Copyright	(c) Edward Kmett 2010-2015
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Portability	GHC only
Safe Haskell	None
Language	Haskell2010

Numeric.AD.Internal.Forward

Description

Unsafe and often partial combinators intended for internal usage.

Handle with care.

Synopsis

data Forward a
- = Forward !a a
- | Lift !a
- | Zero
primal :: Num a => Forward a -> a
tangent :: Num a => Forward a -> a
bundle :: a -> a -> Forward a
unbundle :: Num a => Forward a -> (a, a)
apply :: Num a => (Forward a -> b) -> a -> b
bind :: (Traversable f, Num a) => (f (Forward a) -> b) -> f a -> f b
bind' :: (Traversable f, Num a) => (f (Forward a) -> b) -> f a -> (b, f b)
bindWith :: (Traversable f, Num a) => (a -> b -> c) -> (f (Forward a) -> b) -> f a -> f c
bindWith' :: (Traversable f, Num a) => (a -> b -> c) -> (f (Forward a) -> b) -> f a -> (b, f c)
transposeWith :: (Functor f, Foldable f, Traversable g) => (b -> f a -> c) -> f (g a) -> g b -> g c

Documentation

data Forward a Source #

Forward mode AD

Constructors

Forward !a a
Lift !a
Zero

Instances

(Num a, Bounded a) => Bounded (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods minBound :: Forward a # maxBound :: Forward a #
(Num a, Enum a) => Enum (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods succ :: Forward a -> Forward a # pred :: Forward a -> Forward a # toEnum :: Int -> Forward a # fromEnum :: Forward a -> Int # enumFrom :: Forward a -> [Forward a] # enumFromThen :: Forward a -> Forward a -> [Forward a] # enumFromTo :: Forward a -> Forward a -> [Forward a] # enumFromThenTo :: Forward a -> Forward a -> Forward a -> [Forward a] #
(Num a, Eq a) => Eq (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods (==) :: Forward a -> Forward a -> Bool # (/=) :: Forward a -> Forward a -> Bool #
Floating a => Floating (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods pi :: Forward a # exp :: Forward a -> Forward a # log :: Forward a -> Forward a # sqrt :: Forward a -> Forward a # (**) :: Forward a -> Forward a -> Forward a # logBase :: Forward a -> Forward a -> Forward a # sin :: Forward a -> Forward a # cos :: Forward a -> Forward a # tan :: Forward a -> Forward a # asin :: Forward a -> Forward a # acos :: Forward a -> Forward a # atan :: Forward a -> Forward a # sinh :: Forward a -> Forward a # cosh :: Forward a -> Forward a # tanh :: Forward a -> Forward a # asinh :: Forward a -> Forward a # acosh :: Forward a -> Forward a # atanh :: Forward a -> Forward a # log1p :: Forward a -> Forward a # expm1 :: Forward a -> Forward a # log1pexp :: Forward a -> Forward a # log1mexp :: Forward a -> Forward a #
Fractional a => Fractional (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods (/) :: Forward a -> Forward a -> Forward a # recip :: Forward a -> Forward a # fromRational :: Rational -> Forward a #
Data a => Data (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Forward a -> c (Forward a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Forward a) # toConstr :: Forward a -> Constr # dataTypeOf :: Forward a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Forward a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Forward a)) # gmapT :: (forall b. Data b => b -> b) -> Forward a -> Forward a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Forward a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Forward a -> r # gmapQ :: (forall d. Data d => d -> u) -> Forward a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Forward a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Forward a -> m (Forward a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Forward a -> m (Forward a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Forward a -> m (Forward a) #
Num a => Num (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods (+) :: Forward a -> Forward a -> Forward a # (-) :: Forward a -> Forward a -> Forward a # (*) :: Forward a -> Forward a -> Forward a # negate :: Forward a -> Forward a # abs :: Forward a -> Forward a # signum :: Forward a -> Forward a # fromInteger :: Integer -> Forward a #
(Num a, Ord a) => Ord (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods compare :: Forward a -> Forward a -> Ordering # (<) :: Forward a -> Forward a -> Bool # (<=) :: Forward a -> Forward a -> Bool # (>) :: Forward a -> Forward a -> Bool # (>=) :: Forward a -> Forward a -> Bool # max :: Forward a -> Forward a -> Forward a # min :: Forward a -> Forward a -> Forward a #
