-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | vector-space operations for finite maps using Data.Map
--   
--   Data.Map.Vector provides <tt>MapVector</tt>, a wrapper around
--   <tt>Map</tt> from <tt>containers</tt> which supports constant maps,
--   i.e. maps containing only one value. This allows an identity under
--   intersection and an <tt>Applicative</tt> instance. It also has
--   instances of <tt>AdditiveGroup</tt>, <tt>VectorSpace</tt>,
--   <tt>InnerSpace</tt>, and <tt>HasBasis</tt> with appropriate value
--   types. Provides operations for addition, subtraction, element-wise
--   operations (through <tt>Applicative</tt>), scalar multiplication
--   (through <tt>VectorSpace</tt>), and dot product. Also consider Conal
--   Elliott's <tt>total-map</tt> package.
@package vector-space-map
@version 0.2.1.1

module Data.Map.Vector

-- | Note: <a>&lt;*&gt;</a> in the <a>Applicative</a> instance operates
--   under <i>intersection</i>. i.e.:
--   
--   <pre>
--   &gt;&gt;&gt; (MapVector $ Map.fromList [("x", id)]) &lt;*&gt; (MapVector $ Map.fromList [("y", 3)])
--   MapVector (fromList [])
--   </pre>
--   
--   Use the <a>Applicative</a> instance for elementwise operations:
--   
--   <pre>
--   &gt;&gt;&gt; liftA2 (*) (MapVector $ Map.fromList [("x", 2), ("y", 3)]) (MapVector $ Map.fromList [("x", 5),("y", 7)])
--   MapVector (fromList [("x",10),("y",21)])
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; liftA2 (*) (MapVector $ Map.fromList [("x", 2), ("y", 3)]) (MapVector $ Map.fromList [("y", 7)])
--   MapVector (fromList [("y",21)])
--   </pre>
--   
--   <a>*^</a> in the <a>VectorSpace</a> instance multiplies by the scalar
--   of v. Nesting MapVectors preserves the scalar type, e.g. <tt>Scalar
--   (MapVector k (MapVector k' v))</tt> = <tt>Scalar v</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; 2 *^ (ConstantMap $ MapVector $ Map.fromList [("x", 3 :: Int), ("y", 5)])
--   ConstantMap (MapVector (fromList [("x",6),("y",10)]))
--   </pre>
--   
--   Finally, <a>&lt;.&gt;</a> in <a>InnerSpace</a> is the dot-product
--   operator. Again, it operates under intersection.
--   
--   <pre>
--   &gt;&gt;&gt; (MapVector $ Map.fromList [("x", 2 :: Int), ("y", 3)]) &lt;.&gt; (MapVector $ Map.fromList [("x", 5),("y", 7)])
--   31
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; (pure . MapVector $ Map.fromList [("x", 2 :: Int), ("y", 3)]) &lt;.&gt; (MapVector $ Map.fromList [("a", pure (5::Int))])
--   25
--   </pre>
--   
--   Addition with <a>^+^</a> operates under union.
data MapVector k v
MapVector :: (Map k v) -> MapVector k v

-- | An infinite-dimensional vector with the same value on all dimensions
ConstantMap :: v -> MapVector k v
instance (Data.Data.Data k, Data.Data.Data v, GHC.Classes.Ord k) => Data.Data.Data (Data.Map.Vector.MapVector k v)
instance Data.Traversable.Traversable (Data.Map.Vector.MapVector k)
instance Data.Foldable.Foldable (Data.Map.Vector.MapVector k)
instance (GHC.Classes.Ord k, GHC.Read.Read k, GHC.Read.Read v) => GHC.Read.Read (Data.Map.Vector.MapVector k v)
instance (GHC.Show.Show k, GHC.Show.Show v) => GHC.Show.Show (Data.Map.Vector.MapVector k v)
instance GHC.Base.Functor (Data.Map.Vector.MapVector k)
instance (GHC.Classes.Eq k, GHC.Classes.Eq v) => GHC.Classes.Eq (Data.Map.Vector.MapVector k v)
instance GHC.Base.Semigroup (Data.Map.Vector.MapVector k v)
instance (GHC.Classes.Ord k, GHC.Base.Monoid v) => GHC.Base.Monoid (Data.Map.Vector.MapVector k v)
instance GHC.Classes.Ord k => GHC.Base.Applicative (Data.Map.Vector.MapVector k)
instance (Data.AdditiveGroup.AdditiveGroup v, GHC.Classes.Ord k) => Data.AdditiveGroup.AdditiveGroup (Data.Map.Vector.MapVector k v)
instance (GHC.Classes.Ord k, Data.VectorSpace.VectorSpace v) => Data.VectorSpace.VectorSpace (Data.Map.Vector.MapVector k v)
instance (GHC.Classes.Ord k, Data.VectorSpace.VectorSpace v, Data.VectorSpace.InnerSpace v, Data.AdditiveGroup.AdditiveGroup (Data.VectorSpace.Scalar v)) => Data.VectorSpace.InnerSpace (Data.Map.Vector.MapVector k v)
instance (GHC.Classes.Ord k, Data.Basis.HasBasis v, Data.AdditiveGroup.AdditiveGroup (Data.VectorSpace.Scalar v)) => Data.Basis.HasBasis (Data.Map.Vector.MapVector k v)