ad-4.4.1: Automatic Differentiation

Copyright(c) Edward Kmett 2010-2015
LicenseBSD3
Maintainerekmett@gmail.com
Stabilityexperimental
PortabilityGHC only
Safe HaskellNone
LanguageHaskell2010

Numeric.AD.Mode

Contents

Description

 
Synopsis

AD modes

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

Minimal complete definition

auto

Associated Types

type Scalar t Source #

Methods

isKnownConstant :: t -> Bool Source #

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

isKnownZero :: t -> Bool Source #

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

auto :: Scalar t -> t Source #

Embed a constant

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

Scalar-vector multiplication

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

Vector-scalar multiplication

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

Scalar division

zero :: t Source #

zero = lift 0
Instances
Mode Double Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Double :: Type Source #

Methods

isKnownConstant :: Double -> Bool Source #

isKnownZero :: Double -> Bool Source #

auto :: Scalar Double -> Double Source #

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

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

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

zero :: Double Source #

Mode Float Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Float :: Type Source #

Methods

isKnownConstant :: Float -> Bool Source #

isKnownZero :: Float -> Bool Source #

auto :: Scalar Float -> Float Source #

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

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

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

zero :: Float Source #

Mode Int Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Int :: Type Source #

Methods

isKnownConstant :: Int -> Bool Source #

isKnownZero :: Int -> Bool Source #

auto :: Scalar Int -> Int Source #

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

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

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

zero :: Int Source #

Mode Int8 Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Int8 :: Type Source #

Methods

isKnownConstant :: Int8 -> Bool Source #

isKnownZero :: Int8 -> Bool Source #

auto :: Scalar Int8 -> Int8 Source #

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

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

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

zero :: Int8 Source #

Mode Int16 Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Int16 :: Type Source #

Methods

isKnownConstant :: Int16 -> Bool Source #

isKnownZero :: Int16 -> Bool Source #

auto :: Scalar Int16 -> Int16 Source #

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

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

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

zero :: Int16 Source #

Mode Int32 Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Int32 :: Type Source #

Methods

isKnownConstant :: Int32 -> Bool Source #

isKnownZero :: Int32 -> Bool Source #

auto :: Scalar Int32 -> Int32 Source #

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

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

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

zero :: Int32 Source #

Mode Int64 Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Int64 :: Type Source #

Methods

isKnownConstant :: Int64 -> Bool Source #

isKnownZero :: Int64 -> Bool Source #

auto :: Scalar Int64 -> Int64 Source #

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

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

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

zero :: Int64 Source #

Mode Integer Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Integer :: Type Source #

Methods

isKnownConstant :: Integer -> Bool Source #

isKnownZero :: Integer -> Bool Source #

auto :: Scalar Integer -> Integer Source #

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

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

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

zero :: Integer Source #

Mode Natural Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Natural :: Type Source #

Methods

isKnownConstant :: Natural -> Bool Source #

isKnownZero :: Natural -> Bool Source #

auto :: Scalar Natural -> Natural Source #

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

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

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

zero :: Natural Source #

Mode Word Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Word :: Type Source #

Methods

isKnownConstant :: Word -> Bool Source #

isKnownZero :: Word -> Bool Source #

auto :: Scalar Word -> Word Source #

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

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

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

zero :: Word Source #

Mode Word8 Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Word8 :: Type Source #

Methods

isKnownConstant :: Word8 -> Bool Source #

isKnownZero :: Word8 -> Bool Source #

auto :: Scalar Word8 -> Word8 Source #

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

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

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

zero :: Word8 Source #

Mode Word16 Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Word16 :: Type Source #

Methods

isKnownConstant :: Word16 -> Bool Source #

isKnownZero :: Word16 -> Bool Source #

auto :: Scalar Word16 -> Word16 Source #

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

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

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

zero :: Word16 Source #

Mode Word32 Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Word32 :: Type Source #

Methods

isKnownConstant :: Word32 -> Bool Source #

isKnownZero :: Word32 -> Bool Source #

auto :: Scalar Word32 -> Word32 Source #

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

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

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

zero :: Word32 Source #

Mode Word64 Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar Word64 :: Type Source #

