Numeric.AD.Internal.Forward

Unsafe and often partial combinators intended for internal usage.

Handle with care.

Documentation

data Forward a

Forward mode AD

Constructors

Forward !a a

Lift !a

Zero

Instances

Num a => Jacobian (Forward a)

Defined in Numeric.AD.Internal.Forward

Associated Types

type D (Forward a)

Methods

unary :: (Scalar (Forward a) -> Scalar (Forward a)) -> D (Forward a) -> Forward a -> Forward a

lift1 :: (Scalar (Forward a) -> Scalar (Forward a)) -> (D (Forward a) -> D (Forward a)) -> Forward a -> Forward a

lift1_ :: (Scalar (Forward a) -> Scalar (Forward a)) -> (D (Forward a) -> D (Forward a) -> D (Forward a)) -> Forward a -> Forward a

binary :: (Scalar (Forward a) -> Scalar (Forward a) -> Scalar (Forward a)) -> D (Forward a) -> D (Forward a) -> Forward a -> Forward a -> Forward a

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

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

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

Data a => Data (Forward a)

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 :: forall r r'. (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, Bounded a) => Bounded (Forward a)

Defined in Numeric.AD.Internal.Forward

Methods

minBound :: Forward a

maxBound :: Forward a

(Num a, Enum a) => Enum (Forward a)

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]

Floating a => Floating (Forward a)

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

RealFloat a => RealFloat (Forward a)

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

Num a => Num (Forward a)

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

Fractional a => Fractional (Forward a)

Defined in Numeric.AD.Internal.Forward

Methods

(/) :: Forward a -> Forward a -> Forward a

recip :: Forward a -> Forward a

fromRational :: Rational -> Forward a

Real a => Real (Forward a)

Defined in Numeric.AD.Internal.Forward

Methods

toRational :: Forward a -> Rational

RealFrac a => RealFrac (Forward a)

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)

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)

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)

Defined in Numeric.AD.Internal.Forward

Methods

inverf :: Forward a -> Forward a

inverfc :: Forward a -> Forward a

invnormcdf :: Forward a -> Forward a

(Num a, Eq a) => Eq (Forward a)

Defined in Numeric.AD.Internal.Forward

Methods

(==) :: Forward a -> Forward a -> Bool

(/=) :: Forward a -> Forward a -> Bool

(Num a, Ord a) => Ord (Forward a)

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

type D (Forward a)

Defined in Numeric.AD.Internal.Forward

type D (Forward a) = Id a

type Scalar (Forward a)

Defined in Numeric.AD.Internal.Forward

type Scalar (Forward a) = a

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

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

Calculate the tangent using forward mode AD.

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