Copyright	(c) Edward Kmett 2012-2015
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Portability	GHC only
Safe Haskell	None
Language	Haskell2010

Numeric.AD.Internal.Reverse

Description

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.

Synopsis

data Reverse s a where
- Zero :: Reverse s a
- Lift :: a -> Reverse s a
- Reverse :: !Int -> a -> Reverse s a
newtype Tape = Tape {
- getTape :: IORef Head
}
data Head = Head !Int Cells
data Cells where
- 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
partials :: forall s a. (Reifies s Tape, Num a) => Reverse s a -> [a]
partialArrayOf :: (Reifies s Tape, Num a) => Proxy s -> (Int, Int) -> Reverse s a -> Array Int a
partialMapOf :: (Reifies s Tape, Num a) => Proxy s -> Reverse s a -> IntMap a
derivativeOf :: (Reifies s Tape, Num a) => Proxy s -> Reverse s a -> a
derivativeOf' :: (Reifies s Tape, Num a) => Proxy s -> Reverse s a -> (a, a)
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

Documentation

data Reverse s a where Source #

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) Source #
Instance details 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) Source #
Instance details 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, Num a, Eq a) => Eq (Reverse s a) Source #
Instance details Defined in Numeric.AD.Internal.Reverse Methods (==) :: Reverse s a -> Reverse s a -> Bool # (/=) :: Reverse s a -> Reverse s a -> Bool #
(Reifies s Tape, Floating a) => Floating (Reverse s a) Source #
Instance details 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, Fractional a) => Fractional (Reverse s a) Source #
Instance details 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, Num a) => Num (Reverse s a) Source #
Instance details 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, Num a, Ord a) => Ord (Reverse s a) Source #
Instance details 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 #
(Reifies s Tape, Real a) => Real (Reverse s a) Source #
Instance details Defined in Numeric.AD.Internal.Reverse Methods toRational :: Reverse s a -> Rational #
(Reifies s Tape, RealFloat a) => RealFloat (Reverse s a) Source #
Instance details 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, RealFrac a) => RealFrac (Reverse s a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) => Mode (Reverse s a) Source #
Instance details Defined in Numeric.AD.Internal.Reverse Associated Types type Scalar (Reverse s a) :: Type Source # Methods isKnownConstant :: Reverse s a -> Bool Source # isKnownZero :: Reverse s a -> Bool Source # auto :: Scalar (Reverse s a) -> Reverse s a Source # (^) :: Scalar (Reverse s a) -> Reverse s a -> Reverse s a Source # (^) :: Reverse s a -> Scalar (Reverse s a) -> Reverse s a Source # (^/) :: Reverse s a -> Scalar (Reverse s a) -> Reverse s a Source # zero :: Reverse s a Source #
(Reifies s Tape, Num a) => Jacobian (Reverse s a) Source #
Instance details Defined in Numeric.AD.Internal.Reverse Associated Types type D (Reverse s a) :: Type Source # Methods unary :: (Scalar (Reverse s a) -> Scalar (Reverse s a)) -> D (Reverse s a) -> Reverse s a -> Reverse s a Source # lift1 :: (Scalar (Reverse s a) -> Scalar (Reverse s a)) -> (D (Reverse s a) -> D (Reverse s a)) -> Reverse s a -> Reverse s a Source # 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 Source # 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 Source # 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 Source # 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 Source #
type Scalar (Reverse s a) Source #
Instance details Defined in Numeric.AD.Internal.Reverse type Scalar (Reverse s a) = a
type D (Reverse s a) Source #
Instance details Defined in Numeric.AD.Internal.Reverse type D (Reverse s a) = Id a

newtype Tape Source #

Constructors

Tape
Fields getTape :: IORef Head

data Head Source #

Constructors

Head !Int Cells

data Cells where Source #

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 Source #

Construct a tape that starts with n variables.

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

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 Source #

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

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

Return an IntMap of sparse partials

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

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) Source #

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)) Source #

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

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

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

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

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

varId :: Reverse s a -> Int Source #

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