Safe Haskell	None
Language	Haskell98

Algebra.NormedSpace.Euclidean

Contents

Instances for atomic types
Instances for composed types

Description

Abstraction of normed vector spaces

Synopsis

class (C a, C a v) => Sqr a v where
- normSqr :: v -> a
normSqrFoldable :: (Sqr a v, Foldable f) => f v -> a
normSqrFoldable1 :: (Sqr a v, Foldable f, Functor f) => f v -> a
class Sqr a v => C a v where
- norm :: v -> a
defltNorm :: (C a, Sqr a v) => v -> a

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 #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: Double -> Double #
Sqr Float Float #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: Float -> Float #
Sqr Int Int #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: Int -> Int #
Sqr Integer Integer #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: Integer -> Integer #
(Sqr a v, RealFloat v) => Sqr a (Complex v) #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: Complex v -> a #
Sqr a v => Sqr a [v] #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: [v] -> a #
Sqr a b => Sqr a (T b) #
Instance details Defined in Number.Complex Methods normSqr :: T b -> a #
Sqr a b => Sqr a (T b) #
Instance details Defined in Number.Quaternion Methods normSqr :: T b -> a #
(Sqr a v0, Sqr a v1) => Sqr a (v0, v1) #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: (v0, v1) -> a #
(Ord i, Eq a, Eq v, Sqr a v) => Sqr a (Map i v) #
Instance details Defined in MathObj.DiscreteMap Methods normSqr :: Map i v -> a #
(Sqr a v0, Sqr a v1, Sqr a v2) => Sqr a (v0, v1, v2) #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: (v0, v1, v2) -> a #
(C a, C a) => Sqr (T a) (T a) #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: T a -> T a #
Sqr a v => Sqr (T a) (T v) #
Instance details Defined in MathObj.Wrapper.NumericPrelude Methods normSqr :: T v -> T a #

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 #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: Double -> Double #
C Float Float #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: Float -> Float #
C Int Int #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: Int -> Int #
C Integer Integer #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: Integer -> Integer #
(C a, Sqr a v, RealFloat v) => C a (Complex v) #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: Complex v -> a #
(C a, Sqr a v) => C a [v] #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: [v] -> a #
(C a, Sqr a b) => C a (T b) #
Instance details Defined in Number.Complex Methods norm :: T b -> a #
(C a, Sqr a b) => C a (T b) #
Instance details Defined in Number.Quaternion Methods norm :: T b -> a #
(C a, Sqr a v0, Sqr a v1) => C a (v0, v1) #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: (v0, v1) -> a #
(Ord i, Eq a, Eq v, C a, Sqr a v) => C a (Map i v) #
Instance details Defined in MathObj.DiscreteMap Methods norm :: Map i v -> a #
(C a, Sqr a v0, Sqr a v1, Sqr a v2) => C a (v0, v1, v2) #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: (v0, v1, v2) -> a #
C a v => C (T a) (T v) #
Instance details Defined in MathObj.Wrapper.NumericPrelude Methods norm :: T v -> T a #

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

Instances for atomic types

Instances for composed types