ad-4.3.2.1: Automatic Differentiation

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

Numeric.AD.Jet

Description

 

Synopsis

Documentation

data Jet f a Source #

A Jet is a tower of all (higher order) partial derivatives of a function

At each step, a Jet f is wrapped in another layer worth of f.

a :- f a :- f (f a) :- f (f (f a)) :- ...

Constructors

a :- (Jet f (f a)) infixl 3 

Instances

Functor f => Functor (Jet f) Source # 

Methods

fmap :: (a -> b) -> Jet f a -> Jet f b #

(<$) :: a -> Jet f b -> Jet f a #

Foldable f => Foldable (Jet f) Source # 

Methods

fold :: Monoid m => Jet f m -> m #

foldMap :: Monoid m => (a -> m) -> Jet f a -> m #

foldr :: (a -> b -> b) -> b -> Jet f a -> b #

foldr' :: (a -> b -> b) -> b -> Jet f a -> b #

foldl :: (b -> a -> b) -> b -> Jet f a -> b #

foldl' :: (b -> a -> b) -> b -> Jet f a -> b #

foldr1 :: (a -> a -> a) -> Jet f a -> a #

foldl1 :: (a -> a -> a) -> Jet f a -> a #

toList :: Jet f a -> [a] #

null :: Jet f a -> Bool #

length :: Jet f a -> Int #

elem :: Eq a => a -> Jet f a -> Bool #

maximum :: Ord a => Jet f a -> a #

minimum :: Ord a => Jet f a -> a #

sum :: Num a => Jet f a -> a #

product :: Num a => Jet f a -> a #

Traversable f => Traversable (Jet f) Source # 

Methods

traverse :: Applicative f => (a -> f b) -> Jet f a -> f (Jet f b) #

sequenceA :: Applicative f => Jet f (f a) -> f (Jet f a) #

mapM :: Monad m => (a -> m b) -> Jet f a -> m (Jet f b) #

sequence :: Monad m => Jet f (m a) -> m (Jet f a) #

(Functor f, Show (f Showable), Show a) => Show (Jet f a) Source # 

Methods

showsPrec :: Int -> Jet f a -> ShowS #

show :: Jet f a -> String #

showList :: [Jet f a] -> ShowS #

headJet :: Jet f a -> a Source #

Take the head of a Jet.

tailJet :: Jet f a -> Jet f (f a) Source #

Take the tail of a Jet.

jet :: Functor f => Cofree f a -> Jet f a Source #

Construct a Jet by unzipping the layers of a Cofree Comonad.