Copyright	(c) Edward Kmett 2010-2015
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Portability	GHC only
Safe Haskell	None
Language	Haskell2010

Numeric.AD.Internal.Dense

Description

Dense Forward AD. Useful when the result involves the majority of the input elements. Do not use for hessian and beyond, since they only contain a small number of unique nth derivatives -- (n + k - 1) choose k for functions of k inputs rather than the k^n that would be generated by using Dense, not to mention the redundant intermediate derivatives that would be calculated over and over during that process!

Assumes all instances of f have the same number of elements.

NB: We don't need the full power of Traversable here, we could get by with a notion of zippable that can plug in 0's for the missing entries. This might allow for gradients where f has exponentials like ((->) a)

Documentation

data Dense f a Source #

Constructors

Lift !a
Dense !a (f a)
Zero

Instances

(Traversable f, Num a, Bounded a) => Bounded (Dense f a) #
Methods minBound :: Dense f a # maxBound :: Dense f a #
(Traversable f, Num a, Enum a) => Enum (Dense f a) #
Methods succ :: Dense f a -> Dense f a # pred :: Dense f a -> Dense f a # toEnum :: Int -> Dense f a # fromEnum :: Dense f a -> Int # enumFrom :: Dense f a -> [Dense f a] # enumFromThen :: Dense f a -> Dense f a -> [Dense f a] # enumFromTo :: Dense f a -> Dense f a -> [Dense f a] # enumFromThenTo :: Dense f a -> Dense f a -> Dense f a -> [Dense f a] #
(Traversable f, Num a, Eq a) => Eq (Dense f a) #
Methods (==) :: Dense f a -> Dense f a -> Bool # (/=) :: Dense f a -> Dense f a -> Bool #
(Traversable f, Floating a) => Floating (Dense f a) #
Methods pi :: Dense f a # exp :: Dense f a -> Dense f a # log :: Dense f a -> Dense f a # sqrt :: Dense f a -> Dense f a # (**) :: Dense f a -> Dense f a -> Dense f a # logBase :: Dense f a -> Dense f a -> Dense f a # sin :: Dense f a -> Dense f a # cos :: Dense f a -> Dense f a # tan :: Dense f a -> Dense f a # asin :: Dense f a -> Dense f a # acos :: Dense f a -> Dense f a # atan :: Dense f a -> Dense f a # sinh :: Dense f a -> Dense f a # cosh :: Dense f a -> Dense f a # tanh :: Dense f a -> Dense f a # asinh :: Dense f a -> Dense f a # acosh :: Dense f a -> Dense f a # atanh :: Dense f a -> Dense f a # log1p :: Dense f a -> Dense f a # expm1 :: Dense f a -> Dense f a # log1pexp :: Dense f a -> Dense f a # log1mexp :: Dense f a -> Dense f a #
(Traversable f, Fractional a) => Fractional (Dense f a) #
Methods (/) :: Dense f a -> Dense f a -> Dense f a # recip :: Dense f a -> Dense f a # fromRational :: Rational -> Dense f a #
(Traversable f, Num a) => Num (Dense f a) #
Methods (+) :: Dense f a -> Dense f a -> Dense f a # (-) :: Dense f a -> Dense f a -> Dense f a # (*) :: Dense f a -> Dense f a -> Dense f a # negate :: Dense f a -> Dense f a # abs :: Dense f a -> Dense f a # signum :: Dense f a -> Dense f a # fromInteger :: Integer -> Dense f a #
(Traversable f, Num a, Ord a) => Ord (Dense f a) #
Methods compare :: Dense f a -> Dense f a -> Ordering # (<) :: Dense f a -> Dense f a -> Bool # (<=) :: Dense f a -> Dense f a -> Bool # (>) :: Dense f a -> Dense f a -> Bool # (>=) :: Dense f a -> Dense f a -> Bool # max :: Dense f a -> Dense f a -> Dense f a # min :: Dense f a -> Dense f a -> Dense f a #
