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


-- | n-dimensional arrays
--   
--   n-dimensional arrays founded on numhask.
@package numhask-array
@version 0.3

module NumHask.Array.Constraints
type family IsValidConcat i (a :: [Nat]) (b :: [Nat]) :: Bool
type family Squeeze (a :: [Nat])
type family Concatenate i (a :: [Nat]) (b :: [Nat]) :: [Nat]
type family IsValidTranspose (p :: [Nat]) (a :: [Nat]) :: Bool

-- | Reduces axis i in shape s. Does not maintain singlton dimension.
type family Fold i (s :: [Nat])

-- | Reduces axis i in shape s. Maintains singlton dimension
type family FoldAlong i (s :: [Nat])
type family TailModule i (s :: [Nat])
type family HeadModule i (s :: [Nat])
type family Transpose a


-- | numbers with a shape
module NumHask.Shape

-- | Not everything that has a shape is representable.
--   
--   todo: Structure is a useful alternative concept/naming convention
class HasShape f where {
    type family Shape f;
}
shape :: HasShape f => f a -> Shape f

-- | A <a>Functor</a> <tt>f</tt> is <a>Representable</a> if <a>tabulate</a>
--   and <a>index</a> witness an isomorphism to <tt>(-&gt;) x</tt>.
--   
--   Every <a>Distributive</a> <a>Functor</a> is actually
--   <a>Representable</a>.
--   
--   Every <a>Representable</a> <a>Functor</a> from Hask to Hask is a right
--   adjoint.
--   
--   <pre>
--   <a>tabulate</a> . <a>index</a>  ≡ id
--   <a>index</a> . <a>tabulate</a>  ≡ id
--   <a>tabulate</a> . <a>return</a> ≡ <a>return</a>
--   </pre>
class Distributive f => Representable (f :: Type -> Type) where {
    
    -- | If no definition is provided, this will default to <a>GRep</a>.
    type family Rep (f :: Type -> Type) :: Type;
}

-- | <pre>
--   <a>fmap</a> f . <a>tabulate</a> ≡ <a>tabulate</a> . <a>fmap</a> f
--   </pre>
--   
--   If no definition is provided, this will default to <a>gtabulate</a>.
tabulate :: Representable f => (Rep f -> a) -> f a

-- | If no definition is provided, this will default to <a>gindex</a>.
index :: Representable f => f a -> Rep f -> a


-- | Experimental api following
--   <a>https://pechersky.github.io/haskell-numpy-docs/quickstart.basics.html</a>
module NumHask.Array.Example

module NumHask.Array

-- | an array polymorphic in container and shape
--   
--   <pre>
--   &gt;&gt;&gt; a
--   [[[1, 2, 3, 4],
--     [5, 6, 7, 8],
--     [9, 10, 11, 12]],
--    [[13, 14, 15, 16],
--     [17, 18, 19, 20],
--     [21, 22, 23, 24]]]
--   </pre>
data family Array (c :: Type -> Type) (ds :: [k]) (a :: Type)

-- | an array with dimensions represented at the value level
newtype AnyArray c a
AnyArray :: ([Int], c a) -> AnyArray c a

-- | convert an array with type-level shape to value-level shape
anyArray :: Dimensions ds => Array c (ds :: [Nat]) a -> AnyArray c a

-- | a sweet class of container with attributes necessary to supply the set
--   of operations here
class (Functor f) => Container f
generate :: Container f => Int -> (Int -> a) -> f a
idx :: Container f => f a -> Int -> a
cslice :: Container f => Int -> Int -> f a -> f a
zipWith :: Container f => (a -> a -> a) -> f a -> f a -> f a
chunkItUp :: Container f => [f a] -> Int -> f a -> [f a]
cfoldl' :: Container f => (b -> a -> b) -> b -> f a -> b
cfoldr :: Container f => (a -> b -> b) -> b -> f a -> b
cconcat :: Container f => [f a] -> f a

