Safe Haskell	None
Language	Haskell98

Algebra.NormedSpace.Sum

Description

Abstraction of normed vector spaces

Synopsis

class (C a, C a v) => C a v where
- norm :: v -> a
normFoldable :: (C a v, Foldable f) => f v -> a
normFoldable1 :: (C a v, Foldable f, Functor f) => f v -> a

Documentation

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

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 Source #

Instances

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

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

Default definition for norm that is based on Foldable class.

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

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