Numeric.AD.Rank1.Dense.Representable

Dense forward mode automatic differentiation with representable functors.

Documentation

data Repr f a

Instances

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

Defined in Numeric.AD.Internal.Dense.Representable

Associated Types

type D (Repr f a)

Methods

unary :: (Scalar (Repr f a) -> Scalar (Repr f a)) -> D (Repr f a) -> Repr f a -> Repr f a

lift1 :: (Scalar (Repr f a) -> Scalar (Repr f a)) -> (D (Repr f a) -> D (Repr f a)) -> Repr f a -> Repr f a

lift1_ :: (Scalar (Repr f a) -> Scalar (Repr f a)) -> (D (Repr f a) -> D (Repr f a) -> D (Repr f a)) -> Repr f a -> Repr f a

binary :: (Scalar (Repr f a) -> Scalar (Repr f a) -> Scalar (Repr f a)) -> D (Repr f a) -> D (Repr f a) -> Repr f a -> Repr f a -> Repr f a

lift2 :: (Scalar (Repr f a) -> Scalar (Repr f a) -> Scalar (Repr f a)) -> (D (Repr f a) -> D (Repr f a) -> (D (Repr f a), D (Repr f a))) -> Repr f a -> Repr f a -> Repr f a

lift2_ :: (Scalar (Repr f a) -> Scalar (Repr f a) -> Scalar (Repr f a)) -> (D (Repr f a) -> D (Repr f a) -> D (Repr f a) -> (D (Repr f a), D (Repr f a))) -> Repr f a -> Repr f a -> Repr 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

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

Defined in Numeric.AD.Internal.Dense.Representable

Methods

minBound :: Repr f a

maxBound :: Repr f a

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

Defined in Numeric.AD.Internal.Dense.Representable

Methods

succ :: Repr f a -> Repr f a

pred :: Repr f a -> Repr f a

toEnum :: Int -> Repr f a

fromEnum :: Repr f a -> Int

enumFrom :: Repr f a -> [Repr f a]

enumFromThen :: Repr f a -> Repr f a -> [Repr f a]

enumFromTo :: Repr f a -> Repr f a -> [Repr f a]

enumFromThenTo :: Repr f a -> Repr f a -> Repr f a -> [Repr f a]

(Representable f, Floating a) => Floating (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

pi :: Repr f a

exp :: Repr f a -> Repr f a

log :: Repr f a -> Repr f a

sqrt :: Repr f a -> Repr f a

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

logBase :: Repr f a -> Repr f a -> Repr f a

sin :: Repr f a -> Repr f a

cos :: Repr f a -> Repr f a

tan :: Repr f a -> Repr f a

asin :: Repr f a -> Repr f a

acos :: Repr f a -> Repr f a

atan :: Repr f a -> Repr f a

sinh :: Repr f a -> Repr f a

cosh :: Repr f a -> Repr f a

tanh :: Repr f a -> Repr f a

asinh :: Repr f a -> Repr f a

acosh :: Repr f a -> Repr f a

atanh :: Repr f a -> Repr f a

log1p :: Repr f a -> Repr f a

expm1 :: Repr f a -> Repr f a

log1pexp :: Repr f a -> Repr f a

log1mexp :: Repr f a -> Repr f a

(Representable f, RealFloat a) => RealFloat (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

floatRadix :: Repr f a -> Integer

floatDigits :: Repr f a -> Int

floatRange :: Repr f a -> (Int, Int)

decodeFloat :: Repr f a -> (Integer, Int)

encodeFloat :: Integer -> Int -> Repr f a

exponent :: Repr f a -> Int

significand :: Repr f a -> Repr f a

scaleFloat :: Int -> Repr f a -> Repr f a

isNaN :: Repr f a -> Bool

isInfinite :: Repr f a -> Bool

isDenormalized :: Repr f a -> Bool

isNegativeZero :: Repr f a -> Bool

isIEEE :: Repr f a -> Bool

atan2 :: Repr f a -> Repr f a -> Repr f a

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

Defined in Numeric.AD.Internal.Dense.Representable

Methods

(+) :: Repr f a -> Repr f a -> Repr f a

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

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

negate :: Repr f a -> Repr f a

abs :: Repr f a -> Repr f a

signum :: Repr f a -> Repr f a

fromInteger :: Integer -> Repr f a

(Representable f, Fractional a) => Fractional (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

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

recip :: Repr f a -> Repr f a

fromRational :: Rational -> Repr f a

(Representable f, Real a) => Real (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

toRational :: Repr f a -> Rational

(Representable f, RealFrac a) => RealFrac (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

properFraction :: Integral b => Repr f a -> (b, Repr f a)

truncate :: Integral b => Repr f a -> b

round :: Integral b => Repr f a -> b

ceiling :: Integral b => Repr f a -> b

floor :: Integral b => Repr f a -> b

Show a => Show (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

showsPrec :: Int -> Repr f a -> ShowS

show :: Repr f a -> String

showList :: [Repr f a] -> ShowS

(Representable f, Erf a) => Erf (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

erf :: Repr f a -> Repr f a

erfc :: Repr f a -> Repr f a

erfcx :: Repr f a -> Repr f a

normcdf :: Repr f a -> Repr f a

(Representable f, InvErf a) => InvErf (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

inverf :: Repr f a -> Repr f a

inverfc :: Repr f a -> Repr f a

invnormcdf :: Repr f a -> Repr f a

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

Defined in Numeric.AD.Internal.Dense.Representable

Methods

(==) :: Repr f a -> Repr f a -> Bool

(/=) :: Repr f a -> Repr f a -> Bool

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

Defined in Numeric.AD.Internal.Dense.Representable

Methods

compare :: Repr f a -> Repr f a -> Ordering

(<) :: Repr f a -> Repr f a -> Bool

(<=) :: Repr f a -> Repr f a -> Bool

(>) :: Repr f a -> Repr f a -> Bool

(>=) :: Repr f a -> Repr f a -> Bool

max :: Repr f a -> Repr f a -> Repr f a

min :: Repr f a -> Repr f a -> Repr f a

type D (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

type D (Repr f a) = Id a

type Scalar (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

type Scalar (Repr f a) = a

auto :: Mode t => Scalar t -> t

Embed a constant

Sparse Gradients

grad :: (Representable f, Eq (Rep f), Num a) => (f (Repr f a) -> Repr f a) -> f a -> f a

grad' :: (Representable f, Eq (Rep f), Num a) => (f (Repr f a) -> Repr f a) -> f a -> (a, f a)

gradWith :: (Representable f, Eq (Rep f), Num a) => (a -> a -> b) -> (f (Repr f a) -> Repr f a) -> f a -> f b

gradWith' :: (Representable f, Eq (Rep f), Num a) => (a -> a -> b) -> (f (Repr f a) -> Repr f a) -> f a -> (a, f b)

Sparse Jacobians (synonyms)

jacobian :: (Representable f, Eq (Rep f), Functor g, Num a) => (f (Repr f a) -> g (Repr f a)) -> f a -> g (f a)

jacobian' :: (Representable f, Eq (Rep f), Functor g, Num a) => (f (Repr f a) -> g (Repr f a)) -> f a -> g (a, f a)

jacobianWith :: (Representable f, Eq (Rep f), Functor g, Num a) => (a -> a -> b) -> (f (Repr f a) -> g (Repr f a)) -> f a -> g (f b)

jacobianWith' :: (Representable f, Eq (Rep f), Functor g, Num a) => (a -> a -> b) -> (f (Repr f a) -> g (Repr f a)) -> f a -> g (a, f b)