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 Kahn, 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) => Jacobian (Reverse s a)

Defined in Numeric.AD.Internal.Reverse

Associated Types

type D (Reverse s a)

Methods

unary :: (Scalar (Reverse s a) -> Scalar (Reverse s a)) -> D (Reverse s a) -> Reverse s a -> Reverse s a

lift1 :: (Scalar (Reverse s a) -> Scalar (Reverse s a)) -> (D (Reverse s a) -> D (Reverse s a)) -> Reverse s a -> Reverse s a

lift1_ :: (Scalar (Reverse s a) -> Scalar (Reverse s a)) -> (D (Reverse s a) -> D (Reverse s a) -> D (Reverse s a)) -> Reverse s a -> Reverse s a

binary :: (Scalar (Reverse s a) -> Scalar (Reverse s a) -> Scalar (Reverse s a)) -> D (Reverse s a) -> D (Reverse s a) -> Reverse s a -> Reverse s a -> Reverse s a

lift2 :: (Scalar (Reverse s a) -> Scalar (Reverse s a) -> Scalar (Reverse s a)) -> (D (Reverse s a) -> D (Reverse s a) -> (D (Reverse s a), D (Reverse s a))) -> Reverse s a -> Reverse s a -> Reverse s a

lift2_ :: (Scalar (Reverse s a) -> Scalar (Reverse s a) -> Scalar (Reverse s a)) -> (D (Reverse s a) -> D (Reverse s a) -> D (Reverse s a) -> (D (Reverse s a), D (Reverse s a))) -> Reverse s a -> Reverse s a -> Reverse s a

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

Defined in Numeric.AD.Internal.Reverse

Associated Types

type Scalar (Reverse s a)

Methods

isKnownConstant :: Reverse s a -> Bool

asKnownConstant :: Reverse s a -> Maybe (Scalar (Reverse s a))

isKnownZero :: Reverse s a -> Bool

auto :: Scalar (Reverse s a) -> Reverse s a

(*^) :: Scalar (Reverse s a) -> Reverse s a -> Reverse s a

(^*) :: Reverse s a -> Scalar (Reverse s a) -> Reverse s a

(^/) :: Reverse s a -> Scalar (Reverse s a) -> Reverse s a

zero :: Reverse s a

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

Defined in Numeric.AD.Internal.Reverse

Methods

minBound :: Reverse s a

maxBound :: Reverse s a

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

Defined in Numeric.AD.Internal.Reverse

Methods

succ :: Reverse s a -> Reverse s a

pred :: Reverse s a -> Reverse s a

toEnum :: Int -> Reverse s a

fromEnum :: Reverse s a -> Int

enumFrom :: Reverse s a -> [Reverse s a]

enumFromThen :: Reverse s a -> Reverse s a -> [Reverse s a]

enumFromTo :: Reverse s a -> Reverse s a -> [Reverse s a]

enumFromThenTo :: Reverse s a -> Reverse s a -> Reverse s a -> [Reverse s a]

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

Defined in Numeric.AD.Internal.Reverse

Methods

pi :: Reverse s a

exp :: Reverse s a -> Reverse s a

log :: Reverse s a -> Reverse s a

sqrt :: Reverse s a -> Reverse s a

(**) :: Reverse s a -> Reverse s a -> Reverse s a

logBase :: Reverse s a -> Reverse s a -> Reverse s a

sin :: Reverse s a -> Reverse s a

cos :: Reverse s a -> Reverse s a

tan :: Reverse s a -> Reverse s a

asin :: Reverse s a -> Reverse s a

acos :: Reverse s a -> Reverse s a

atan :: Reverse s a -> Reverse s a

sinh :: Reverse s a -> Reverse s a

cosh :: Reverse s a -> Reverse s a

tanh :: Reverse s a -> Reverse s a

asinh :: Reverse s a -> Reverse s a

acosh :: Reverse s a -> Reverse s a

atanh :: Reverse s a -> Reverse s a

log1p :: Reverse s a -> Reverse s a

expm1 :: Reverse s a -> Reverse s a

log1pexp :: Reverse s a -> Reverse s a

log1mexp :: Reverse s a -> Reverse s a

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

Defined in Numeric.AD.Internal.Reverse

Methods

floatRadix :: Reverse s a -> Integer

floatDigits :: Reverse s a -> Int

floatRange :: Reverse s a -> (Int, Int)