-- | convert from n-dim shape index to a flat index
--   
--   <pre>
--   &gt;&gt;&gt; ind [2,3,4] [1,1,1]
--   17
--   </pre>
ind :: [Int] -> [Int] -> Int

-- | convert from a flat index to a shape index
--   
--   <pre>
--   &gt;&gt;&gt; unind [2,3,4] 17
--   [1,1,1]
--   </pre>
unind :: [Int] -> Int -> [Int]

-- | convert the top layer of a SomeArray to a [SomeArray]
flatten1 :: Container c => AnyArray c a -> [AnyArray c a]
type Vector c n = Array c '[n]
type Matrix c m n = Array c '[m, n]

-- | outer product
--   
--   todo: reconcile with numhask version
--   
--   <pre>
--   &gt;&gt;&gt; v NumHask.Array.&gt;&lt; v
--   [[1, 2, 3],
--    [2, 4, 6],
--    [3, 6, 9]]
--   </pre>
(><) :: forall c (r :: [Nat]) (s :: [Nat]) a. (Container c, CommutativeRing a, Dimensions r, Dimensions s, Dimensions ((++) r s)) => Array c r a -> Array c s a -> Array c ((++) r s) a

-- | matrix multiplication
--   
--   <pre>
--   &gt;&gt;&gt; let a = [1, 2, 3, 4] :: Array [] '[2, 2] Int
--   
--   &gt;&gt;&gt; let b = [5, 6, 7, 8] :: Array [] '[2, 2] Int
--   
--   &gt;&gt;&gt; a
--   [[1, 2],
--    [3, 4]]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; b
--   [[5, 6],
--    [7, 8]]
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; mmult a b
--   [[19, 22],
--    [43, 50]]
--   </pre>
mmult :: forall c m n k a. (Hilbert (Vector c k a), Dimensions '[m, k], Dimensions '[k, n], Dimensions '[m, n], Container c) => Matrix c (m :: Nat) (k :: Nat) a -> Matrix c k n a -> Matrix c m n a

-- | extract the row of a matrix
row :: forall c i a m n. (Dimensions '[m, n], Container c, KnownNat i, (<) i m ~  'True) => Proxy i -> Matrix c m n a -> Vector c n a
rank2Shape :: Dimensions '[m, n] => Matrix c (m :: Nat) (n :: Nat) a -> (Int, Int)
unsafeRow :: forall c a m n. (Container c, Dimensions '[m, n]) => Int -> Matrix c (m :: Nat) (n :: Nat) a -> Vector c n a
unsafeCol :: forall c a m n. (Container c, Dimensions '[m, n]) => Int -> Matrix c (m :: Nat) (n :: Nat) a -> Vector c m a

-- | extract the column of a matrix
col :: forall c j a m n. (Dimensions '[m, n], Container c, KnownNat j, (<) j n ~  'True) => Proxy j -> Matrix c m n a -> Vector c m a

-- | <pre>
--   &gt;&gt;&gt; unsafeIndex a [0,2,1]
--   10
--   </pre>
unsafeIndex :: (Container c, Dimensions r) => Array c (r :: [Nat]) a -> [Int] -> a

-- | <pre>
--   &gt;&gt;&gt; unsafeSlice [[0,1],[2],[1,2]] a :: Array [] '[2,1,2] Int
--   [[[10, 11]],
--    [[22, 23]]]
--   </pre>
unsafeSlice :: (Container c, IsList (c a), Item (c a) ~ a, Dimensions r, Dimensions r0) => [[Int]] -> Array c (r :: [Nat]) a -> Array c (r0 :: [Nat]) a

-- | todo: an ambiguous type variable has snuck in here somewhere
--   
--   <pre>
--   slice (Proxy :: Proxy '[ '[0,1],'[2],'[1,2]]) a
--   </pre>
--   
--   <ul>
--   <li><i>[[10, 11</i> ],</li>
--   <li><i>[22, 23</i> ]]</li>
--   </ul>
slice :: (SingKind a1, SingI a2, Container c, IsList (c a3), Dimensions r, Dimensions r0, Item (c a3) ~# a3, Demote a1 ~# Integer) => proxy a2 -> Array c r a3 -> Array c r0 a3

