (Chain 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) -> AD (Chain s) a -> Array Int a

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

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

Return an IntMap of sparse partials

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

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

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

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