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

Numeric.AD.Mode

Contents

AD modes

Description

Synopsis

AD modes

class (Num t, Num (Scalar t)) => Mode t where #

Minimal complete definition

auto

Associated Types

type Scalar t #

Methods

isKnownConstant :: t -> Bool #

allowed to return False for items with a zero derivative, but we'll give more NaNs than strictly necessary

isKnownZero :: t -> Bool #

allowed to return False for zero, but we give more NaN's than strictly necessary

auto :: Scalar t -> t #

Embed a constant

(*^) :: Scalar t -> t -> t infixr 7 #

Scalar-vector multiplication

(^*) :: t -> Scalar t -> t infixl 7 #

Vector-scalar multiplication

(^/) :: Fractional (Scalar t) => t -> Scalar t -> t infixr 7 #

Scalar division

zero :: t #

zero = lift 0

Instances

Mode Double #
Associated Types type Scalar Double :: * # Methods isKnownConstant :: Double -> Bool # isKnownZero :: Double -> Bool # auto :: Scalar Double -> Double # (^) :: Scalar Double -> Double -> Double # (^) :: Double -> Scalar Double -> Double # (^/) :: Double -> Scalar Double -> Double # zero :: Double #
Mode Float #
Associated Types type Scalar Float :: * # Methods isKnownConstant :: Float -> Bool # isKnownZero :: Float -> Bool # auto :: Scalar Float -> Float # (^) :: Scalar Float -> Float -> Float # (^) :: Float -> Scalar Float -> Float # (^/) :: Float -> Scalar Float -> Float # zero :: Float #
Mode Int #
Associated Types type Scalar Int :: * # Methods isKnownConstant :: Int -> Bool # isKnownZero :: Int -> Bool # auto :: Scalar Int -> Int # (^) :: Scalar Int -> Int -> Int # (^) :: Int -> Scalar Int -> Int # (^/) :: Int -> Scalar Int -> Int # zero :: Int #
Mode Int8 #
Associated Types type Scalar Int8 :: * # Methods isKnownConstant :: Int8 -> Bool # isKnownZero :: Int8 -> Bool # auto :: Scalar Int8 -> Int8 # (^) :: Scalar Int8 -> Int8 -> Int8 # (^) :: Int8 -> Scalar Int8 -> Int8 # (^/) :: Int8 -> Scalar Int8 -> Int8 # zero :: Int8 #
Mode Int16 #
Associated Types type Scalar Int16 :: * # Methods isKnownConstant :: Int16 -> Bool # isKnownZero :: Int16 -> Bool # auto :: Scalar Int16 -> Int16 # (^) :: Scalar Int16 -> Int16 -> Int16 # (^) :: Int16 -> Scalar Int16 -> Int16 # (^/) :: Int16 -> Scalar Int16 -> Int16 # zero :: Int16 #
Mode Int32 #
Associated Types type Scalar Int32 :: * # Methods isKnownConstant :: Int32 -> Bool # isKnownZero :: Int32 -> Bool # auto :: Scalar Int32 -> Int32 # (^) :: Scalar Int32 -> Int32 -> Int32 # (^) :: Int32 -> Scalar Int32 -> Int32 # (^/) :: Int32 -> Scalar Int32 -> Int32 # zero :: Int32 #
Mode Int64 #
Associated Types type Scalar Int64 :: * # Methods isKnownConstant :: Int64 -> Bool # isKnownZero :: Int64 -> Bool # auto :: Scalar Int64 -> Int64 # (^) :: Scalar Int64 -> Int64 -> Int64 # (^) :: Int64 -> Scalar Int64 -> Int64 # (^/) :: Int64 -> Scalar Int64 -> Int64 # zero :: Int64 #
Mode Integer #
Associated Types type Scalar Integer :: * # Methods isKnownConstant :: Integer -> Bool # isKnownZero :: Integer -> Bool # auto :: Scalar Integer -> Integer # (^) :: Scalar Integer -> Integer -> Integer # (^) :: Integer -> Scalar Integer -> Integer # (^/) :: Integer -> Scalar Integer -> Integer # zero :: Integer #
Mode Natural #