-- | <pre>
--   &gt;&gt;&gt; foldAlong (Proxy :: Proxy 1) (\_ -&gt; ([0..3] :: Array [] '[4] Int)) a
--   [[0, 1, 2, 3],
--    [0, 1, 2, 3]]
--   </pre>
--   
--   todo: resolution of a primitive and a scalar eg Expected type: Array
--   '[10] Int -&gt; Array '[] Int Actual type: Array '[10] (Array '[] Int)
--   -&gt; Array '[] Int
foldAlong :: forall c s vw uvw uw w a. (Container c, KnownNat s, Dimensions uvw, uw ~ Fold s uvw, w ~ Drop 1 vw, vw ~ TailModule s uvw) => Proxy s -> (Array c vw a -> Array c w a) -> Array c uvw a -> Array c uw a

-- | todo: No instance for (Container (Array [] '[]) error
--   
--   <pre>
--   mapAlong (Proxy :: Proxy 0) (\x -&gt; NumHask.Array.zipWith (*) x x) a
--   </pre>
--   
--   <ul>
--   <li><i>[[1, 4, 9, 16</i> ,</li>
--   <li><i>25, 36, 49, 64</i> ,</li>
--   <li><i>81, 100, 121, 144</i> ],</li>
--   <li><i>[169, 196, 225, 256</i> ,</li>
--   <li><i>289, 324, 361, 400</i> ,</li>
--   <li><i>441, 484, 529, 576</i> ]]</li>
--   </ul>
mapAlong :: forall c s uvw vw a. (Container c, KnownNat s, Dimensions uvw, vw ~ HeadModule s uvw) => Proxy s -> (Array c vw a -> Array c vw a) -> Array c uvw a -> Array c uvw a

-- | <pre>
--   &gt;&gt;&gt; concatenate (Proxy :: Proxy 2) a a
--   [[[1, 2, 3, 4, 1, 2, 3, 4],
--     [5, 6, 7, 8, 5, 6, 7, 8],
--     [9, 10, 11, 12, 9, 10, 11, 12]],
--    [[13, 14, 15, 16, 13, 14, 15, 16],
--     [17, 18, 19, 20, 17, 18, 19, 20],
--     [21, 22, 23, 24, 21, 22, 23, 24]]]
--   </pre>
concatenate :: forall c s r t a. (Container c, SingI s, Dimensions r, Dimensions t, IsValidConcat s t r ~  'True) => Proxy s -> Array c r a -> Array c t a -> Array c (Concatenate s t r) a

-- | <pre>
--   &gt;&gt;&gt; NumHask.Array.transpose a
--   [[[1, 2],
--     [3, 4],
--     [5, 6]],
--    [[7, 8],
--     [9, 10],
--     [11, 12]],
--    [[13, 14],
--     [15, 16],
--     [17, 18]],
--    [[19, 20],
--     [21, 22],
--     [23, 24]]]
--   </pre>
transpose :: forall c s t a. (t ~ Transpose s, Container c, Dimensions s, Dimensions t) => Array c (s :: [Nat]) a -> Array c (t :: [Nat]) a

