Data.VectorSpace

Vector spaces

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

Documentation

module Data.AdditiveGroup

class AdditiveGroup v => VectorSpace v where

Vector space v.

Associated Types

type Scalar v :: *

Methods

(*^) :: Scalar v -> v -> v infixr 7

Scale a vector

(*^) :: (Generic v, VectorSpace (VRep v), Scalar (VRep v) ~ Scalar v) => Scalar v -> v -> v infixr 7

Scale a vector

Instances

VectorSpace Double

Associated Types

type Scalar Double :: *

Methods

(*^) :: Scalar Double -> Double -> Double

VectorSpace Float

Associated Types

type Scalar Float :: *

Methods

(*^) :: Scalar Float -> Float -> Float

VectorSpace Int

Associated Types

type Scalar Int :: *

Methods

(*^) :: Scalar Int -> Int -> Int

VectorSpace Integer

Associated Types

type Scalar Integer :: *

Methods

(*^) :: Scalar Integer -> Integer -> Integer

VectorSpace CSChar

Associated Types

type Scalar CSChar :: *

Methods

(*^) :: Scalar CSChar -> CSChar -> CSChar

VectorSpace CShort

Associated Types

type Scalar CShort :: *

Methods

(*^) :: Scalar CShort -> CShort -> CShort

VectorSpace CInt

Associated Types

type Scalar CInt :: *

Methods

(*^) :: Scalar CInt -> CInt -> CInt

VectorSpace CLong

Associated Types

type Scalar CLong :: *

Methods

(*^) :: Scalar CLong -> CLong -> CLong

VectorSpace CLLong

Associated Types

type Scalar CLLong :: *

Methods

(*^) :: Scalar CLLong -> CLLong -> CLLong

VectorSpace CFloat

Associated Types

type Scalar CFloat :: *

Methods

(*^) :: Scalar CFloat -> CFloat -> CFloat

VectorSpace CDouble

Associated Types

type Scalar CDouble :: *

Methods

(*^) :: Scalar CDouble -> CDouble -> CDouble

VectorSpace CIntMax

Associated Types

type Scalar CIntMax :: *

Methods

(*^) :: Scalar CIntMax -> CIntMax -> CIntMax

VectorSpace v => VectorSpace (Maybe v)

Associated Types

type Scalar (Maybe v) :: *

Methods

(*^) :: Scalar (Maybe v) -> Maybe v -> Maybe v

Integral a => VectorSpace (Ratio a)

Associated Types

type Scalar (Ratio a) :: *

Methods

(*^) :: Scalar (Ratio a) -> Ratio a -> Ratio a

(RealFloat v, VectorSpace v) => VectorSpace (Complex v)

Associated Types

type Scalar (Complex v) :: *

Methods

(*^) :: Scalar (Complex v) -> Complex v -> Complex v

VectorSpace v => VectorSpace (a -> v)

Associated Types

type Scalar (a -> v) :: *

Methods

(*^) :: Scalar (a -> v) -> (a -> v) -> a -> v

VectorSpace a => VectorSpace (Rec0 a s)

Associated Types

type Scalar (Rec0 a s) :: *

Methods

(*^) :: Scalar (Rec0 a s) -> Rec0 a s -> Rec0 a s

(VectorSpace u, (~) * s (Scalar u), VectorSpace v, (~) * s (Scalar v)) => VectorSpace (u, v)

Associated Types

type Scalar (u, v) :: *

Methods

(*^) :: Scalar (u, v) -> (u, v) -> (u, v)

(HasTrie a, VectorSpace v) => VectorSpace ((:->:) a v)

Associated Types

type Scalar ((:->:) a v) :: *

Methods

(*^) :: Scalar (a :->: v) -> (a :->: v) -> a :->: v

(HasTrie (Basis u), VectorSpace v) => VectorSpace ((:-*) u v)

Associated Types

type Scalar ((:-*) u v) :: *

Methods

(*^) :: Scalar (u :-* v) -> (u :-* v) -> u :-* v

(HasBasis a, HasTrie (Basis a), VectorSpace u) => VectorSpace ((:>) a u)

Associated Types

type Scalar ((:>) a u) :: *

Methods

(*^) :: Scalar (a :> u) -> (a :> u) -> a :> u

(VectorSpace (f p), VectorSpace (g p), (~) * (Scalar (f p)) (Scalar (g p))) => VectorSpace ((:*:) f g p)

Associated Types

type Scalar ((:*:) f g p) :: *

Methods

(*^) :: Scalar ((f :*: g) p) -> (f :*: g) p -> (f :*: g) p

(VectorSpace u, (~) * s (Scalar u), VectorSpace v, (~) * s (Scalar v), VectorSpace w, (~) * s (Scalar w)) => VectorSpace (u, v, w)