Associated Types type Scalar Natural :: * # Methods isKnownConstant :: Natural -> Bool # isKnownZero :: Natural -> Bool # auto :: Scalar Natural -> Natural # (^) :: Scalar Natural -> Natural -> Natural # (^) :: Natural -> Scalar Natural -> Natural # (^/) :: Natural -> Scalar Natural -> Natural # zero :: Natural #
Mode Word #
Associated Types type Scalar Word :: * # Methods isKnownConstant :: Word -> Bool # isKnownZero :: Word -> Bool # auto :: Scalar Word -> Word # (^) :: Scalar Word -> Word -> Word # (^) :: Word -> Scalar Word -> Word # (^/) :: Word -> Scalar Word -> Word # zero :: Word #
Mode Word8 #
Associated Types type Scalar Word8 :: * # Methods isKnownConstant :: Word8 -> Bool # isKnownZero :: Word8 -> Bool # auto :: Scalar Word8 -> Word8 # (^) :: Scalar Word8 -> Word8 -> Word8 # (^) :: Word8 -> Scalar Word8 -> Word8 # (^/) :: Word8 -> Scalar Word8 -> Word8 # zero :: Word8 #
Mode Word16 #
Associated Types type Scalar Word16 :: * # Methods isKnownConstant :: Word16 -> Bool # isKnownZero :: Word16 -> Bool # auto :: Scalar Word16 -> Word16 # (^) :: Scalar Word16 -> Word16 -> Word16 # (^) :: Word16 -> Scalar Word16 -> Word16 # (^/) :: Word16 -> Scalar Word16 -> Word16 # zero :: Word16 #
Mode Word32 #
Associated Types type Scalar Word32 :: * # Methods isKnownConstant :: Word32 -> Bool # isKnownZero :: Word32 -> Bool # auto :: Scalar Word32 -> Word32 # (^) :: Scalar Word32 -> Word32 -> Word32 # (^) :: Word32 -> Scalar Word32 -> Word32 # (^/) :: Word32 -> Scalar Word32 -> Word32 # zero :: Word32 #
Mode Word64 #
Associated Types type Scalar Word64 :: * # Methods isKnownConstant :: Word64 -> Bool # isKnownZero :: Word64 -> Bool # auto :: Scalar Word64 -> Word64 # (^) :: Scalar Word64 -> Word64 -> Word64 # (^) :: Word64 -> Scalar Word64 -> Word64 # (^/) :: Word64 -> Scalar Word64 -> Word64 # zero :: Word64 #
Mode ForwardDouble #
Associated Types type Scalar ForwardDouble :: * # Methods isKnownConstant :: ForwardDouble -> Bool # isKnownZero :: ForwardDouble -> Bool # auto :: Scalar ForwardDouble -> ForwardDouble # (^) :: Scalar ForwardDouble -> ForwardDouble -> ForwardDouble # (^) :: ForwardDouble -> Scalar ForwardDouble -> ForwardDouble # (^/) :: ForwardDouble -> Scalar ForwardDouble -> ForwardDouble # zero :: ForwardDouble #
Integral a => Mode (Ratio a) #
Associated Types type Scalar (Ratio a) :: * # Methods isKnownConstant :: Ratio a -> Bool # isKnownZero :: Ratio a -> Bool # auto :: Scalar (Ratio a) -> Ratio a # (^) :: Scalar (Ratio a) -> Ratio a -> Ratio a # (^) :: Ratio a -> Scalar (Ratio a) -> Ratio a # (^/) :: Ratio a -> Scalar (Ratio a) -> Ratio a # zero :: Ratio a #
RealFloat a => Mode (Complex a) #
Associated Types type Scalar (Complex a) :: * # Methods isKnownConstant :: Complex a -> Bool # isKnownZero :: Complex a -> Bool # auto :: Scalar (Complex a) -> Complex a # (^) :: Scalar (Complex a) -> Complex a -> Complex a # (^) :: Complex a -> Scalar (Complex a) -> Complex a # (^/) :: Complex a -> Scalar (Complex a) -> Complex a # zero :: Complex a #
(Mode t, Mode (Scalar t)) => Mode (On t) #
Associated Types type Scalar (On t) :: * # Methods isKnownConstant :: On t -> Bool # isKnownZero :: On t -> Bool # auto :: Scalar (On t) -> On t # (^) :: Scalar (On t) -> On t -> On t # (^) :: On t -> Scalar (On t) -> On t # (^/) :: On t -> Scalar (On t) -> On t # zero :: On t #
