| Copyright | (c) Conal Elliott and Andy J Gill 2008 |
|---|---|
| License | BSD3 |
| Maintainer | conal@conal.net, andygill@ku.edu |
| Stability | experimental |
| Safe Haskell | None |
| Language | Haskell98 |
Data.VectorSpace
Description
Vector spaces
This version uses associated types instead of fundeps and requires ghc-6.10 or later
- 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
Vector space v.
Associated Types
type Scalar v :: *
Instances
(^/) :: (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.
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.