Associated Types

type Scalar (u, v, w) :: *

Methods

(*^) :: Scalar (u, v, w) -> (u, v, w) -> (u, v, w)

VectorSpace (f p) => VectorSpace (M1 i c f p)

Associated Types

type Scalar (M1 i c f p) :: *

Methods

(*^) :: Scalar (M1 i c f p) -> M1 i c f p -> M1 i c f p

(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)

Associated Types

type Scalar (u, v, w, x) :: *

Methods

(*^) :: Scalar (u, v, w, x) -> (u, v, w, x) -> (u, v, w, x)

(^/) :: (VectorSpace v, s ~ Scalar v, Fractional s) => v -> s -> v infixr 7

Vector divided by scalar

(^*) :: (VectorSpace v, s ~ Scalar v) => v -> s -> v infixl 7

Vector multiplied by scalar

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

Adds inner (dot) products.

Methods

(<.>) :: v -> v -> Scalar v infixr 7

Inner/dot product

(<.>) :: (Generic v, InnerSpace (VRep v), Scalar (VRep v) ~ Scalar v) => v -> v -> Scalar v infixr 7

Inner/dot product

Instances

InnerSpace Double

Methods

(<.>) :: Double -> Double -> Scalar Double

InnerSpace Float

Methods

(<.>) :: Float -> Float -> Scalar Float

InnerSpace Int

Methods

(<.>) :: Int -> Int -> Scalar Int

InnerSpace Integer

Methods

(<.>) :: Integer -> Integer -> Scalar Integer

InnerSpace CSChar

Methods

(<.>) :: CSChar -> CSChar -> Scalar CSChar

InnerSpace CShort

Methods

(<.>) :: CShort -> CShort -> Scalar CShort

InnerSpace CInt

Methods

(<.>) :: CInt -> CInt -> Scalar CInt

InnerSpace CLong

Methods

(<.>) :: CLong -> CLong -> Scalar CLong

InnerSpace CLLong

Methods

(<.>) :: CLLong -> CLLong -> Scalar CLLong

InnerSpace CFloat

Methods

(<.>) :: CFloat -> CFloat -> Scalar CFloat

InnerSpace CDouble

Methods

(<.>) :: CDouble -> CDouble -> Scalar CDouble

InnerSpace CIntMax

Methods

(<.>) :: CIntMax -> CIntMax -> Scalar CIntMax

InnerSpace a => InnerSpace (Maybe a)

Methods

(<.>) :: Maybe a -> Maybe a -> Scalar (Maybe a)

Integral a => InnerSpace (Ratio a)

Methods

(<.>) :: Ratio a -> Ratio a -> Scalar (Ratio a)

(RealFloat v, InnerSpace v) => InnerSpace (Complex v)

Methods

(<.>) :: Complex v -> Complex v -> Scalar (Complex v)

InnerSpace v => InnerSpace (a -> v)

Methods

(<.>) :: (a -> v) -> (a -> v) -> Scalar (a -> v)

InnerSpace a => InnerSpace (Rec0 a s)

Methods

(<.>) :: Rec0 a s -> Rec0 a s -> Scalar (Rec0 a s)

(InnerSpace u, (~) * s (Scalar u), InnerSpace v, (~) * s (Scalar v)) => InnerSpace (u, v)

Methods

(<.>) :: (u, v) -> (u, v) -> Scalar (u, v)

(InnerSpace u, (~) * s (Scalar u), AdditiveGroup s, HasBasis a, HasTrie (Basis a)) => InnerSpace ((:>) a u)

Methods

(<.>) :: (a :> u) -> (a :> u) -> Scalar (a :> u)

(InnerSpace (f p), InnerSpace (g p), (~) * (Scalar (f p)) (Scalar (g p)), Num (Scalar (f p))) => InnerSpace ((:*:) f g p)

Methods

(<.>) :: (f :*: g) p -> (f :*: g) p -> Scalar ((f :*: g) p)

(InnerSpace u, (~) * s (Scalar u), InnerSpace v, (~) * s (Scalar v), InnerSpace w, (~) * s (Scalar w)) => InnerSpace (u, v, w)

Methods

(<.>) :: (u, v, w) -> (u, v, w) -> Scalar (u, v, w)

InnerSpace (f p) => InnerSpace (M1 i c f p)

Methods

(<.>) :: M1 i c f p -> M1 i c f p -> Scalar (M1 i c f p)

(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)

Methods

(<.>) :: (u, v, w, x) -> (u, v, w, x) -> Scalar (u, v, w, x)

lerp :: VectorSpace v => v -> v -> Scalar v -> v

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

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

Linear combination of vectors

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

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

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

Length of a vector. See also magnitudeSq.

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

Vector in same direction as given one but with length of one. If given the zero vector, then return it.

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

project u v computes the projection of v onto u.