(Traversable f, Real a) => Real (Dense f a) #
Methods toRational :: Dense f a -> Rational #
(Traversable f, RealFloat a) => RealFloat (Dense f a) #
Methods floatRadix :: Dense f a -> Integer # floatDigits :: Dense f a -> Int # floatRange :: Dense f a -> (Int, Int) # decodeFloat :: Dense f a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Dense f a # exponent :: Dense f a -> Int # significand :: Dense f a -> Dense f a # scaleFloat :: Int -> Dense f a -> Dense f a # isNaN :: Dense f a -> Bool # isInfinite :: Dense f a -> Bool # isDenormalized :: Dense f a -> Bool # isNegativeZero :: Dense f a -> Bool # isIEEE :: Dense f a -> Bool # atan2 :: Dense f a -> Dense f a -> Dense f a #
(Traversable f, RealFrac a) => RealFrac (Dense f a) #
Methods properFraction :: Integral b => Dense f a -> (b, Dense f a) # truncate :: Integral b => Dense f a -> b # round :: Integral b => Dense f a -> b # ceiling :: Integral b => Dense f a -> b # floor :: Integral b => Dense f a -> b #
Show a => Show (Dense f a) Source #
Methods showsPrec :: Int -> Dense f a -> ShowS # show :: Dense f a -> String # showList :: [Dense f a] -> ShowS #
(Traversable f, Erf a) => Erf (Dense f a) #
Methods erf :: Dense f a -> Dense f a # erfc :: Dense f a -> Dense f a # erfcx :: Dense f a -> Dense f a # normcdf :: Dense f a -> Dense f a #
(Traversable f, InvErf a) => InvErf (Dense f a) #
Methods inverf :: Dense f a -> Dense f a # inverfc :: Dense f a -> Dense f a # invnormcdf :: Dense f a -> Dense f a #
(Num a, Traversable f) => Mode (Dense f a) Source #
Associated Types type Scalar (Dense f a) :: * 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 #
(Traversable f, Num a) => Jacobian (Dense f a) Source #
Associated Types type D (Dense f a) :: * Source # Methods unary :: (Scalar (Dense f a) -> Scalar (Dense f a)) -> D (Dense f a) -> Dense f a -> Dense f a Source # lift1 :: (Scalar (Dense f a) -> Scalar (Dense f a)) -> (D (Dense f a) -> D (Dense f a)) -> Dense f a -> Dense f a Source # lift1_ :: (Scalar (Dense f a) -> Scalar (Dense f a)) -> (D (Dense f a) -> D (Dense f a) -> D (Dense f a)) -> Dense f a -> Dense f a Source # binary :: (Scalar (Dense f a) -> Scalar (Dense f a) -> Scalar (Dense f a)) -> D (Dense f a) -> D (Dense f a) -> Dense f a -> Dense f a -> Dense f a Source # lift2 :: (Scalar (Dense f a) -> Scalar (Dense f a) -> Scalar (Dense f a)) -> (D (Dense f a) -> D (Dense f a) -> (D (Dense f a), D (Dense f a))) -> Dense f a -> Dense f a -> Dense f a Source # lift2_ :: (Scalar (Dense f a) -> Scalar (Dense f a) -> Scalar (Dense f a)) -> (D (Dense f a) -> D (Dense f a) -> D (Dense f a) -> (D (Dense f a), D (Dense f a))) -> Dense f a -> Dense f a -> Dense f a Source #
type Scalar (Dense f a) Source #
type Scalar (Dense f a) = a
type D (Dense f a) Source #
type D (Dense f a) = Id a

ds :: f a -> Dense f a -> f a Source #

ds' :: Num a => f a -> Dense f a -> (a, f a) Source #

vars :: (Traversable f, Num a) => f a -> f (Dense f a) Source #

apply :: (Traversable f, Num a) => (f (Dense f a) -> b) -> f a -> b Source #