| Copyright | (c) Conal Elliott and Andy J Gill 2008 |
|---|---|
| License | BSD3 |
| Maintainer | conal@conal.net, andygill@ku.edu |
| Stability | experimental |
| Safe Haskell | Safe |
| Language | Haskell98 |
Data.VectorSpace
Description
Vector spaces
This version uses associated types instead of fundeps and requires ghc-6.10 or later
Synopsis
- module Data.AdditiveGroup
- class AdditiveGroup v => VectorSpace v where
- (^/) :: (VectorSpace v, s ~ Scalar v, Fractional s) => v -> s -> v
- (^*) :: (VectorSpace v, s ~ Scalar v) => v -> s -> v
- class (VectorSpace v, AdditiveGroup (Scalar v)) => InnerSpace v where
- lerp :: VectorSpace v => v -> v -> Scalar v -> v
- linearCombo :: VectorSpace v => [(v, Scalar v)] -> v
- magnitudeSq :: (InnerSpace v, s ~ Scalar v) => v -> s
- magnitude :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> s
- normalized :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> v
- project :: (InnerSpace v, s ~ Scalar v, Fractional s) => v -> v -> v
Documentation
module Data.AdditiveGroup
class AdditiveGroup v => VectorSpace v where Source #
Vector space v.
Minimal complete definition
Nothing
Methods
(*^) :: Scalar v -> v -> v infixr 7 Source #
Scale a vector
(*^) :: (Generic v, VectorSpace (VRep v), Scalar (VRep v) ~ Scalar v) => Scalar v -> v -> v infixr 7 Source #
Scale a vector
Instances
(^/) :: (VectorSpace v, s ~ Scalar v, Fractional s) => v -> s -> v infixr 7 Source #
Vector divided by scalar
(^*) :: (VectorSpace v, s ~ Scalar v) => v -> s -> v infixl 7 Source #
Vector multiplied by scalar
class (VectorSpace v, AdditiveGroup (Scalar v)) => InnerSpace v where Source #
Adds inner (dot) products.
Minimal complete definition
Nothing
Methods
(<.>) :: v -> v -> Scalar v infixr 7 Source #
Inner/dot product
(<.>) :: (Generic v, InnerSpace (VRep v), Scalar (VRep v) ~ Scalar v) => v -> v -> Scalar v infixr 7 Source #
Inner/dot product
Instances
lerp :: VectorSpace v => v -> v -> Scalar v -> v Source #
Linear interpolation between a (when t==0) and b (when t==1).
linearCombo :: VectorSpace v => [(v, Scalar v)] -> v Source #
Linear combination of vectors
magnitudeSq :: (InnerSpace v, s ~ Scalar v) => v -> s Source #
Square of the length of a vector. Sometimes useful for efficiency.
See also magnitude.
magnitude :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> s Source #
Length of a vector. See also magnitudeSq.
normalized :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> v Source #
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 Source #
project u v computes the projection of v onto u.