Add more array utility functions

src/Data/NumIdr/Array/Array.idr

@@ -83,7 +83,7 @@ rank : Array s a -> Nat
 rank = length . shape
 
 
-
+export
 shapeEq : (arr : Array s a) -> s = shape arr
 shapeEq (MkArray _ _ _ _) = Refl
 
@@ -302,10 +302,15 @@ concat axis a b = let sA = shape a
                       -- TODO: prove that the type-level shape and `s` are equivalent
                   in  believe_me $ MkArray COrder sts s (unsafeFromIns (product s) ins)
 
-
-
-display : Show a => Array s a -> IO ()
-display = printLn . PrimArray.toList . getPrim
+export
+stack : {s : _} -> (axis : Fin (S rk)) -> Vect n (Array {rk} s a) -> Array (insertAt axis n s) a
+stack axis arrs = rewrite sym (lengthCorrect arrs) in
+  fromFunction _ (\is => case getAxisInd axis (rewrite sym (lengthCorrect arrs) in is) of
+                           (i,is') => index is' (index i arrs))
+  where
+    getAxisInd : {0 rk : _} -> {s : _} -> (ax : Fin (S rk)) -> Coords (insertAt ax n s) -> (Fin n, Coords s)
+    getAxisInd FZ (i :: is) = (i, is)
+    getAxisInd {s=_::_} (FS ax) (i :: is) = mapSnd (i::) (getAxisInd ax is)
 
 
 --------------------------------------------------------------------------------
@@ -392,9 +397,8 @@ export
 {s : _} -> Monoid a => Monoid (Array s a) where
   neutral = repeat s neutral
 
--- the shape must be known at runtime due to `fromInteger`. If `fromInteger`
+-- The shape must be known at runtime here due to `fromInteger`. If `fromInteger`
 -- were moved into its own interface, this constraint could be removed.
-
 export
 {s : _} -> Num a => Num (Array s a) where
   (+) = zipWith (+)
@@ -444,3 +448,30 @@ Show a => Show (Array s a) where
                       then List.replicate d ("[]" :: Prelude.Nil)
                       else map (insertPunct s) $ splitWindow (length strs `div` d) strs
         in  "[" :: (concat $ intersperse [", "] secs) `snoc` "]"
+
+
+--------------------------------------------------------------------------------
+-- Numeric array operations
+--------------------------------------------------------------------------------
+
+
+export
+lerp : Neg a => a -> Array s a -> Array s a -> Array s a
+lerp t a b = zipWith (+) (a *. (1 - t)) (b *. t)
+
+
+export
+normSq : Num a => Array s a -> a
+normSq arr = sum $ zipWith (*) arr arr
+
+export
+norm : Array s Double -> Double
+norm = sqrt . normSq
+
+export
+normalize : Array s Double -> Array s Double
+normalize arr = if all (==0) arr then arr else map (/ norm arr) arr
+
+export
+pnorm : (p : Double) -> Array s Double -> Double
+pnorm p = (`pow` recip p) . sum . map (`pow` p)

src/Data/NumIdr/Matrix.idr

@@ -102,3 +102,10 @@ export
 hconcat : Matrix m n a -> Matrix m n' a -> Matrix m (n + n') a
 hconcat = concat 1
 
+
+export
+kronecker : Num a => Vector m a -> Vector n a -> Matrix m n a
+kronecker a b = rewrite dimEq a in rewrite dimEq b in
+                fromFunction [dim a, dim b]
+                  (\[i,j] => Vector.index (rewrite dimEq a in i) a *
+                             Vector.index (rewrite dimEq b in j) b)

src/Data/NumIdr/Multiply.idr

@@ -3,7 +3,7 @@ module Data.NumIdr.Multiply
 %default total
 
 
-infixr 7 *.
+infixr 9 *.
 
 ||| A generalized multiplication/transformation operator. This interface is
 ||| necessary since the standard multiplication operator is homogenous.

src/Data/NumIdr/Vector.idr

@@ -11,6 +11,14 @@ Vector : Nat -> Type -> Type
 Vector n = Array [n]
 
 
+public export
+dim : Vector n a -> Nat
+dim = head . shape
+
+export
+dimEq : (v : Vector n a) -> n = dim v
+dimEq v = cong head $ shapeEq v
+
 --------------------------------------------------------------------------------
 -- Vector constructors
 --------------------------------------------------------------------------------
@@ -107,3 +115,4 @@ export
 perp : Neg a => Vector 2 a -> Vector 2 a -> a
 perp a b = a.x * b.y - a.y * b.x
 
+