Add vector & matrix modules

src/Data/NumIdr/Vector.idr

@@ -0,0 +1,91 @@
+module Data.NumIdr.Vector
+
+import Data.Vect
+import public Data.NumIdr.Array
+
+%default total
+
+public export
+Vector : Nat -> Type -> Type
+Vector n = Array [n]
+
+
+--------------------------------------------------------------------------------
+-- Vector constructors
+--------------------------------------------------------------------------------
+
+
+export
+vector : Vect n a -> Vector n a
+vector v = rewrite sym (lengthCorrect v)
+           in fromVect [length v] $          -- the order doesn't matter here, as
+           rewrite lengthCorrect v in        -- there is only 1 axis
+           rewrite multOneLeftNeutral n in v
+
+export
+basis : Num a => {n : _} -> (i : Fin n) -> Vector n a
+basis i = fromFunction _ (\[j] => if i == j then 1 else 0)
+
+
+export
+unit2D : (ang : Double) -> Vector 2 Double
+unit2D ang = vector [cos ang, sin ang]
+
+export
+unit3D : (pol, az : Double) -> Vector 3 Double
+unit3D pol az = vector [cos az * sin pol, sin az * sin pol, cos pol]
+
+
+
+--------------------------------------------------------------------------------
+-- Indexing
+--------------------------------------------------------------------------------
+
+
+export
+index : Fin n -> Vector n a -> a
+index n = Array.index [n]
+
+
+-- Named projections
+export
+(.x) : Vector (1 + n) a -> a
+(.x) = index FZ
+
+export
+(.y) : Vector (2 + n) a -> a
+(.y) = index (FS FZ)
+
+export
+(.z) : Vector (3 + n) a -> a
+(.z) = index (FS (FS FZ))
+
+
+--------------------------------------------------------------------------------
+-- Swizzling
+--------------------------------------------------------------------------------
+
+
+export
+swizzle : Vect n (Fin m) -> Vector m a -> Vector n a
+swizzle p v = rewrite sym (lengthCorrect p)
+              in fromFunction [length p] (\[i] =>
+                index (index (rewrite sym (lengthCorrect p) in i) p) v
+              )
+
+
+
+--------------------------------------------------------------------------------
+-- Vector operations
+--------------------------------------------------------------------------------
+
+
+export
+dot : Num a => Vector n a -> Vector n a -> a
+dot = sum .: zipWith (*)
+
+
+export
+perp : Neg a => Vector 2 a -> Vector 2 a -> a
+perp a b = a.x * b.y - a.y * b.x
+