Modulevector-space-0.19Haskell2010

Data.VectorSpace

Vector spaces

This version uses associated types instead of fundeps and requires ghc-6.10 or later

2 classes
8 values

Packagevector-space-0.19
Exports10
LanguageHaskell2010
LicenceBSD-3-Clause
SourceVectorSpace.hs

module Data.AdditiveGroup

classclass AdditiveGroup v => VectorSpace v where

Vector space v.

Associated types

type family Scalar v

Methods

(*^) :: Scalar v -> v -> vinfixr 7
Scale a vector

Instances27VectorSpace, …

VectorSpace IntegerDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace CDoubleDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace CFloatDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace CIntDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace CIntMaxDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace CLLongDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace CLongDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace CSCharDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace CShortDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace DoubleDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace FloatDefined in vector-space-0.19 · Data.VectorSpace
VectorSpace IntDefined in vector-space-0.19 · Data.VectorSpace
Integral a => VectorSpace (Ratio a)Defined in vector-space-0.19 · Data.VectorSpace
VectorSpace (Diff (VRep p)) => VectorSpace (GenericDiff p)Defined in vector-space-0.19 · Data.AffineSpace
VectorSpace v => VectorSpace (Maybe v)Defined in vector-space-0.19 · Data.VectorSpace
(RealFloat v, VectorSpace v) => VectorSpace (Complex v)Defined in vector-space-0.19 · Data.VectorSpace
VectorSpace v => VectorSpace (a -> v)Defined in vector-space-0.19 · Data.VectorSpace
(HasTrie (Basis u), VectorSpace v) => VectorSpace (u :-* v)Defined in vector-space-0.19 · Data.LinearMap
(HasTrie a, VectorSpace v) => VectorSpace (a :->: v)Defined in vector-space-0.19 · Data.VectorSpace
(HasBasis a, HasTrie (Basis a), VectorSpace u) => VectorSpace (a :> u)Defined in vector-space-0.19 · Data.Maclaurin
(VectorSpace u, s ~ Scalar u, VectorSpace v, s ~ Scalar v) => VectorSpace (u, v)Defined in vector-space-0.19 · Data.VectorSpace
VectorSpace a => VectorSpace (Rec0 a s)Defined in vector-space-0.19 · Data.VectorSpace
(AffineSpace (f p), AffineSpace (g p), VectorSpace (Diff (f p)), VectorSpace (Diff (g p)), Scalar (Diff (f p)) ~ Scalar (Diff (g p))) => VectorSpace (AffineDiffProductSpace f g p)Defined in vector-space-0.19 · Data.AffineSpace
(VectorSpace u, s ~ Scalar u, VectorSpace v, s ~ Scalar v, VectorSpace w, s ~ Scalar w) => VectorSpace (u, v, w)Defined in vector-space-0.19 · Data.VectorSpace
(VectorSpace (f p), VectorSpace (g p), Scalar (f p) ~ Scalar (g p)) => VectorSpace ((:*:) f g p)Defined in vector-space-0.19 · Data.VectorSpace
(VectorSpace u, s ~ Scalar u, VectorSpace v, s ~ Scalar v, VectorSpace w, s ~ Scalar w, VectorSpace x, s ~ Scalar x) => VectorSpace (u, v, w, x)Defined in vector-space-0.19 · Data.VectorSpace
VectorSpace (f p) => VectorSpace (M1 i c f p)Defined in vector-space-0.19 · Data.VectorSpace

value(^/) :: (VectorSpace v, s ~ Scalar v, Fractional s) => v -> s -> v

Vector divided by scalar

value(^*) :: (VectorSpace v, s ~ Scalar v) => v -> s -> v

Vector multiplied by scalar

classclass (VectorSpace v, AdditiveGroup (Scalar v)) => InnerSpace v where

Adds inner (dot) products.

Methods

(<.>) :: v -> v -> Scalar vinfixr 7
Inner/dot product

Instances25InnerSpace, …

InnerSpace IntegerDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace CDoubleDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace CFloatDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace CIntDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace CIntMaxDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace CLLongDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace CLongDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace CSCharDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace CShortDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace DoubleDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace FloatDefined in vector-space-0.19 · Data.VectorSpace
InnerSpace IntDefined in vector-space-0.19 · Data.VectorSpace
Integral a => InnerSpace (Ratio a)Defined in vector-space-0.19 · Data.VectorSpace
InnerSpace a => InnerSpace (Maybe a)Defined in vector-space-0.19 · Data.VectorSpace
(RealFloat v, InnerSpace v) => InnerSpace (Complex v)Defined in vector-space-0.19 · Data.VectorSpace
(AdditiveGroup (Scalar (Diff (VRep p))), InnerSpace (Diff (VRep p))) => InnerSpace (GenericDiff p)Defined in vector-space-0.19 · Data.AffineSpace
InnerSpace v => InnerSpace (a -> v)Defined in vector-space-0.19 · Data.VectorSpace
(InnerSpace u, s ~ Scalar u, AdditiveGroup s, HasBasis a, HasTrie (Basis a)) => InnerSpace (a :> u)Defined in vector-space-0.19 · Data.Maclaurin
(InnerSpace u, s ~ Scalar u, InnerSpace v, s ~ Scalar v) => InnerSpace (u, v)Defined in vector-space-0.19 · Data.VectorSpace
InnerSpace a => InnerSpace (Rec0 a s)Defined in vector-space-0.19 · Data.VectorSpace
(AdditiveGroup (Scalar (Diff (g p))), AffineSpace (f p), AffineSpace (g p), InnerSpace (Diff (f p)), InnerSpace (Diff (g p)), Scalar (Diff (f p)) ~ Scalar (Diff (g p)), Num (Scalar (Diff (f p)))) => InnerSpace (AffineDiffProductSpace f g p)Defined in vector-space-0.19 · Data.AffineSpace
(InnerSpace u, s ~ Scalar u, InnerSpace v, s ~ Scalar v, InnerSpace w, s ~ Scalar w) => InnerSpace (u, v, w)Defined in vector-space-0.19 · Data.VectorSpace
(InnerSpace (f p), InnerSpace (g p), Scalar (f p) ~ Scalar (g p), Num (Scalar (f p))) => InnerSpace ((:*:) f g p)Defined in vector-space-0.19 · Data.VectorSpace
(InnerSpace u, s ~ Scalar u, InnerSpace v, s ~ Scalar v, InnerSpace w, s ~ Scalar w, InnerSpace x, s ~ Scalar x) => InnerSpace (u, v, w, x)Defined in vector-space-0.19 · Data.VectorSpace
InnerSpace (f p) => InnerSpace (M1 i c f p)Defined in vector-space-0.19 · Data.VectorSpace

valuelerp :: VectorSpace v => v -> v -> Scalar v -> v

Linear interpolation between a (when t==0) and b (when t==1).

valuelinearCombo :: VectorSpace v => [(v, Scalar v)] -> v

Linear combination of vectors

valuemagnitudeSq :: (InnerSpace v, s ~ Scalar v) => v -> s

Square of the length of a vector. Sometimes useful for efficiency. See also magnitude.

valuemagnitude :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> s

Length of a vector. See also magnitudeSq.

valuenormalized :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> v

Vector in same direction as given one but with length of one. Divides by zero for the zero vector.

valueproject :: (InnerSpace v, s ~ Scalar v, Fractional s) => v -> v -> v

project u v computes the projection of v onto u.