Modulenumeric-prelude-0.4.4Haskell98

Algebra.NormedSpace.Euclidean

Abstraction of normed vector spaces

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

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

Minimal definition: normSqr

normSqr :: v -> a
Square of the Euclidean norm of a vector. This is sometimes easier to implement.

Instances13Sqr, …

Sqr Integer IntegerDefined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
Sqr Double DoubleDefined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
Sqr Float FloatDefined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
Sqr Int IntDefined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
Sqr a b => Sqr a (T b)Defined in numeric-prelude-0.4.4 · Number.Complex
Sqr a b => Sqr a (T b)Defined in numeric-prelude-0.4.4 · Number.Quaternion
Sqr a v => Sqr a [v]Defined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
(Sqr a v, RealFloat v) => Sqr a (Complex v)Defined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
(Ord i, Eq a, Eq v, Sqr a v) => Sqr a (Map i v)Defined in numeric-prelude-0.4.4 · MathObj.DiscreteMap · orphan
(Sqr a v0, Sqr a v1) => Sqr a (v0, v1)Defined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
(Sqr a v0, Sqr a v1, Sqr a v2) => Sqr a (v0, v1, v2)Defined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
Sqr a v => Sqr (T a) (T v)Defined in numeric-prelude-0.4.4 · MathObj.Wrapper.NumericPrelude
(C a, C a) => Sqr (T a) (T a)Defined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean

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

Default definition for normSqr that is based on Foldable class.

valuenormSqrFoldable1 :: (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.

classclass Sqr a v => C a v where

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

Minimal definition: norm

Instances12C, …

C Integer IntegerDefined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
C Double DoubleDefined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
C Float FloatDefined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
C Int IntDefined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
(C a, Sqr a b) => C a (T b)Defined in numeric-prelude-0.4.4 · Number.Complex
(C a, Sqr a b) => C a (T b)Defined in numeric-prelude-0.4.4 · Number.Quaternion
(C a, Sqr a v) => C a [v]Defined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
(C a, Sqr a v, RealFloat v) => C a (Complex v)Defined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
(Ord i, Eq a, Eq v, C a, Sqr a v) => C a (Map i v)Defined in numeric-prelude-0.4.4 · MathObj.DiscreteMap · orphan
(C a, Sqr a v0, Sqr a v1) => C a (v0, v1)Defined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
(C a, Sqr a v0, Sqr a v1, Sqr a v2) => C a (v0, v1, v2)Defined in numeric-prelude-0.4.4 · Algebra.NormedSpace.Euclidean
C a v => C (T a) (T v)Defined in numeric-prelude-0.4.4 · MathObj.Wrapper.NumericPrelude

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

Instances for atomic types

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