decodeFloat :: Reverse s a -> (Integer, Int)

encodeFloat :: Integer -> Int -> Reverse s a

exponent :: Reverse s a -> Int

significand :: Reverse s a -> Reverse s a

scaleFloat :: Int -> Reverse s a -> Reverse s a

isNaN :: Reverse s a -> Bool

isInfinite :: Reverse s a -> Bool

isDenormalized :: Reverse s a -> Bool

isNegativeZero :: Reverse s a -> Bool

isIEEE :: Reverse s a -> Bool

atan2 :: Reverse s a -> Reverse s a -> Reverse s a

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

Defined in Numeric.AD.Internal.Reverse

Methods

(+) :: Reverse s a -> Reverse s a -> Reverse s a

(-) :: Reverse s a -> Reverse s a -> Reverse s a

(*) :: Reverse s a -> Reverse s a -> Reverse s a

negate :: Reverse s a -> Reverse s a

abs :: Reverse s a -> Reverse s a

signum :: Reverse s a -> Reverse s a

fromInteger :: Integer -> Reverse s a

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

Defined in Numeric.AD.Internal.Reverse

Methods

(/) :: Reverse s a -> Reverse s a -> Reverse s a

recip :: Reverse s a -> Reverse s a

fromRational :: Rational -> Reverse s a

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

Defined in Numeric.AD.Internal.Reverse

Methods

toRational :: Reverse s a -> Rational

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

Defined in Numeric.AD.Internal.Reverse

Methods

properFraction :: Integral b => Reverse s a -> (b, Reverse s a)

truncate :: Integral b => Reverse s a -> b

round :: Integral b => Reverse s a -> b

ceiling :: Integral b => Reverse s a -> b

floor :: Integral b => Reverse s a -> b

Show a => Show (Reverse s a)

Defined in Numeric.AD.Internal.Reverse

Methods

showsPrec :: Int -> Reverse s a -> ShowS

show :: Reverse s a -> String

showList :: [Reverse s a] -> ShowS

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

Defined in Numeric.AD.Internal.Reverse

Methods

erf :: Reverse s a -> Reverse s a

erfc :: Reverse s a -> Reverse s a

erfcx :: Reverse s a -> Reverse s a

normcdf :: Reverse s a -> Reverse s a

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

Defined in Numeric.AD.Internal.Reverse

Methods

inverf :: Reverse s a -> Reverse s a

inverfc :: Reverse s a -> Reverse s a

invnormcdf :: Reverse s a -> Reverse s a

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

Defined in Numeric.AD.Internal.Reverse

Methods

(==) :: Reverse s a -> Reverse s a -> Bool

(/=) :: Reverse s a -> Reverse s a -> Bool

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

Defined in Numeric.AD.Internal.Reverse

Methods

compare :: Reverse s a -> Reverse s a -> Ordering

(<) :: Reverse s a -> Reverse s a -> Bool

(<=) :: Reverse s a -> Reverse s a -> Bool

(>) :: Reverse s a -> Reverse s a -> Bool

(>=) :: Reverse s a -> Reverse s a -> Bool

max :: Reverse s a -> Reverse s a -> Reverse s a

min :: Reverse s a -> Reverse s a -> Reverse s a

type D (Reverse s a)

Defined in Numeric.AD.Internal.Reverse

type D (Reverse s a) = Id a

type Scalar (Reverse s a)

Defined in Numeric.AD.Internal.Reverse

type Scalar (Reverse s a) = 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.

reifyTypeableTape :: Int -> (forall s. (Typeable 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