Methods

isKnownConstant :: Word64 -> Bool Source #

isKnownZero :: Word64 -> Bool Source #

auto :: Scalar Word64 -> Word64 Source #

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

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

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

zero :: Word64 Source #

Mode ForwardDouble Source # 
Instance details

Defined in Numeric.AD.Internal.Forward.Double

Associated Types

type Scalar ForwardDouble :: Type Source #

Methods

isKnownConstant :: ForwardDouble -> Bool Source #

isKnownZero :: ForwardDouble -> Bool Source #

auto :: Scalar ForwardDouble -> ForwardDouble Source #

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

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

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

zero :: ForwardDouble Source #

Integral a => Mode (Ratio a) Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar (Ratio a) :: Type Source #

Methods

isKnownConstant :: Ratio a -> Bool Source #

isKnownZero :: Ratio a -> Bool Source #

auto :: Scalar (Ratio a) -> Ratio a Source #

(*^) :: Scalar (Ratio a) -> Ratio a -> Ratio a Source #

(^*) :: Ratio a -> Scalar (Ratio a) -> Ratio a Source #

(^/) :: Ratio a -> Scalar (Ratio a) -> Ratio a Source #

zero :: Ratio a Source #

RealFloat a => Mode (Complex a) Source # 
Instance details

Defined in Numeric.AD.Mode

Associated Types

type Scalar (Complex a) :: Type Source #

Methods

isKnownConstant :: Complex a -> Bool Source #

isKnownZero :: Complex a -> Bool Source #

auto :: Scalar (Complex a) -> Complex a Source #

(*^) :: Scalar (Complex a) -> Complex a -> Complex a Source #

(^*) :: Complex a -> Scalar (Complex a) -> Complex a Source #

(^/) :: Complex a -> Scalar (Complex a) -> Complex a Source #

zero :: Complex a Source #

(Mode t, Mode (Scalar t)) => Mode (On t) Source # 
Instance details

Defined in Numeric.AD.Internal.On

Associated Types

type Scalar (On t) :: Type Source #

Methods

isKnownConstant :: On t -> Bool Source #

isKnownZero :: On t -> Bool Source #

auto :: Scalar (On t) -> On t Source #

(*^) :: Scalar (On t) -> On t -> On t Source #

(^*) :: On t -> Scalar (On t) -> On t Source #

(^/) :: On t -> Scalar (On t) -> On t Source #

zero :: On t Source #

Num a => Mode (Id a) Source # 
Instance details

Defined in Numeric.AD.Internal.Identity

Associated Types

type Scalar (Id a) :: Type Source #

Methods

isKnownConstant :: Id a -> Bool Source #

isKnownZero :: Id a -> Bool Source #

auto :: Scalar (Id a) -> Id a Source #

(*^) :: Scalar (Id a) -> Id a -> Id a Source #

(^*) :: Id a -> Scalar (Id a) -> Id a Source #

(^/) :: Id a -> Scalar (Id a) -> Id a Source #

zero :: Id a Source #

Num a => Mode (Tower a) Source # 
Instance details

Defined in Numeric.AD.Internal.Tower

Associated Types

type Scalar (Tower a) :: Type Source #

Methods

isKnownConstant :: Tower a -> Bool Source #

isKnownZero :: Tower a -> Bool Source #

auto :: Scalar (Tower a) -> Tower a Source #

(*^) :: Scalar (Tower a) -> Tower a -> Tower a Source #

(^*) :: Tower a -> Scalar (Tower a) -> Tower a Source #

(^/) :: Tower a -> Scalar (Tower a) -> Tower a Source #

zero :: Tower a Source #

Num a => Mode (Sparse a) Source # 
Instance details

Defined in Numeric.AD.Internal.Sparse

Associated Types

type Scalar (Sparse a) :: Type Source #

Methods

isKnownConstant :: Sparse a -> Bool Source #

isKnownZero :: Sparse a -> Bool Source #