Real a => Real (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods toRational :: Forward a -> Rational #
RealFloat a => RealFloat (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods floatRadix :: Forward a -> Integer # floatDigits :: Forward a -> Int # floatRange :: Forward a -> (Int, Int) # decodeFloat :: Forward a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Forward a # exponent :: Forward a -> Int # significand :: Forward a -> Forward a # scaleFloat :: Int -> Forward a -> Forward a # isNaN :: Forward a -> Bool # isInfinite :: Forward a -> Bool # isDenormalized :: Forward a -> Bool # isNegativeZero :: Forward a -> Bool # isIEEE :: Forward a -> Bool # atan2 :: Forward a -> Forward a -> Forward a #
RealFrac a => RealFrac (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods properFraction :: Integral b => Forward a -> (b, Forward a) # truncate :: Integral b => Forward a -> b # round :: Integral b => Forward a -> b # ceiling :: Integral b => Forward a -> b # floor :: Integral b => Forward a -> b #
Show a => Show (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods showsPrec :: Int -> Forward a -> ShowS # show :: Forward a -> String # showList :: [Forward a] -> ShowS #
Erf a => Erf (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods erf :: Forward a -> Forward a # erfc :: Forward a -> Forward a # erfcx :: Forward a -> Forward a # normcdf :: Forward a -> Forward a #
InvErf a => InvErf (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Methods inverf :: Forward a -> Forward a # inverfc :: Forward a -> Forward a # invnormcdf :: Forward a -> Forward a #
Num a => Mode (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Associated Types type Scalar (Forward a) :: Type Source # Methods isKnownConstant :: Forward a -> Bool Source # isKnownZero :: Forward a -> Bool Source # auto :: Scalar (Forward a) -> Forward a Source # (^) :: Scalar (Forward a) -> Forward a -> Forward a Source # (^) :: Forward a -> Scalar (Forward a) -> Forward a Source # (^/) :: Forward a -> Scalar (Forward a) -> Forward a Source # zero :: Forward a Source #
Num a => Jacobian (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward Associated Types type D (Forward a) :: Type Source # Methods unary :: (Scalar (Forward a) -> Scalar (Forward a)) -> D (Forward a) -> Forward a -> Forward a Source # lift1 :: (Scalar (Forward a) -> Scalar (Forward a)) -> (D (Forward a) -> D (Forward a)) -> Forward a -> Forward a Source # lift1_ :: (Scalar (Forward a) -> Scalar (Forward a)) -> (D (Forward a) -> D (Forward a) -> D (Forward a)) -> Forward a -> Forward a Source # binary :: (Scalar (Forward a) -> Scalar (Forward a) -> Scalar (Forward a)) -> D (Forward a) -> D (Forward a) -> Forward a -> Forward a -> Forward a Source # lift2 :: (Scalar (Forward a) -> Scalar (Forward a) -> Scalar (Forward a)) -> (D (Forward a) -> D (Forward a) -> (D (Forward a), D (Forward a))) -> Forward a -> Forward a -> Forward a Source # lift2_ :: (Scalar (Forward a) -> Scalar (Forward a) -> Scalar (Forward a)) -> (D (Forward a) -> D (Forward a) -> D (Forward a) -> (D (Forward a), D (Forward a))) -> Forward a -> Forward a -> Forward a Source #
type Scalar (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward type Scalar (Forward a) = a
type D (Forward a) Source #
Instance details Defined in Numeric.AD.Internal.Forward type D (Forward a) = Id a

primal :: Num a => Forward a -> a Source #

tangent :: Num a => Forward a -> a Source #

Calculate the tangent using forward mode AD.

bundle :: a -> a -> Forward a Source #

unbundle :: Num a => Forward a -> (a, a) Source #

apply :: Num a => (Forward a -> b) -> a -> b Source #

bind :: (Traversable f, Num a) => (f (Forward a) -> b) -> f a -> f b Source #

bind' :: (Traversable f, Num a) => (f (Forward a) -> b) -> f a -> (b, f b) Source #

bindWith :: (Traversable f, Num a) => (a -> b -> c) -> (f (Forward a) -> b) -> f a -> f c Source #

bindWith' :: (Traversable f, Num a) => (a -> b -> c) -> (f (Forward a) -> b) -> f a -> (b, f c) Source #

transposeWith :: (Functor f, Foldable f, Traversable g) => (b -> f a -> c) -> f (g a) -> g b -> g c Source #