Modulevector-space-0.19Haskell2010

Data.LinearMap

Linear maps

1 type
22 values

Packagevector-space-0.19
Exports23
LanguageHaskell2010
LicenceBSD-3-Clause
SourceLinearMap.hs

newtypenewtype (:-*) u v

Linear map, represented as an optional memo-trie from basis to values, where Nothing means the zero map (an optimization).

Instances3AdditiveGroup, VectorSpace, Scalar

(HasTrie (Basis u), AdditiveGroup v) => AdditiveGroup (u :-* v)Defined in vector-space-0.19 · Data.LinearMap
(HasTrie (Basis u), VectorSpace v) => VectorSpace (u :-* v)Defined in vector-space-0.19 · Data.LinearMap
type Scalar (u :-* v) = Scalar vDefined in vector-space-0.19 · Data.LinearMap

valuelinear :: (HasBasis u, HasTrie (Basis u)) => (u -> v) -> u :-* v

Function (assumed linear) as linear map.

valuelapply

:: (VectorSpace v, Scalar u ~ Scalar v, HasBasis u, HasTrie (Basis u))
=> u :-* v
-> u
-> v

Apply a linear map to a vector.

valueatBasis :: (AdditiveGroup v, HasTrie (Basis u)) => u :-* v -> Basis u -> v

Evaluate a linear map on a basis element.

valueidL :: (HasBasis u, HasTrie (Basis u)) => u :-* u

Identity linear map

value(*.*)

:: (HasTrie (Basis u), HasBasis v, HasTrie (Basis v), VectorSpace w, Scalar v ~ Scalar w)
=> v :-* w
-> u :-* v
-> u :-* w

Compose linear maps

valueinLMap :: (LMap' r s -> LMap' t u) -> r :-* s -> t :-* u

valueinLMap2

:: LMap' r s -> LMap' t u -> LMap' v w
-> r :-* s
-> t :-* u
-> v :-* w

valueinLMap3

:: LMap' r s -> LMap' t u -> LMap' v w -> LMap' x y
-> r :-* s
-> t :-* u
-> v :-* w
-> x :-* y

valueliftMS :: (a -> b) -> MSum a -> MSum b

valueliftMS2

:: (AdditiveGroup a, AdditiveGroup b)
=> a -> b -> c
-> MSum a
-> MSum b
-> MSum c

valueliftMS3

:: (AdditiveGroup a, AdditiveGroup b, AdditiveGroup c)
=> a -> b -> c -> d
-> MSum a
-> MSum b
-> MSum c
-> MSum d

valueliftL :: Functor f => (a -> b) -> MSum (f a) -> MSum (f b)

Apply a linear function to each element of a linear map. liftL f l == linear f *.* l, but works more efficiently.

valueliftL2

:: (Applicative f, AdditiveGroup (f a), AdditiveGroup (f b))
=> a -> b -> c
-> MSum (f a)
-> MSum (f b)
-> MSum (f c)

Apply a linear binary function (not to be confused with a bilinear function) to each element of a linear map.

valueliftL3

:: (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)

Apply a linear ternary function (not to be confused with a trilinear function) to each element of a linear map.

valueexlL :: (HasBasis a, HasTrie (Basis a), HasBasis b, HasTrie (Basis b), Scalar a ~ Scalar b) => (a, b) :-* a

valueexrL :: (HasBasis a, HasTrie (Basis a), HasBasis b, HasTrie (Basis b), Scalar a ~ Scalar b) => (a, b) :-* b

valueforkL

:: (HasTrie (Basis a), HasBasis c, HasBasis d)
=> a :-* c
-> a :-* d
-> a :-* (c, d)

valuefirstL

:: (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)

valuesecondL

:: (HasBasis u, HasBasis v, HasBasis v', HasTrie (Basis u), HasTrie (Basis v), Scalar u ~ Scalar v, Scalar u ~ Scalar v')
=> v :-* v'
-> (u, v) :-* (u, v')

valueinlL :: (HasBasis a, HasTrie (Basis a), HasBasis b) => a :-* (a, b)

valueinrL :: (HasBasis a, HasBasis b, HasTrie (Basis b)) => b :-* (a, b)

valuejoinL

:: (HasBasis a, HasTrie (Basis a), HasBasis b, HasTrie (Basis b), Scalar a ~ Scalar b, Scalar a ~ Scalar c, VectorSpace c)
=> a :-* c
-> b :-* c
-> (a, b) :-* c