Numeric.AD.Mode

AD modes

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

Minimal complete definition

Nothing

Associated Types

type Scalar t

type Scalar t = t

Methods

isKnownConstant :: t -> Bool

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

asKnownConstant :: t -> Maybe (Scalar t)

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

default auto :: Scalar t ~ t => Scalar t -> t

(*^) :: 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 ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Associated Types

type Scalar ForwardDouble

Methods

isKnownConstant :: ForwardDouble -> Bool

asKnownConstant :: ForwardDouble -> Maybe (Scalar ForwardDouble)

isKnownZero :: ForwardDouble -> Bool

auto :: Scalar ForwardDouble -> ForwardDouble

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

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

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

zero :: ForwardDouble

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

Mode KahnFloat

Defined in Numeric.AD.Internal.Kahn.Float

Associated Types

type Scalar KahnFloat

Methods

isKnownConstant :: KahnFloat -> Bool

asKnownConstant :: KahnFloat -> Maybe (Scalar KahnFloat)

isKnownZero :: KahnFloat -> Bool

auto :: Scalar KahnFloat -> KahnFloat

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

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

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

zero :: KahnFloat

Mode SparseDouble

Defined in Numeric.AD.Internal.Sparse.Double

Associated Types

type Scalar SparseDouble

Methods

isKnownConstant :: SparseDouble -> Bool

asKnownConstant :: SparseDouble -> Maybe (Scalar SparseDouble)

isKnownZero :: SparseDouble -> Bool

auto :: Scalar SparseDouble -> SparseDouble

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

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

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

zero :: SparseDouble

Mode TowerDouble

Defined in Numeric.AD.Internal.Tower.Double

Associated Types

type Scalar TowerDouble

Methods

isKnownConstant :: TowerDouble -> Bool

asKnownConstant :: TowerDouble -> Maybe (Scalar TowerDouble)

isKnownZero :: TowerDouble -> Bool

auto :: Scalar TowerDouble -> TowerDouble

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

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

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

zero :: TowerDouble

Mode Int16

Defined in Numeric.AD.Mode

Associated Types

type Scalar Int16

Methods

isKnownConstant :: Int16 -> Bool

asKnownConstant :: Int16 -> Maybe (Scalar Int16)

isKnownZero :: Int16 -> Bool

auto :: Scalar Int16 -> Int16

(*^) :: Scalar Int16 -> Int16 -> Int16

(^*) :: Int16 -> Scalar Int16 -> Int16

(^/) :: Int16 -> Scalar Int16 -> Int16

zero :: Int16

Mode Int32

Defined in Numeric.AD.Mode

Associated Types

type Scalar Int32

Methods

isKnownConstant :: Int32 -> Bool

asKnownConstant :: Int32 -> Maybe (Scalar Int32)

isKnownZero :: Int32 -> Bool

auto :: Scalar Int32 -> Int32

(*^) :: Scalar Int32 -> Int32 -> Int32

(^*) :: Int32 -> Scalar Int32 -> Int32

(^/) :: Int32 -> Scalar Int32 -> Int32

zero :: Int32

Mode Int64

Defined in Numeric.AD.Mode

Associated Types

type Scalar Int64

Methods

isKnownConstant :: Int64 -> Bool

asKnownConstant :: Int64 -> Maybe (Scalar Int64)

isKnownZero :: Int64 -> Bool

auto :: Scalar Int64 -> Int64

(*^) :: Scalar Int64 -> Int64 -> Int64

(^*) :: Int64 -> Scalar Int64 -> Int64

(^/) :: Int64 -> Scalar Int64 -> Int64

zero :: Int64

Mode Int8

Defined in Numeric.AD.Mode

Associated Types

type Scalar Int8

Methods

isKnownConstant :: Int8 -> Bool

asKnownConstant :: Int8 -> Maybe (Scalar Int8)

isKnownZero :: Int8 -> Bool

auto :: Scalar Int8 -> Int8

(*^) :: Scalar Int8 -> Int8 -> Int8

(^*) :: Int8 -> Scalar Int8 -> Int8

(^/) :: Int8 -> Scalar Int8 -> Int8

zero :: Int8

Mode Word16

Defined in Numeric.AD.Mode

Associated Types

type Scalar Word16

Methods

isKnownConstant :: Word16 -> Bool

asKnownConstant :: Word16 -> Maybe (Scalar Word16)

