ad-4.2.2: Automatic Differentiation

Copyright(c) Edward Kmett 2010-2015
PortabilityGHC only
Safe HaskellNone



This module provides reverse-mode Automatic Differentiation implementation using linear time topological sorting after the fact.

For this form of reverse-mode AD we use StableName to recover sharing information from the tape to avoid combinatorial explosion, and thus run asymptotically faster than it could without such sharing information, but the use of side-effects contained herein is benign.



newtype Kahn a Source

Kahn is a Mode using reverse-mode automatic differentiation that provides fast diffFU, diff2FU, grad, grad2 and a fast jacobian when you have a significantly smaller number of outputs than inputs.


Kahn (Tape a (Kahn a)) 


(Num a, Bounded a) => Bounded (Kahn a) 
(Num a, Enum a) => Enum (Kahn a) 
(Num a, Eq a) => Eq (Kahn a) 
Floating a => Floating (Kahn a) 
Fractional a => Fractional (Kahn a) 
Num a => Num (Kahn a) 
(Num a, Ord a) => Ord (Kahn a) 
Real a => Real (Kahn a) 
RealFloat a => RealFloat (Kahn a) 
RealFrac a => RealFrac (Kahn a) 
Show a => Show (Kahn a) 
MuRef (Kahn a) 
Erf a => Erf (Kahn a) 
InvErf a => InvErf (Kahn a) 
Num a => Mode (Kahn a) 
Num a => Jacobian (Kahn a) 
Num a => Grad (Kahn a) [a] (a, [a]) a 
Typeable (* -> *) Kahn 
Grad i o o' a => Grad (Kahn a -> i) (a -> o) (a -> o') a 
type DeRef (Kahn a) = Tape a 
type Scalar (Kahn a) = a 
type D (Kahn a) = Id a 

data Tape a t Source

A Tape records the information needed back propagate from the output to each input during reverse Mode AD.


Lift !a 
Var !a !Int 
Binary !a a a t t 
Unary !a a t 


(Data a, Data t) => Data (Tape a t) 
(Show a, Show t) => Show (Tape a t) 
Typeable (* -> * -> *) Tape 

partials :: forall a. Num a => Kahn a -> [(Int, a)] Source

This returns a list of contributions to the partials. The variable ids returned in the list are likely not unique!

partialArray :: Num a => (Int, Int) -> Kahn a -> Array Int a Source

Return an Array of partials given bounds for the variable IDs.

partialMap :: Num a => Kahn a -> IntMap a Source

Return an IntMap of sparse partials

derivative :: Num a => Kahn a -> a Source

derivative' :: Num a => Kahn a -> (a, a) Source

vgrad :: Grad i o o' a => i -> o Source

vgrad' :: Grad i o o' a => i -> o' Source

class Num a => Grad i o o' a | i -> a o o', o -> a i o', o' -> a i o where Source


pack :: i -> [Kahn a] -> Kahn a Source

unpack :: ([a] -> [a]) -> o Source

unpack' :: ([a] -> (a, [a])) -> o' Source


Num a => Grad (Kahn a) [a] (a, [a]) a 
Grad i o o' a => Grad (Kahn a -> i) (a -> o) (a -> o') a 

bind :: Traversable f => f a -> (f (Kahn a), (Int, Int)) Source

unbind :: Functor f => f (Kahn a) -> Array Int a -> f a Source

unbindMap :: (Functor f, Num a) => f (Kahn a) -> IntMap a -> f a Source

unbindWith :: (Functor f, Num a) => (a -> b -> c) -> f (Kahn a) -> Array Int b -> f c Source

unbindMapWithDefault :: (Functor f, Num a) => b -> (a -> b -> c) -> f (Kahn a) -> IntMap b -> f c Source

primal :: Num a => Kahn a -> a Source

var :: a -> Int -> Kahn a Source