Safe Haskell	Safe
Language	Haskell98

Data.Map.Vector

Synopsis

data MapVector k v
- = MapVector (Map k v)
- | ConstantMap v

Documentation

data MapVector k v Source #

Note: <*> in the Applicative instance operates under intersection. i.e.:

>>> (MapVector $ Map.fromList [("x", id)]) <*> (MapVector $ Map.fromList [("y", 3)])
MapVector (fromList [])

Use the Applicative instance for elementwise operations:

>>> liftA2 (*) (MapVector $ Map.fromList [("x", 2), ("y", 3)]) (MapVector $ Map.fromList [("x", 5),("y", 7)])
MapVector (fromList [("x",10),("y",21)])

>>> liftA2 (*) (MapVector $ Map.fromList [("x", 2), ("y", 3)]) (MapVector $ Map.fromList [("y", 7)])
MapVector (fromList [("y",21)])

*^ in the VectorSpace instance multiplies by the scalar of v. Nesting MapVectors preserves the scalar type, e.g. Scalar (MapVector k (MapVector k' v)) = Scalar v.

>>> 2 *^ (ConstantMap $ MapVector $ Map.fromList [("x", 3 :: Int), ("y", 5)])
ConstantMap (MapVector (fromList [("x",6),("y",10)]))

Finally, <.> in InnerSpace is the dot-product operator. Again, it operates under intersection.

>>> (MapVector $ Map.fromList [("x", 2 :: Int), ("y", 3)]) <.> (MapVector $ Map.fromList [("x", 5),("y", 7)])
31

>>> (pure . MapVector $ Map.fromList [("x", 2 :: Int), ("y", 3)]) <.> (MapVector $ Map.fromList [("a", pure (5::Int))])
25

Addition with ^+^ operates under union.

Constructors

MapVector (Map k v)
ConstantMap v	An infinite-dimensional vector with the same value on all dimensions