isKnownZero :: Word16 -> Bool

auto :: Scalar Word16 -> Word16

(*^) :: Scalar Word16 -> Word16 -> Word16

(^*) :: Word16 -> Scalar Word16 -> Word16

(^/) :: Word16 -> Scalar Word16 -> Word16

zero :: Word16

Mode Word32

Defined in Numeric.AD.Mode

Associated Types

type Scalar Word32

Methods

isKnownConstant :: Word32 -> Bool

asKnownConstant :: Word32 -> Maybe (Scalar Word32)

isKnownZero :: Word32 -> Bool

auto :: Scalar Word32 -> Word32

(*^) :: Scalar Word32 -> Word32 -> Word32

(^*) :: Word32 -> Scalar Word32 -> Word32

(^/) :: Word32 -> Scalar Word32 -> Word32

zero :: Word32

Mode Word64

Defined in Numeric.AD.Mode

Associated Types

type Scalar Word64

Methods

isKnownConstant :: Word64 -> Bool

asKnownConstant :: Word64 -> Maybe (Scalar Word64)

isKnownZero :: Word64 -> Bool

auto :: Scalar Word64 -> Word64

(*^) :: Scalar Word64 -> Word64 -> Word64

(^*) :: Word64 -> Scalar Word64 -> Word64

(^/) :: Word64 -> Scalar Word64 -> Word64

zero :: Word64

Mode Word8

Defined in Numeric.AD.Mode

Associated Types

type Scalar Word8

Methods

isKnownConstant :: Word8 -> Bool

asKnownConstant :: Word8 -> Maybe (Scalar Word8)

isKnownZero :: Word8 -> Bool

auto :: Scalar Word8 -> Word8

(*^) :: Scalar Word8 -> Word8 -> Word8

(^*) :: Word8 -> Scalar Word8 -> Word8

(^/) :: Word8 -> Scalar Word8 -> Word8

zero :: Word8

Mode Integer

Defined in Numeric.AD.Mode

Associated Types

type Scalar Integer

Methods

isKnownConstant :: Integer -> Bool

asKnownConstant :: Integer -> Maybe (Scalar Integer)

isKnownZero :: Integer -> Bool

auto :: Scalar Integer -> Integer

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

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

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

zero :: Integer

Mode Natural

Defined in Numeric.AD.Mode

Associated Types

type Scalar Natural

Methods

isKnownConstant :: Natural -> Bool

asKnownConstant :: Natural -> Maybe (Scalar Natural)

isKnownZero :: Natural -> Bool

auto :: Scalar Natural -> Natural

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

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

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

zero :: Natural

Mode Double

Defined in Numeric.AD.Mode

Associated Types

type Scalar Double

Methods

isKnownConstant :: Double -> Bool

asKnownConstant :: Double -> Maybe (Scalar Double)

isKnownZero :: Double -> Bool

auto :: Scalar Double -> Double

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

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

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

zero :: Double

Mode Float

Defined in Numeric.AD.Mode

Associated Types

type Scalar Float

Methods

isKnownConstant :: Float -> Bool

asKnownConstant :: Float -> Maybe (Scalar Float)

isKnownZero :: Float -> Bool

auto :: Scalar Float -> Float

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

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

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

zero :: Float

Mode Int

Defined in Numeric.AD.Mode

Associated Types

type Scalar Int

Methods

isKnownConstant :: Int -> Bool

asKnownConstant :: Int -> Maybe (Scalar Int)

isKnownZero :: Int -> Bool

auto :: Scalar Int -> Int

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

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

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

zero :: Int

Mode Word

Defined in Numeric.AD.Mode

Associated Types

type Scalar Word

Methods

isKnownConstant :: Word -> Bool

asKnownConstant :: Word -> Maybe (Scalar Word)

isKnownZero :: Word -> Bool

auto :: Scalar Word -> Word

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

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

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

zero :: Word

Num a => Mode (Forward a)

Defined in Numeric.AD.Internal.Forward

Associated Types

type Scalar (Forward a)

Methods

isKnownConstant :: Forward a -> Bool

asKnownConstant :: Forward a -> Maybe (Scalar (Forward a))

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

Num a => Mode (Id a)

Defined in Numeric.AD.Internal.Identity

Associated Types

type Scalar (Id a)

Methods

isKnownConstant :: Id a -> Bool

asKnownConstant :: Id a -> Maybe (Scalar (Id a))

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 (Kahn a)

