Safe Haskell	None
Language	Haskell98

Algebra.NormedSpace.Euclidean

Contents

Description

Abstraction of normed vector spaces

Synopsis

Documentation

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

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

Minimal definition: normSqr

Minimal complete definition

Methods

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

Instances

Sqr Double Double Source #
Methods normSqr :: Double -> Double Source #
Sqr Float Float Source #
Methods normSqr :: Float -> Float Source #
Sqr Int Int Source #
Methods normSqr :: Int -> Int Source #
Sqr Integer Integer Source #
Methods normSqr :: Integer -> Integer Source #
(Sqr a v, RealFloat v) => Sqr a (Complex v) Source #
Methods normSqr :: Complex v -> a Source #
Sqr a v => Sqr a [v] Source #
Methods normSqr :: [v] -> a Source #
Sqr a b => Sqr a (T b) Source #
Methods normSqr :: T b -> a Source #
Sqr a b => Sqr a (T b) Source #
Methods normSqr :: T b -> a Source #
(Sqr a v0, Sqr a v1) => Sqr a (v0, v1) Source #
Methods normSqr :: (v0, v1) -> a Source #
(Sqr a v0, Sqr a v1, Sqr a v2) => Sqr a (v0, v1, v2) Source #
Methods normSqr :: (v0, v1, v2) -> a Source #
(C a, C a) => Sqr (T a) (T a) Source #
Methods normSqr :: T a -> T a Source #
Sqr a v => Sqr (T a) (T v) Source #
Methods normSqr :: T v -> T a Source #

Default definition for normSqr that is based on Foldable class.

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 Source #

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

Minimal definition: norm

Minimal complete definition

Methods

norm :: v -> a Source #

Euclidean norm of a vector.

Instances

C Double Double Source #
Methods norm :: Double -> Double Source #
C Float Float Source #
Methods norm :: Float -> Float Source #
C Int Int Source #
Methods norm :: Int -> Int Source #
C Integer Integer Source #
Methods norm :: Integer -> Integer Source #
(C a, Sqr a v, RealFloat v) => C a (Complex v) Source #
Methods norm :: Complex v -> a Source #
(C a, Sqr a v) => C a [v] Source #
Methods norm :: [v] -> a Source #
(C a, Sqr a b) => C a (T b) Source #
Methods norm :: T b -> a Source #
(C a, Sqr a b) => C a (T b) Source #
Methods norm :: T b -> a Source #
(C a, Sqr a v0, Sqr a v1) => C a (v0, v1) Source #
Methods norm :: (v0, v1) -> a Source #
(C a, Sqr a v0, Sqr a v1, Sqr a v2) => C a (v0, v1, v2) Source #
Methods norm :: (v0, v1, v2) -> a Source #
C a v => C (T a) (T v) Source #
Methods norm :: T v -> T a Source #

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

Instances for atomic types