Instances

Functor (MapVector k) Source #
Instance details Defined in Data.Map.Vector Methods fmap :: (a -> b) -> MapVector k a -> MapVector k b # (<$) :: a -> MapVector k b -> MapVector k a #
Ord k => Applicative (MapVector k) Source #
Instance details Defined in Data.Map.Vector Methods pure :: a -> MapVector k a # (<>) :: MapVector k (a -> b) -> MapVector k a -> MapVector k b # liftA2 :: (a -> b -> c) -> MapVector k a -> MapVector k b -> MapVector k c # (>) :: MapVector k a -> MapVector k b -> MapVector k b # (<*) :: MapVector k a -> MapVector k b -> MapVector k a #
Foldable (MapVector k) Source #
Instance details Defined in Data.Map.Vector Methods fold :: Monoid m => MapVector k m -> m # foldMap :: Monoid m => (a -> m) -> MapVector k a -> m # foldr :: (a -> b -> b) -> b -> MapVector k a -> b # foldr' :: (a -> b -> b) -> b -> MapVector k a -> b # foldl :: (b -> a -> b) -> b -> MapVector k a -> b # foldl' :: (b -> a -> b) -> b -> MapVector k a -> b # foldr1 :: (a -> a -> a) -> MapVector k a -> a # foldl1 :: (a -> a -> a) -> MapVector k a -> a # toList :: MapVector k a -> [a] # null :: MapVector k a -> Bool # length :: MapVector k a -> Int # elem :: Eq a => a -> MapVector k a -> Bool # maximum :: Ord a => MapVector k a -> a # minimum :: Ord a => MapVector k a -> a # sum :: Num a => MapVector k a -> a # product :: Num a => MapVector k a -> a #
Traversable (MapVector k) Source #
Instance details Defined in Data.Map.Vector Methods traverse :: Applicative f => (a -> f b) -> MapVector k a -> f (MapVector k b) # sequenceA :: Applicative f => MapVector k (f a) -> f (MapVector k a) # mapM :: Monad m => (a -> m b) -> MapVector k a -> m (MapVector k b) # sequence :: Monad m => MapVector k (m a) -> m (MapVector k a) #
(Eq k, Eq v) => Eq (MapVector k v) Source #
Instance details Defined in Data.Map.Vector Methods (==) :: MapVector k v -> MapVector k v -> Bool # (/=) :: MapVector k v -> MapVector k v -> Bool #
(Data k, Data v, Ord k) => Data (MapVector k v) Source #
Instance details Defined in Data.Map.Vector Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MapVector k v -> c (MapVector k v) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (MapVector k v) # toConstr :: MapVector k v -> Constr # dataTypeOf :: MapVector k v -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (MapVector k v)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (MapVector k v)) # gmapT :: (forall b. Data b => b -> b) -> MapVector k v -> MapVector k v # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MapVector k v -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MapVector k v -> r # gmapQ :: (forall d. Data d => d -> u) -> MapVector k v -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> MapVector k v -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> MapVector k v -> m (MapVector k v) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> MapVector k v -> m (MapVector k v) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> MapVector k v -> m (MapVector k v) #
(Ord k, Read k, Read v) => Read (MapVector k v) Source #
Instance details Defined in Data.Map.Vector Methods readsPrec :: Int -> ReadS (MapVector k v) # readList :: ReadS [MapVector k v] # readPrec :: ReadPrec (MapVector k v) # readListPrec :: ReadPrec [MapVector k v] #
(Show k, Show v) => Show (MapVector k v) Source #
Instance details Defined in Data.Map.Vector Methods showsPrec :: Int -> MapVector k v -> ShowS # show :: MapVector k v -> String # showList :: [MapVector k v] -> ShowS #
Semigroup (MapVector k v) Source #
Instance details Defined in Data.Map.Vector Methods (<>) :: MapVector k v -> MapVector k v -> MapVector k v # sconcat :: NonEmpty (MapVector k v) -> MapVector k v # stimes :: Integral b => b -> MapVector k v -> MapVector k v #
(Ord k, Monoid v) => Monoid (MapVector k v) Source #	Respects the inner `Monoid`, unlike `Map`.
Instance details Defined in Data.Map.Vector Methods mempty :: MapVector k v # mappend :: MapVector k v -> MapVector k v -> MapVector k v # mconcat :: [MapVector k v] -> MapVector k v #
(Ord k, HasBasis v, AdditiveGroup (Scalar v)) => HasBasis (MapVector k v) Source #
Instance details Defined in Data.Map.Vector Associated Types type Basis (MapVector k v) :: * # Methods basisValue :: Basis (MapVector k v) -> MapVector k v # decompose :: MapVector k v -> [(Basis (MapVector k v), Scalar (MapVector k v))] # decompose' :: MapVector k v -> Basis (MapVector k v) -> Scalar (MapVector k v) #
(Ord k, VectorSpace v) => VectorSpace (MapVector k v) Source #
Instance details Defined in Data.Map.Vector Associated Types type Scalar (MapVector k v) :: * # Methods (*^) :: Scalar (MapVector k v) -> MapVector k v -> MapVector k v #
(Ord k, VectorSpace v, InnerSpace v, AdditiveGroup (Scalar v)) => InnerSpace (MapVector k v) Source #
Instance details Defined in Data.Map.Vector Methods (<.>) :: MapVector k v -> MapVector k v -> Scalar (MapVector k v) #
(AdditiveGroup v, Ord k) => AdditiveGroup (MapVector k v) Source #
Instance details Defined in Data.Map.Vector Methods zeroV :: MapVector k v # (^+^) :: MapVector k v -> MapVector k v -> MapVector k v # negateV :: MapVector k v -> MapVector k v # (^-^) :: MapVector k v -> MapVector k v -> MapVector k v #
type Basis (MapVector k v) Source #
Instance details Defined in Data.Map.Vector type Basis (MapVector k v) = (k, Basis v)
type Scalar (MapVector k v) Source #
Instance details Defined in Data.Map.Vector type Scalar (MapVector k v) = Scalar v