Defined in Numeric.AD.Internal.Kahn

Associated Types

type Scalar (Kahn a)

Methods

isKnownConstant :: Kahn a -> Bool

asKnownConstant :: Kahn a -> Maybe (Scalar (Kahn a))

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

(Mode t, Mode (Scalar t), Num (Scalar (Scalar t))) => Mode (On t)

Defined in Numeric.AD.Internal.On

Associated Types

type Scalar (On t)

Methods

isKnownConstant :: On t -> Bool

asKnownConstant :: On t -> Maybe (Scalar (On t))

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

Reifies s Tape => Mode (ReverseDouble s)

Defined in Numeric.AD.Internal.Reverse.Double

Associated Types

type Scalar (ReverseDouble s)

Methods

isKnownConstant :: ReverseDouble s -> Bool

asKnownConstant :: ReverseDouble s -> Maybe (Scalar (ReverseDouble s))

isKnownZero :: ReverseDouble s -> Bool

auto :: Scalar (ReverseDouble s) -> ReverseDouble s

(*^) :: Scalar (ReverseDouble s) -> ReverseDouble s -> ReverseDouble s

(^*) :: ReverseDouble s -> Scalar (ReverseDouble s) -> ReverseDouble s

(^/) :: ReverseDouble s -> Scalar (ReverseDouble s) -> ReverseDouble s

zero :: ReverseDouble s

Num a => Mode (Sparse a)

Defined in Numeric.AD.Internal.Sparse

Associated Types

type Scalar (Sparse a)

Methods

isKnownConstant :: Sparse a -> Bool

asKnownConstant :: Sparse a -> Maybe (Scalar (Sparse a))

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 (Tower a)

Defined in Numeric.AD.Internal.Tower

Associated Types

type Scalar (Tower a)

Methods

isKnownConstant :: Tower a -> Bool

asKnownConstant :: Tower a -> Maybe (Scalar (Tower a))

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

RealFloat a => Mode (Complex a)

Defined in Numeric.AD.Mode

Associated Types

type Scalar (Complex a)

Methods

isKnownConstant :: Complex a -> Bool

asKnownConstant :: Complex a -> Maybe (Scalar (Complex a))

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

Integral a => Mode (Ratio a)

Defined in Numeric.AD.Mode

Associated Types

type Scalar (Ratio a)

Methods

isKnownConstant :: Ratio a -> Bool

asKnownConstant :: Ratio a -> Maybe (Scalar (Ratio a))

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

(Num a, Traversable f) => Mode (Dense f a)

Defined in Numeric.AD.Internal.Dense

Associated Types

type Scalar (Dense f a)

Methods

isKnownConstant :: Dense f a -> Bool

asKnownConstant :: Dense f a -> Maybe (Scalar (Dense f a))

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

(Representable f, Num a) => Mode (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Associated Types

type Scalar (Repr f a)

Methods

isKnownConstant :: Repr f a -> Bool

asKnownConstant :: Repr f a -> Maybe (Scalar (Repr f a))

isKnownZero :: Repr f a -> Bool

auto :: Scalar (Repr f a) -> Repr f a

(*^) :: Scalar (Repr f a) -> Repr f a -> Repr f a

(^*) :: Repr f a -> Scalar (Repr f a) -> Repr f a

(^/) :: Repr f a -> Scalar (Repr f a) -> Repr f a

zero :: Repr f a

(Reifies s Tape, Num a) => Mode (Reverse s a)

Defined in Numeric.AD.Internal.Reverse

Associated Types

type Scalar (Reverse s a)

Methods

isKnownConstant :: Reverse s a -> Bool

asKnownConstant :: Reverse s a -> Maybe (Scalar (Reverse s a))

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

Mode a => Mode (AD s a)

Defined in Numeric.AD.Internal.Type

Associated Types

type Scalar (AD s a)

Methods

isKnownConstant :: AD s a -> Bool

asKnownConstant :: AD s a -> Maybe (Scalar (AD s a))

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

(Mode a, Mode b, Chosen s, Scalar a ~ Scalar b) => Mode (Or s a b)

Defined in Numeric.AD.Internal.Or

Associated Types

type Scalar (Or s a b)

Methods

isKnownConstant :: Or s a b -> Bool

asKnownConstant :: Or s a b -> Maybe (Scalar (Or s a b))

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

pattern KnownZero :: Mode s => s

pattern Auto :: Mode s => Scalar s -> s