Copyright	(c) Lars Brünjes, 2016
License	MIT
Maintainer	brunjlar@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010
Extensions	TypeSynonymInstances FlexibleContexts FlexibleInstances RankNTypes ExplicitForAll

Data.Utils.Analytic

Description

This module defines the numeric class Analytic, "differentiable" functions Diff f g and an adapted version of gradWith'.

Synopsis

Documentation

class (Floating a, Ord a) => Analytic a where Source #

Class Analytic is a helper class for defining differentiable functions.

Minimal complete definition

Methods

Instances

Analytic Double Source #
Methods fromDouble :: Double -> Double Source #
Reifies * s Tape => Analytic (Reverse s Double) Source #
Methods fromDouble :: Double -> Reverse s Double Source #

newtype Diff f g Source #

Type Diff f g can be thought of as the type of "differentiable" functions f Double -> g Double.

Constructors

Diff
Fields runDiff :: forall a. Analytic a => f a -> g a

Instances

Category (* -> *) Diff Source #
Methods id :: cat a a # (.) :: cat b c -> cat a b -> cat a c #

type Diff' = forall a. Analytic a => a -> a Source #

Type Diff' can be thought of as the type of differentiable functions Double -> Double.

Lifts a differentiable function by pointwise application.

Arguments

:: Traversable t
=> (Double -> Double -> a)	how to combine argument and gradient
-> Diff t Identity	differentiable function
-> t Double	function argument
-> (Double, t a)	function value and combination of argument and gradient

Computes the gradient of an analytic function and combines it with the argument.

>>> gradWith' (\_ d -> d) (Diff $ \[x, y] -> Identity $ x * x + 3 * y + 7) [2, 1]
(14.0,[4.0,3.0])