-- | <pre>
--   &gt;&gt;&gt; let a = [1..24] :: Array [] '[2,1,3,4,1] Int
--   
--   &gt;&gt;&gt; a
--   [[[[[1],
--       [2],
--       [3],
--       [4]],
--      [[5],
--       [6],
--       [7],
--       [8]],
--      [[9],
--       [10],
--       [11],
--       [12]]]],
--    [[[[13],
--       [14],
--       [15],
--       [16]],
--      [[17],
--       [18],
--       [19],
--       [20]],
--      [[21],
--       [22],
--       [23],
--       [24]]]]]
--   
--   &gt;&gt;&gt; squeeze a
--   [[[1, 2, 3, 4],
--     [5, 6, 7, 8],
--     [9, 10, 11, 12]],
--    [[13, 14, 15, 16],
--     [17, 18, 19, 20],
--     [21, 22, 23, 24]]]
--   </pre>
squeeze :: forall c s t a. t ~ Squeeze s => Array c s a -> Array c t a
singleton :: (Dimensions r, Container c) => a -> Array c (r :: [Nat]) a
instance Data.Foldable.Foldable c => Data.Foldable.Foldable (NumHask.Array.Array c ds)
instance GHC.Base.Functor c => GHC.Base.Functor (NumHask.Array.Array c ds)
instance NumHask.Array.Container Data.Vector.Vector
instance NumHask.Array.Container []
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c) => Data.Distributive.Distributive (NumHask.Array.Array c r)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c) => Data.Functor.Rep.Representable (NumHask.Array.Array c r)
instance (GHC.Show.Show a, GHC.Show.Show (GHC.Exts.Item (c a)), NumHask.Array.Container c, GHC.Exts.IsList (c a)) => GHC.Show.Show (NumHask.Array.AnyArray c a)
instance (GHC.Show.Show a, GHC.Show.Show (GHC.Exts.Item (c a)), GHC.Exts.IsList (c a), NumHask.Array.Container c, Numeric.Dimensions.Dims.Dimensions ds) => GHC.Show.Show (NumHask.Array.Array c ds a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Additive.Additive a) => NumHask.Algebra.Abstract.Additive.Additive (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Additive.Subtractive a) => NumHask.Algebra.Abstract.Additive.Subtractive (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Multiplicative.Multiplicative a) => NumHask.Algebra.Abstract.Multiplicative.Multiplicative (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Multiplicative.Divisive a) => NumHask.Algebra.Abstract.Multiplicative.Divisive (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Multiplicative.Multiplicative a, NumHask.Algebra.Abstract.Additive.Additive a) => NumHask.Algebra.Abstract.Ring.Distributive (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Ring.IntegralDomain a) => NumHask.Algebra.Abstract.Ring.IntegralDomain (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Field.Field a) => NumHask.Algebra.Abstract.Field.Field (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Field.ExpField a) => NumHask.Algebra.Abstract.Field.ExpField (NumHask.Array.Array c r a)
instance (Data.Foldable.Foldable (NumHask.Array.Array c r), Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Field.UpperBoundedField a) => NumHask.Algebra.Abstract.Field.UpperBoundedField (NumHask.Array.Array c r a)
instance (Data.Foldable.Foldable (NumHask.Array.Array c r), Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Field.LowerBoundedField a) => NumHask.Algebra.Abstract.Field.LowerBoundedField (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Multiplicative.Multiplicative a, NumHask.Analysis.Metric.Signed a) => NumHask.Analysis.Metric.Signed (NumHask.Array.Array c r a)
instance (GHC.Classes.Eq (c a), Data.Foldable.Foldable (NumHask.Array.Array c r), Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Analysis.Metric.Epsilon a) => NumHask.Analysis.Metric.Epsilon (NumHask.Array.Array c r a)
instance (Data.Foldable.Foldable (NumHask.Array.Array c r), Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Field.ExpField a, NumHask.Algebra.Abstract.Additive.Subtractive a, NumHask.Analysis.Metric.Normed a a) => NumHask.Analysis.Metric.Metric (NumHask.Array.Array c r a) a
