Add documentation

src/Data/NumIdr/Matrix.idr

@@ -8,10 +8,12 @@ import Data.NumIdr.Vector
 %default total
 
 
+||| A matrix is a rank-2 array.
 public export
 Matrix : Nat -> Nat -> Type -> Type
 Matrix m n = Array [m,n]
 
+||| A synonym for a square matrix with dimensions of length `n`.
 public export
 Matrix' : Nat -> Type -> Type
 Matrix' n = Matrix n n
@@ -22,26 +24,30 @@ Matrix' n = Matrix n n
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+||| Construct a matrix with the given order and elements.
 export
 matrix' : {m, n : _} -> Order -> Vect m (Vect n a) -> Matrix m n a
 matrix' ord x = array' [m,n] ord x
 
+||| Construct a matrix with the given elements.
 export
 matrix : {m, n : _} -> Vect m (Vect n a) -> Matrix m n a
 matrix = matrix' COrder
 
 
+||| Construct a matrix with a specific value along the diagonal.
+|||
+||| @ diag  The value to repeat along the diagonal
+||| @ other The value to repeat elsewhere
 export
 repeatDiag : {m, n : _} -> (diag, other : a) -> Matrix m n a
-repeatDiag d o = fromFunction [m,n]
-   (\[i,j] => if i `eq` j then d else o)
-  where
-    eq : {0 m,n : Nat} -> Fin m -> Fin n -> Bool
-    eq FZ FZ = True
-    eq (FS x) (FS y) = eq x y
-    eq FZ (FS _) = False
-    eq (FS _) FZ = False
+repeatDiag d o = fromFunctionNB [m,n]
+   (\[i,j] => if i == j then d else o)
 
+||| Construct a matrix given its diagonal elements.
+|||
+||| @ diag  The elements of the matrix's diagonal
+||| @ other The value to repeat elsewhere
 export
 fromDiag : {m, n : _} -> (diag : Vect (minimum m n) a) -> (other : a) -> Matrix m n a
 fromDiag ds o = fromFunction [m,n] (\[i,j] => maybe o (`index` ds) $ i `eq` j)
@@ -53,15 +59,18 @@ fromDiag ds o = fromFunction [m,n] (\[i,j] => maybe o (`index` ds) $ i `eq` j)
     eq (FS _) FZ = Nothing
 
 
+||| The `n`-dimensional identity matrix.
 export
 identity : Num a => {n : _} -> Matrix' n a
 identity = repeatDiag 1 0
 
 
+||| Calculate the matrix that scales a vector by the given value.
 export
 scaling : Num a => {n : _} -> a -> Matrix' n a
 scaling x = repeatDiag x 0
 
+||| Calculate the rotation matrix of an angle.
 export
 rotation2D : Double -> Matrix' 2 Double
 rotation2D a = matrix [[cos a, - sin a], [sin a, cos a]]
@@ -72,19 +81,24 @@ rotation2D a = matrix [[cos a, - sin a], [sin a, cos a]]
 --------------------------------------------------------------------------------
 
 
+||| Index the matrix at the given coordinates.
 export
 index : Fin m -> Fin n -> Matrix m n a -> a
 index m n = index [m,n]
 
+||| Index the matrix at the given coordinates, returning `Nothing` if the
+||| coordinates are out of bounds.
 export
 indexNB : Nat -> Nat -> Matrix m n a -> Maybe a
 indexNB m n = indexNB [m,n]
 
 
+||| Return a row of the matrix as a vector.
 export
 getRow : Fin m -> Matrix m n a -> Vector n a
 getRow r mat = rewrite sym (minusZeroRight n) in indexRange [One r, All] mat
 
+||| Return a column of the matrix as a vector.
 export
 getColumn : Fin n -> Matrix m n a -> Vector m a
 getColumn c mat = rewrite sym (minusZeroRight m) in indexRange [All, One c] mat
@@ -94,19 +108,22 @@ getColumn c mat = rewrite sym (minusZeroRight m) in indexRange [All, One c] mat
 -- Operations
 --------------------------------------------------------------------------------
 
+||| Concatenate two matrices vertically.
 export
 vconcat : Matrix m n a -> Matrix m' n a -> Matrix (m + m') n a
 vconcat = concat 0
 
+||| Concatenate two matrices horizontally.
 export
 hconcat : Matrix m n a -> Matrix m n' a -> Matrix m (n + n') a
 hconcat = concat 1
 
 
+||| Calculate the kronecker product of two vectors as a matrix.
 export
 kronecker : Num a => Vector m a -> Vector n a -> Matrix m n a
 kronecker a b with (viewShape a, viewShape b)
-  _ | (Shape [m], Shape [n]) = fromFunction [m,n] (\[i,j] => index i a * index j b)
+  _ | (Shape [m], Shape [n]) = fromFunction [m,n] (\[i,j] => a !! i * b !! j)
 
 
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