Numeric.AD.Mode

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