Numeric.AD.Internal.Kahn.Double

This module provides reverse-mode Automatic Differentiation implementation using linear time topological sorting after the fact.

For this form of reverse-mode AD we use 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 KahnDouble

Kahn 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

Kahn (Tape KahnDouble)

Instances

Jacobian KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Associated Types

type D KahnDouble

Methods

unary :: (Scalar KahnDouble -> Scalar KahnDouble) -> D KahnDouble -> KahnDouble -> KahnDouble

lift1 :: (Scalar KahnDouble -> Scalar KahnDouble) -> (D KahnDouble -> D KahnDouble) -> KahnDouble -> KahnDouble

lift1_ :: (Scalar KahnDouble -> Scalar KahnDouble) -> (D KahnDouble -> D KahnDouble -> D KahnDouble) -> KahnDouble -> KahnDouble

binary :: (Scalar KahnDouble -> Scalar KahnDouble -> Scalar KahnDouble) -> D KahnDouble -> D KahnDouble -> KahnDouble -> KahnDouble -> KahnDouble

lift2 :: (Scalar KahnDouble -> Scalar KahnDouble -> Scalar KahnDouble) -> (D KahnDouble -> D KahnDouble -> (D KahnDouble, D KahnDouble)) -> KahnDouble -> KahnDouble -> KahnDouble

lift2_ :: (Scalar KahnDouble -> Scalar KahnDouble -> Scalar KahnDouble) -> (D KahnDouble -> D KahnDouble -> D KahnDouble -> (D KahnDouble, D KahnDouble)) -> KahnDouble -> KahnDouble -> KahnDouble

Mode KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Associated Types

type Scalar KahnDouble

Methods

isKnownConstant :: KahnDouble -> Bool

asKnownConstant :: KahnDouble -> Maybe (Scalar KahnDouble)

isKnownZero :: KahnDouble -> Bool

auto :: Scalar KahnDouble -> KahnDouble

(*^) :: Scalar KahnDouble -> KahnDouble -> KahnDouble

(^*) :: KahnDouble -> Scalar KahnDouble -> KahnDouble

(^/) :: KahnDouble -> Scalar KahnDouble -> KahnDouble

zero :: KahnDouble

Enum KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

succ :: KahnDouble -> KahnDouble

pred :: KahnDouble -> KahnDouble

toEnum :: Int -> KahnDouble

fromEnum :: KahnDouble -> Int

enumFrom :: KahnDouble -> [KahnDouble]

enumFromThen :: KahnDouble -> KahnDouble -> [KahnDouble]

enumFromTo :: KahnDouble -> KahnDouble -> [KahnDouble]

enumFromThenTo :: KahnDouble -> KahnDouble -> KahnDouble -> [KahnDouble]

Floating KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

pi :: KahnDouble

exp :: KahnDouble -> KahnDouble

log :: KahnDouble -> KahnDouble

sqrt :: KahnDouble -> KahnDouble

(**) :: KahnDouble -> KahnDouble -> KahnDouble

logBase :: KahnDouble -> KahnDouble -> KahnDouble

sin :: KahnDouble -> KahnDouble

cos :: KahnDouble -> KahnDouble

tan :: KahnDouble -> KahnDouble

asin :: KahnDouble -> KahnDouble

acos :: KahnDouble -> KahnDouble

atan :: KahnDouble -> KahnDouble

sinh :: KahnDouble -> KahnDouble

cosh :: KahnDouble -> KahnDouble

tanh :: KahnDouble -> KahnDouble

asinh :: KahnDouble -> KahnDouble

acosh :: KahnDouble -> KahnDouble

atanh :: KahnDouble -> KahnDouble

log1p :: KahnDouble -> KahnDouble

expm1 :: KahnDouble -> KahnDouble

log1pexp :: KahnDouble -> KahnDouble

log1mexp :: KahnDouble -> KahnDouble

RealFloat KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

floatRadix :: KahnDouble -> Integer

floatDigits :: KahnDouble -> Int

floatRange :: KahnDouble -> (Int, Int)

decodeFloat :: KahnDouble -> (Integer, Int)

encodeFloat :: Integer -> Int -> KahnDouble

exponent :: KahnDouble -> Int

significand :: KahnDouble -> KahnDouble

scaleFloat :: Int -> KahnDouble -> KahnDouble

isNaN :: KahnDouble -> Bool

isInfinite :: KahnDouble -> Bool

isDenormalized :: KahnDouble -> Bool

isNegativeZero :: KahnDouble -> Bool

isIEEE :: KahnDouble -> Bool

atan2 :: KahnDouble -> KahnDouble -> KahnDouble

Num KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

(+) :: KahnDouble -> KahnDouble -> KahnDouble

(-) :: KahnDouble -> KahnDouble -> KahnDouble

(*) :: KahnDouble -> KahnDouble -> KahnDouble

negate :: KahnDouble -> KahnDouble

abs :: KahnDouble -> KahnDouble

signum :: KahnDouble -> KahnDouble

fromInteger :: Integer -> KahnDouble

Fractional KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

(/) :: KahnDouble -> KahnDouble -> KahnDouble

recip :: KahnDouble -> KahnDouble

fromRational :: Rational -> KahnDouble

Real KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

toRational :: KahnDouble -> Rational

RealFrac KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

properFraction :: Integral b => KahnDouble -> (b, KahnDouble)

truncate :: Integral b => KahnDouble -> b

round :: Integral b => KahnDouble -> b

ceiling :: Integral b => KahnDouble -> b

floor :: Integral b => KahnDouble -> b

Show KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

showsPrec :: Int -> KahnDouble -> ShowS

show :: KahnDouble -> String

showList :: [KahnDouble] -> ShowS

MuRef KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Associated Types

type DeRef KahnDouble :: Type -> Type

Methods

mapDeRef :: Applicative f => (forall b. (MuRef b, DeRef KahnDouble ~ DeRef b) => b -> f u) -> KahnDouble -> f (DeRef KahnDouble u)