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Data.Integral.Integral a) => NumHask.Data.Integral.Integral (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Multiplicative.Multiplicative a) => NumHask.Algebra.Linear.Hadamard.HadamardMultiplication (NumHask.Array.Array c r) a
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Multiplicative.Divisive a) => NumHask.Algebra.Linear.Hadamard.HadamardDivision (NumHask.Array.Array c r) a
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Additive.Additive a) => NumHask.Algebra.Abstract.Action.AdditiveAction (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Additive.Subtractive a) => NumHask.Algebra.Abstract.Action.SubtractiveAction (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Multiplicative.Multiplicative a) => NumHask.Algebra.Abstract.Action.MultiplicativeAction (NumHask.Array.Array c r a)
instance (Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Multiplicative.Divisive a) => NumHask.Algebra.Abstract.Action.DivisiveAction (NumHask.Array.Array c r a)
instance (NumHask.Algebra.Abstract.Action.Actor (NumHask.Array.Array c r a) Data.Type.Equality.~ a, Data.Foldable.Foldable (NumHask.Array.Array c r), NumHask.Algebra.Abstract.Ring.Distributive a, NumHask.Algebra.Abstract.Ring.CommutativeRing a, NumHask.Algebra.Abstract.Ring.Semiring a, Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c) => NumHask.Analysis.Banach.Hilbert (NumHask.Array.Array c r a)
instance (Data.Foldable.Foldable (NumHask.Array.Array c r), Numeric.Dimensions.Dims.Dimensions r, NumHask.Array.Container c, NumHask.Algebra.Abstract.Ring.CommutativeRing a, NumHask.Algebra.Abstract.Multiplicative.Multiplicative a) => NumHask.Algebra.Abstract.TensorProduct.TensorProduct (NumHask.Array.Array c r a)
instance (GHC.Classes.Eq (c a), NumHask.Array.Container c, Numeric.Dimensions.Dims.Dimensions r, NumHask.Algebra.Abstract.Lattice.JoinSemiLattice a) => NumHask.Algebra.Abstract.Lattice.JoinSemiLattice (NumHask.Array.Array c r a)
instance (GHC.Classes.Eq (c a), NumHask.Array.Container c, Numeric.Dimensions.Dims.Dimensions r, NumHask.Algebra.Abstract.Lattice.MeetSemiLattice a) => NumHask.Algebra.Abstract.Lattice.MeetSemiLattice (NumHask.Array.Array c r a)
instance (GHC.Classes.Eq (c a), NumHask.Array.Container c, Numeric.Dimensions.Dims.Dimensions r, NumHask.Algebra.Abstract.Lattice.BoundedJoinSemiLattice a) => NumHask.Algebra.Abstract.Lattice.BoundedJoinSemiLattice (NumHask.Array.Array c r a)
instance (GHC.Classes.Eq (c a), NumHask.Array.Container c, Numeric.Dimensions.Dims.Dimensions r, NumHask.Algebra.Abstract.Lattice.BoundedMeetSemiLattice a) => NumHask.Algebra.Abstract.Lattice.BoundedMeetSemiLattice (NumHask.Array.Array c r a)
instance forall k (c :: * -> *) (ds :: [k]) t. Control.DeepSeq.NFData (NumHask.Array.Array c ds t)
instance Numeric.Dimensions.Dims.Dimensions r => NumHask.Shape.HasShape (NumHask.Array.Array c r)
instance (GHC.Classes.Eq (c t), Numeric.Dimensions.Dims.Dimensions ds) => GHC.Classes.Eq (NumHask.Array.Array c ds t)
instance (GHC.Exts.Item (NumHask.Array.Array c r a) Data.Type.Equality.~ GHC.Exts.Item (c a), Numeric.Dimensions.Dims.Dimensions r, NumHask.Algebra.Abstract.Additive.Additive a, GHC.Exts.IsList (c a)) => GHC.Exts.IsList (NumHask.Array.Array c r a)
instance (GHC.Base.Functor (NumHask.Array.Array c r), Data.Foldable.Foldable (NumHask.Array.Array c r), NumHask.Algebra.Abstract.Additive.Additive (NumHask.Array.Array c r a), NumHask.Analysis.Metric.Normed a a, NumHask.Algebra.Abstract.Field.ExpField a) => NumHask.Analysis.Metric.Normed (NumHask.Array.Array c r a) a