| Copyright | (C) 2012-2015 Edward Kmett |
|---|---|
| License | BSD-style (see the file LICENSE) |
| Maintainer | Edward Kmett <ekmett@gmail.com> |
| Stability | provisional |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell98 |
Linear.Vector
Description
Operations on free vector spaces.
- class Functor f => Additive f where
- newtype E t = E {}
- negated :: (Functor f, Num a) => f a -> f a
- (^*) :: (Functor f, Num a) => f a -> a -> f a
- (*^) :: (Functor f, Num a) => a -> f a -> f a
- (^/) :: (Functor f, Fractional a) => f a -> a -> f a
- sumV :: (Foldable f, Additive v, Num a) => f (v a) -> v a
- basis :: (Additive t, Traversable t, Num a) => [t a]
- basisFor :: (Traversable t, Num a) => t b -> [t a]
- scaled :: (Traversable t, Num a) => t a -> t (t a)
- outer :: (Functor f, Functor g, Num a) => f a -> g a -> f (g a)
- unit :: (Additive t, Num a) => ASetter' (t a) a -> t a
Documentation
class Functor f => Additive f where Source #
A vector is an additive group with additional structure.
Methods
The zero vector
zero :: (GAdditive (Rep1 f), Generic1 f, Num a) => f a Source #
The zero vector
(^+^) :: Num a => f a -> f a -> f a infixl 6 Source #
Compute the sum of two vectors
>>>V2 1 2 ^+^ V2 3 4V2 4 6
(^+^) :: Num a => f a -> f a -> f a infixl 6 Source #
Compute the sum of two vectors
>>>V2 1 2 ^+^ V2 3 4V2 4 6
(^-^) :: Num a => f a -> f a -> f a infixl 6 Source #
Compute the difference between two vectors
>>>V2 4 5 ^-^ V2 3 1V2 1 4
(^-^) :: Num a => f a -> f a -> f a infixl 6 Source #
Compute the difference between two vectors
>>>V2 4 5 ^-^ V2 3 1V2 1 4
lerp :: Num a => a -> f a -> f a -> f a Source #
Linearly interpolate between two vectors.
liftU2 :: (a -> a -> a) -> f a -> f a -> f a Source #
Apply a function to merge the 'non-zero' components of two vectors, unioning the rest of the values.
liftU2 :: Applicative f => (a -> a -> a) -> f a -> f a -> f a Source #
Apply a function to merge the 'non-zero' components of two vectors, unioning the rest of the values.
liftI2 :: (a -> b -> c) -> f a -> f b -> f c Source #
Apply a function to the components of two vectors.
- For a dense vector this is equivalent to
liftA2. - For a sparse vector this is equivalent to
intersectionWith.
liftI2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c Source #
Apply a function to the components of two vectors.
- For a dense vector this is equivalent to
liftA2. - For a sparse vector this is equivalent to
intersectionWith.
Instances
| Additive [] Source # | |
| Additive Maybe Source # | |
| Additive Identity Source # | |
| Additive Complex Source # | |
| Additive ZipList Source # | |
| Additive IntMap Source # | |
| Additive Vector Source # | |
| Additive V0 Source # | |
| Additive V1 Source # | |
| Additive V2 Source # | |
| Additive V3 Source # | |
| Additive V4 Source # | |
| Additive Plucker Source # | |
| Additive Quaternion Source # | |
| Additive ((->) b) Source # | |
| Ord k => Additive (Map k) Source # | |
| (Eq k, Hashable k) => Additive (HashMap k) Source # | |
| Additive f => Additive (Point f) Source # | |
| Dim k n => Additive (V k n) Source # | |
Basis element
Instances
negated :: (Functor f, Num a) => f a -> f a Source #
Compute the negation of a vector
>>>negated (V2 2 4)V2 (-2) (-4)
(^*) :: (Functor f, Num a) => f a -> a -> f a infixl 7 Source #
Compute the right scalar product
>>>V2 3 4 ^* 2V2 6 8
(*^) :: (Functor f, Num a) => a -> f a -> f a infixl 7 Source #
Compute the left scalar product
>>>2 *^ V2 3 4V2 6 8
(^/) :: (Functor f, Fractional a) => f a -> a -> f a infixl 7 Source #
Compute division by a scalar on the right.
sumV :: (Foldable f, Additive v, Num a) => f (v a) -> v a Source #
Sum over multiple vectors
>>>sumV [V2 1 1, V2 3 4]V2 4 5
basis :: (Additive t, Traversable t, Num a) => [t a] Source #
Produce a default basis for a vector space. If the dimensionality
of the vector space is not statically known, see basisFor.
basisFor :: (Traversable t, Num a) => t b -> [t a] Source #
Produce a default basis for a vector space from which the argument is drawn.
scaled :: (Traversable t, Num a) => t a -> t (t a) Source #
Produce a diagonal (scale) matrix from a vector.
>>>scaled (V2 2 3)V2 (V2 2 0) (V2 0 3)