Algebra.NormedSpace.Sum

Abstraction of normed vector spaces

Documentation

class (C a, C a v) => C a v where

The super class is only needed to state the laws v == zero == norm v == zero norm (scale x v) == abs x * norm v norm (u+v) <= norm u + norm v

Methods

norm :: v -> a

Instances

C Double Double

C Float Float

C Int Int

C Integer Integer

(C a v, RealFloat v) => C a (Complex v)

(C a, C a v) => C a [v]

(C a, C a v) => C a (T v)

(C a, C a v0, C a v1) => C a (v0, v1)

(Ord i, Eq a, Eq v, C a v) => C a (Map i v)

(C a, C a v0, C a v1, C a v2) => C a (v0, v1, v2)

(C a, C a) => C (T a) (T a)

C a v => C (T a) (T v)

normFoldable :: (C a v, Foldable f) => f v -> a

Default definition for norm that is based on Foldable class.

normFoldable1 :: (C a v, Foldable f, Functor f) => f v -> a

Default definition for norm that is based on Foldable class and the argument vector has at least one component.