| Stability | experimental |
|---|---|
| Maintainer | conal@conal.net, andygill@ku.edu |
| Safe Haskell | None |
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 whereSource
Vector space v.
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 -> vSource
Vector divided by scalar
(^*) :: (VectorSpace v, s ~ Scalar v) => v -> s -> vSource
Vector multiplied by scalar
class (VectorSpace v, AdditiveGroup (Scalar v)) => InnerSpace v whereSource
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 -> vSource
Linear interpolation between a (when t==0) and b (when t==1).
linearCombo :: VectorSpace v => [(v, Scalar v)] -> vSource
Linear combination of vectors
magnitudeSq :: (InnerSpace v, s ~ Scalar v) => v -> sSource
Square of the length of a vector. Sometimes useful for efficiency.
See also magnitude.
magnitude :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> sSource
Length of a vector. See also magnitudeSq.
normalized :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> vSource
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 -> vSource
project u v computes the projection of v onto u.