Erf KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

erf :: KahnDouble -> KahnDouble

erfc :: KahnDouble -> KahnDouble

erfcx :: KahnDouble -> KahnDouble

normcdf :: KahnDouble -> KahnDouble

InvErf KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

inverf :: KahnDouble -> KahnDouble

inverfc :: KahnDouble -> KahnDouble

invnormcdf :: KahnDouble -> KahnDouble

Eq KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

(==) :: KahnDouble -> KahnDouble -> Bool

(/=) :: KahnDouble -> KahnDouble -> Bool

Ord KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

Methods

compare :: KahnDouble -> KahnDouble -> Ordering

(<) :: KahnDouble -> KahnDouble -> Bool

(<=) :: KahnDouble -> KahnDouble -> Bool

(>) :: KahnDouble -> KahnDouble -> Bool

(>=) :: KahnDouble -> KahnDouble -> Bool

max :: KahnDouble -> KahnDouble -> KahnDouble

min :: KahnDouble -> KahnDouble -> KahnDouble

Grad i o o' => Grad (KahnDouble -> i) (Double -> o) (Double -> o')

Defined in Numeric.AD.Internal.Kahn.Double

Methods

pack :: (KahnDouble -> i) -> [KahnDouble] -> KahnDouble

unpack :: (List -> List) -> Double -> o

unpack' :: (List -> (Double, List)) -> Double -> o'

type D KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

type D KahnDouble = Id Double

type Scalar KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

type Scalar KahnDouble = Double

type DeRef KahnDouble

Defined in Numeric.AD.Internal.Kahn.Double

type DeRef KahnDouble = Tape

data Tape t

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

Constructors

Zero

Lift !Double

Var !Double !Int

Binary !Double !Double !Double t t

Unary !Double !Double t

Instances

Data t => Data (Tape t)

Defined in Numeric.AD.Internal.Kahn.Double

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Tape t -> c (Tape t)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Tape t)

toConstr :: Tape t -> Constr

dataTypeOf :: Tape t -> DataType

dataCast1 :: Typeable t0 => (forall d. Data d => c (t0 d)) -> Maybe (c (Tape t))

dataCast2 :: Typeable t0 => (forall d e. (Data d, Data e) => c (t0 d e)) -> Maybe (c (Tape t))

gmapT :: (forall b. Data b => b -> b) -> Tape t -> Tape t

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Tape t -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Tape t -> r

gmapQ :: (forall d. Data d => d -> u) -> Tape t -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Tape t -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Tape t -> m (Tape t)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Tape t -> m (Tape t)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Tape t -> m (Tape t)

Show t => Show (Tape t)

Defined in Numeric.AD.Internal.Kahn.Double

Methods

showsPrec :: Int -> Tape t -> ShowS

show :: Tape t -> String

showList :: [Tape t] -> ShowS

partials :: KahnDouble -> [(Int, Double)]

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

partialArray :: (Int, Int) -> KahnDouble -> UArray Int Double

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

partialMap :: KahnDouble -> IntMap Double

Return an IntMap of sparse partials

derivative :: KahnDouble -> Double

derivative' :: KahnDouble -> (Double, Double)

vgrad :: Grad i o o' => i -> o

vgrad' :: Grad i o o' => i -> o'

class Grad i o o' | i -> o o', o -> i o', o' -> i o where

Methods

pack :: i -> [KahnDouble] -> KahnDouble

unpack :: (List -> List) -> o

unpack' :: (List -> (Double, List)) -> o'

Instances

Grad i o o' => Grad (KahnDouble -> i) (Double -> o) (Double -> o')

Defined in Numeric.AD.Internal.Kahn.Double

Methods

pack :: (KahnDouble -> i) -> [KahnDouble] -> KahnDouble

unpack :: (List -> List) -> Double -> o

unpack' :: (List -> (Double, List)) -> Double -> o'

bind :: Traversable f => f Double -> (f KahnDouble, (Int, Int))

unbind :: Functor f => f KahnDouble -> UArray Int Double -> f Double

unbindMap :: Functor f => f KahnDouble -> IntMap Double -> f Double

unbindWithUArray :: (Functor f, IArray UArray b) => (Double -> b -> c) -> f KahnDouble -> UArray Int b -> f c

unbindWithArray :: Functor f => (Double -> b -> c) -> f KahnDouble -> Array Int b -> f c

unbindMapWithDefault :: Functor f => b -> (Double -> b -> c) -> f KahnDouble -> IntMap b -> f c

primal :: KahnDouble -> Double

var :: Double -> Int -> KahnDouble

varId :: KahnDouble -> Int