auto :: Scalar (Sparse a) -> Sparse a Source #

(*^) :: Scalar (Sparse a) -> Sparse a -> Sparse a Source #

(^*) :: Sparse a -> Scalar (Sparse a) -> Sparse a Source #

(^/) :: Sparse a -> Scalar (Sparse a) -> Sparse a Source #

zero :: Sparse a Source #

Reifies s Tape => Mode (ReverseDouble s) Source # 
Instance details

Defined in Numeric.AD.Internal.Reverse.Double

Associated Types

type Scalar (ReverseDouble s) :: Type Source #

Methods

isKnownConstant :: ReverseDouble s -> Bool Source #

isKnownZero :: ReverseDouble s -> Bool Source #

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

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

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

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

zero :: ReverseDouble s Source #

Num a => Mode (Kahn a) Source # 
Instance details

Defined in Numeric.AD.Internal.Kahn

Associated Types

type Scalar (Kahn a) :: Type Source #

Methods

isKnownConstant :: Kahn a -> Bool Source #

isKnownZero :: Kahn a -> Bool Source #

auto :: Scalar (Kahn a) -> Kahn a Source #

(*^) :: Scalar (Kahn a) -> Kahn a -> Kahn a Source #

(^*) :: Kahn a -> Scalar (Kahn a) -> Kahn a Source #

(^/) :: Kahn a -> Scalar (Kahn a) -> Kahn a Source #

zero :: Kahn a Source #

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 #

Mode a => Mode (AD s a) Source # 
Instance details

Defined in Numeric.AD.Internal.Type

Associated Types

type Scalar (AD s a) :: Type Source #

Methods

isKnownConstant :: AD s a -> Bool Source #

isKnownZero :: AD s a -> Bool Source #

auto :: Scalar (AD s a) -> AD s a Source #

(*^) :: Scalar (AD s a) -> AD s a -> AD s a Source #

(^*) :: AD s a -> Scalar (AD s a) -> AD s a Source #

(^/) :: AD s a -> Scalar (AD s a) -> AD s a Source #

zero :: AD s a Source #

(Reifies s Tape, Num a) => Mode (Reverse s a) Source # 
Instance details

Defined in Numeric.AD.Internal.Reverse

Associated Types

type Scalar (Reverse s a) :: Type Source #

Methods

isKnownConstant :: Reverse s a -> Bool Source #

isKnownZero :: Reverse s a -> Bool Source #

auto :: Scalar (Reverse s a) -> Reverse s a Source #

(*^) :: Scalar (Reverse s a) -> Reverse s a -> Reverse s a Source #

(^*) :: Reverse s a -> Scalar (Reverse s a) -> Reverse s a Source #

(^/) :: Reverse s a -> Scalar (Reverse s a) -> Reverse s a Source #

zero :: Reverse s a Source #

(Num a, Traversable f) => Mode (Dense f a) Source # 
Instance details

Defined in Numeric.AD.Internal.Dense

Associated Types

type Scalar (Dense f a) :: Type Source #

Methods

isKnownConstant :: Dense f a -> Bool Source #

isKnownZero :: Dense f a -> Bool Source #

auto :: Scalar (Dense f a) -> Dense f a Source #

(*^) :: Scalar (Dense f a) -> Dense f a -> Dense f a Source #

(^*) :: Dense f a -> Scalar (Dense f a) -> Dense f a Source #

(^/) :: Dense f a -> Scalar (Dense f a) -> Dense f a Source #

zero :: Dense f a Source #

(Mode a, Mode b, Chosen s, Scalar a ~ Scalar b) => Mode (Or s a b) Source # 
Instance details

Defined in Numeric.AD.Internal.Or

Associated Types

type Scalar (Or s a b) :: Type Source #

Methods

isKnownConstant :: Or s a b -> Bool Source #

isKnownZero :: Or s a b -> Bool Source #

auto :: Scalar (Or s a b) -> Or s a b Source #

(*^) :: Scalar (Or s a b) -> Or s a b -> Or s a b Source #

(^*) :: Or s a b -> Scalar (Or s a b) -> Or s a b Source #

(^/) :: Or s a b -> Scalar (Or s a b) -> Or s a b Source #

zero :: Or s a b Source #