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

Instances

VectorSpace Double

VectorSpace Float

VectorSpace Int

VectorSpace Integer

VectorSpace CSChar

VectorSpace CShort

VectorSpace CInt

VectorSpace CLong

VectorSpace CLLong

VectorSpace CFloat

VectorSpace CDouble

VectorSpace CIntMax

Integral a => VectorSpace (Ratio a)

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

VectorSpace v => VectorSpace (Maybe v)

VectorSpace v => VectorSpace (a -> v)

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

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

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

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

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

(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)

(^/) :: (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

Instances

InnerSpace Double

InnerSpace Float

InnerSpace Int

InnerSpace Integer

InnerSpace CSChar

InnerSpace CShort

InnerSpace CInt

InnerSpace CLong

InnerSpace CLLong

InnerSpace CFloat

InnerSpace CDouble

InnerSpace CIntMax

Integral a => InnerSpace (Ratio a)

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

InnerSpace a => InnerSpace (Maybe a)

InnerSpace v => InnerSpace (a -> v)

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

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

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

(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)

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.