Algebra.NormedSpace.Euclidean

Abstraction of normed vector spaces

Documentation

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

Helper class for C that does not need an algebraic type a.

Minimal definition: normSqr

Methods

normSqr :: v -> a

Square of the Euclidean norm of a vector. This is sometimes easier to implement.

Instances

Sqr Double Double

Sqr Float Float

Sqr Int Int

Sqr Integer Integer

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

Sqr a v => Sqr a [v]

Sqr a b => Sqr a (T b)

Sqr a b => Sqr a (T b)

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

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

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

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

Sqr a v => Sqr (T a) (T v)

normSqrFoldable :: (Sqr a v, Foldable f) => f v -> a

Default definition for normSqr that is based on Foldable class.

normSqrFoldable1 :: (Sqr a v, Foldable f, Functor f) => f v -> a

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

class Sqr a v => C a v where

A vector space equipped with an Euclidean or a Hilbert norm.

Minimal definition: norm

Methods

norm :: v -> a

Euclidean norm of a vector.

Instances

C Double Double

C Float Float

C Int Int

C Integer Integer

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

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

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

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

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

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

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

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

defltNorm :: (C a, Sqr a v) => v -> a

Instances for atomic types

Instances for composed types