Safe Haskell	None
Language	Haskell2010

NumHask.Analysis.Banach

Description

Metric classes

Synopsis

class (ExpField (Actor h), Normed h (Actor h), DivisiveAction h) => Banach h where
- normalizeL1 :: h -> h
- normalizeL2 :: h -> h
class Distributive (Actor h) => Hilbert h where
- (<.>) :: h -> h -> Actor h

Documentation

Banach (with Norm) laws form rules around size and direction of a number, with a potential crossing into another codomain.

a == singleton zero || normalizeL2 a *. normL2 a == a

Minimal complete definition

Nothing

Methods

the inner product: a distributive fold

a <.> b == b <.> a
a <.> (b +c) == a <.> b + a <.> c
a <.> (s *. b + c) == s * (a <.> b) + a <.> c

(s0 *. a) . (s1 *. b) == s0 * s1 * (a . b)

Methods

(<.>) :: h -> h -> Actor h infix 8 Source #