| Copyright | (c) Conal Elliott 2008-2012 |
|---|---|
| License | BSD3 |
| Maintainer | conal@conal.net |
| Stability | experimental |
| Safe Haskell | None |
| Language | Haskell98 |
Data.LinearMap
Description
Linear maps
- data u :-* v
- linear :: (HasBasis u, HasTrie (Basis u)) => (u -> v) -> u :-* v
- lapply :: (VectorSpace v, Scalar u ~ Scalar v, HasBasis u, HasTrie (Basis u)) => (u :-* v) -> u -> v
- atBasis :: (AdditiveGroup v, HasTrie (Basis u)) => (u :-* v) -> Basis u -> v
- idL :: (HasBasis u, HasTrie (Basis u)) => u :-* u
- (*.*) :: (HasBasis u, HasTrie (Basis u), HasBasis v, HasTrie (Basis v), VectorSpace w, Scalar v ~ Scalar w) => (v :-* w) -> (u :-* v) -> u :-* w
- inLMap :: (LMap' r s -> LMap' t u) -> (r :-* s) -> t :-* u
- inLMap2 :: (LMap' r s -> LMap' t u -> LMap' v w) -> (r :-* s) -> (t :-* u) -> v :-* w
- inLMap3 :: (LMap' r s -> LMap' t u -> LMap' v w -> LMap' x y) -> (r :-* s) -> (t :-* u) -> (v :-* w) -> x :-* y
- liftMS :: AdditiveGroup a => (a -> b) -> MSum a -> MSum b
- liftMS2 :: (AdditiveGroup a, AdditiveGroup b) => (a -> b -> c) -> MSum a -> MSum b -> MSum c
- liftMS3 :: (AdditiveGroup a, AdditiveGroup b, AdditiveGroup c) => (a -> b -> c -> d) -> MSum a -> MSum b -> MSum c -> MSum d
- liftL :: (Functor f, AdditiveGroup (f a)) => (a -> b) -> MSum (f a) -> MSum (f b)
- liftL2 :: (Applicative f, AdditiveGroup (f a), AdditiveGroup (f b)) => (a -> b -> c) -> MSum (f a) -> MSum (f b) -> MSum (f c)
- liftL3 :: (Applicative f, AdditiveGroup (f a), AdditiveGroup (f b), AdditiveGroup (f c)) => (a -> b -> c -> d) -> MSum (f a) -> MSum (f b) -> MSum (f c) -> MSum (f d)
- firstL :: (HasBasis u, HasBasis u', HasBasis v, HasTrie (Basis u), HasTrie (Basis v), Scalar u ~ Scalar v, Scalar u ~ Scalar u') => (u :-* u') -> (u, v) :-* (u', v)
Documentation
Linear map, represented as an optional memo-trie from basis to
values, where Nothing means the zero map (an optimization).
Instances
| (HasTrie (Basis u), AdditiveGroup v) => AdditiveGroup ((:-*) u v) | |
| (HasTrie (Basis u), VectorSpace v) => VectorSpace ((:-*) u v) | |
| type Scalar ((:-*) u v) = Scalar v |
linear :: (HasBasis u, HasTrie (Basis u)) => (u -> v) -> u :-* v Source
Function (assumed linear) as linear map.
lapply :: (VectorSpace v, Scalar u ~ Scalar v, HasBasis u, HasTrie (Basis u)) => (u :-* v) -> u -> v Source
Apply a linear map to a vector.
atBasis :: (AdditiveGroup v, HasTrie (Basis u)) => (u :-* v) -> Basis u -> v Source
Evaluate a linear map on a basis element.
(*.*) :: (HasBasis u, HasTrie (Basis u), HasBasis v, HasTrie (Basis v), VectorSpace w, Scalar v ~ Scalar w) => (v :-* w) -> (u :-* v) -> u :-* w infixr 9 Source
Compose linear maps
inLMap3 :: (LMap' r s -> LMap' t u -> LMap' v w -> LMap' x y) -> (r :-* s) -> (t :-* u) -> (v :-* w) -> x :-* y Source
liftMS :: AdditiveGroup a => (a -> b) -> MSum a -> MSum b Source
liftMS2 :: (AdditiveGroup a, AdditiveGroup b) => (a -> b -> c) -> MSum a -> MSum b -> MSum c Source
liftMS3 :: (AdditiveGroup a, AdditiveGroup b, AdditiveGroup c) => (a -> b -> c -> d) -> MSum a -> MSum b -> MSum c -> MSum d Source
liftL :: (Functor f, AdditiveGroup (f a)) => (a -> b) -> MSum (f a) -> MSum (f b) Source
Apply a linear function to each element of a linear map.
liftL f l == linear f *.* l, but works more efficiently.
liftL2 :: (Applicative f, AdditiveGroup (f a), AdditiveGroup (f b)) => (a -> b -> c) -> MSum (f a) -> MSum (f b) -> MSum (f c) Source
Apply a linear binary function (not to be confused with a bilinear function) to each element of a linear map.
liftL3 :: (Applicative f, AdditiveGroup (f a), AdditiveGroup (f b), AdditiveGroup (f c)) => (a -> b -> c -> d) -> MSum (f a) -> MSum (f b) -> MSum (f c) -> MSum (f d) Source
Apply a linear ternary function (not to be confused with a trilinear function) to each element of a linear map.