Data.Utils.Analytic

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

Documentation

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

Class Analytic is a helper class for defining differentiable functions.

Minimal complete definition

fromDouble

Methods

fromDouble :: Double -> a

Instances

Analytic Double

Methods

fromDouble :: Double -> Double

Reifies * s Tape => Analytic (Reverse s Double)

Methods

fromDouble :: Double -> Reverse s Double

newtype Diff f g

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

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

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

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

diff :: Functor f => Diff' -> Diff f f

Lifts a differentiable function by pointwise application.

gradWith'

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])