Num a => Mode (Id a) #
Associated Types type Scalar (Id a) :: * # Methods isKnownConstant :: Id a -> Bool # isKnownZero :: Id a -> Bool # auto :: Scalar (Id a) -> Id a # (^) :: Scalar (Id a) -> Id a -> Id a # (^) :: Id a -> Scalar (Id a) -> Id a # (^/) :: Id a -> Scalar (Id a) -> Id a # zero :: Id a #
Num a => Mode (Tower a) #
Associated Types type Scalar (Tower a) :: * # Methods isKnownConstant :: Tower a -> Bool # isKnownZero :: Tower a -> Bool # auto :: Scalar (Tower a) -> Tower a # (^) :: Scalar (Tower a) -> Tower a -> Tower a # (^) :: Tower a -> Scalar (Tower a) -> Tower a # (^/) :: Tower a -> Scalar (Tower a) -> Tower a # zero :: Tower a #
Num a => Mode (Sparse a) #
Associated Types type Scalar (Sparse a) :: * # Methods isKnownConstant :: Sparse a -> Bool # isKnownZero :: Sparse a -> Bool # auto :: Scalar (Sparse a) -> Sparse a # (^) :: Scalar (Sparse a) -> Sparse a -> Sparse a # (^) :: Sparse a -> Scalar (Sparse a) -> Sparse a # (^/) :: Sparse a -> Scalar (Sparse a) -> Sparse a # zero :: Sparse a #
Num a => Mode (Kahn a) #
Associated Types type Scalar (Kahn a) :: * # Methods isKnownConstant :: Kahn a -> Bool # isKnownZero :: Kahn a -> Bool # auto :: Scalar (Kahn a) -> Kahn a # (^) :: Scalar (Kahn a) -> Kahn a -> Kahn a # (^) :: Kahn a -> Scalar (Kahn a) -> Kahn a # (^/) :: Kahn a -> Scalar (Kahn a) -> Kahn a # zero :: Kahn a #
Num a => Mode (Forward a) #
Associated Types type Scalar (Forward a) :: * # Methods isKnownConstant :: Forward a -> Bool # isKnownZero :: Forward a -> Bool # auto :: Scalar (Forward a) -> Forward a # (^) :: Scalar (Forward a) -> Forward a -> Forward a # (^) :: Forward a -> Scalar (Forward a) -> Forward a # (^/) :: Forward a -> Scalar (Forward a) -> Forward a # zero :: Forward a #
Mode a => Mode (AD s a) #
Associated Types type Scalar (AD s a) :: * # Methods isKnownConstant :: AD s a -> Bool # isKnownZero :: AD s a -> Bool # auto :: Scalar (AD s a) -> AD s a # (^) :: Scalar (AD s a) -> AD s a -> AD s a # (^) :: AD s a -> Scalar (AD s a) -> AD s a # (^/) :: AD s a -> Scalar (AD s a) -> AD s a # zero :: AD s a #
(Reifies * s Tape, Num a) => Mode (Reverse s a) #
Associated Types type Scalar (Reverse s a) :: * # Methods isKnownConstant :: Reverse s a -> Bool # 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 #
(Num a, Traversable f) => Mode (Dense f a) #
Associated Types type Scalar (Dense f a) :: * # Methods isKnownConstant :: Dense f a -> Bool # isKnownZero :: Dense f a -> Bool # auto :: Scalar (Dense f a) -> Dense f a # (^) :: Scalar (Dense f a) -> Dense f a -> Dense f a # (^) :: Dense f a -> Scalar (Dense f a) -> Dense f a # (^/) :: Dense f a -> Scalar (Dense f a) -> Dense f a # zero :: Dense f a #
(Mode a, Mode b, Chosen s, (~) * (Scalar a) (Scalar b)) => Mode (Or s a b) #
Associated Types type Scalar (Or s a b) :: * # Methods isKnownConstant :: Or s a b -> Bool # isKnownZero :: Or s a b -> Bool # auto :: Scalar (Or s a b) -> Or s a b # (^) :: Scalar (Or s a b) -> Or s a b -> Or s a b # (^) :: Or s a b -> Scalar (Or s a b) -> Or s a b # (^/) :: Or s a b -> Scalar (Or s a b) -> Or s a b # zero :: Or s a b #