numeric-prelude-0.1.1: An experimental alternative hierarchy of numeric type classesSource codeContentsIndex
Algebra.NormedSpace.Euclidean
Portabilityrequires multi-parameter type classes
Stabilityprovisional
Maintainernumericprelude@henning-thielemann.de
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
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 whereSource

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

Minimal definition: normSqr

Methods
normSqr :: v -> aSource
Square of the Euclidean norm of a vector. This is sometimes easier to implement.
show/hide Instances
Sqr Double Double
Sqr Float Float
Sqr Int Int
Sqr Integer Integer
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)
class Sqr a v => C a v whereSource
Methods
norm :: v -> aSource
Euclidean norm of a vector.
show/hide Instances
C Double Double
C Float Float
C Int Int
C Integer Integer
(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)
defltNorm :: (C a, Sqr a v) => v -> aSource
Instances for atomic types
Instances for composed types
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