add foldBack to Vector and Matrix

src/FSharp/Matrix.fs

@@ -46,6 +46,16 @@ module Matrix =
                 acc <- f acc (A.Item(i,j))
         acc
 
+    /// Fold a function over all matrix elements in reverse order.
+    let inline foldBack (f: float -> 'a -> 'a) (acc0: 'a) (A: #Matrix<float>) =
+        let n = A.RowCount
+        let m = A.ColumnCount
+        let mutable acc = acc0
+        for i in n-1 .. -1 .. 0 do
+            for j in n-1 .. -1 .. 0 do
+                acc <- f (A.Item(i,j)) acc
+        acc
+
     /// Fold a matrix by applying a given function to all matrix elements.
     let inline foldi (f: int -> int -> 'a -> float -> 'a) (acc0: 'a) (A: #Matrix<float>) =
         let n = A.RowCount

src/FSharp/Vector.fs

@@ -93,6 +93,13 @@ module Vector =
             acc <- f acc (v.Item(i))
         acc
 
+    /// Fold all entries of a vector in reverse order.
+    let inline foldBack (f: float -> 'a -> 'a) (acc0: 'a) (v: #Vector<float>) =
+        let mutable acc = acc0
+        for i=2 to v.Count do
+            acc <- f (v.Item(v.Count - i)) acc
+        acc
+
     /// Fold all entries of a vector using a position dependent folding function.
     let inline foldi (f: int -> 'a -> float -> 'a) (acc0: 'a) (v: #Vector<float>) =
         let mutable acc = acc0
@@ -145,7 +152,7 @@ module Vector =
             w.[i] <- p
         w
 
-    /// Scans a vector; like fold but returns the intermediate result.
+    /// Scans a vector in reverse order; like foldBack but returns the intermediate result.
     let inline scanBack (f: float -> float -> float) (v: #Vector<float>) =
         let w = v.Clone()
         let mutable p = v.Item(v.Count-1)
@@ -161,7 +168,7 @@ module Vector =
             p <- f p (v.Item(i))
         p
 
-    /// Reduces a vector: the result of this function will be f(v[1], ..., f(v[n-2], f(v[n-1],v[n]))...).
+    /// Reduces a vector in reverse order: the result of this function will be f(v[1], ..., f(v[n-2], f(v[n-1],v[n]))...).
     let inline reduceBack (f: float -> float -> float) (v: #Vector<float>) =
         let mutable p = v.Item(v.Count-1)
         for i=2 to v.Count do

src/FSharpUnitTests/Program.fs

@@ -75,7 +75,9 @@ let VectorTests =
         spec "Vector.mapi"
             (Vector.mapi (fun i x -> float i / 100.0) largev |> should equal largev)
         spec "Vector.fold"
-            (Vector.fold (fun a b -> a + b) 0.0 smallv |> should equal 1.5)
+            (Vector.fold (fun a b -> a - b) 0.0 smallv |> should equal -1.5)
+        spec "Vector.foldBack"
+            (Vector.foldBack (fun a b -> a - b) 0.0 smallv |> should equal 0.0)
         spec "Vector.foldi"
             (Vector.foldi (fun i a b -> a + b) 0.0 smallv |> should equal 1.5)
         spec "Vector.forall"
@@ -90,9 +92,9 @@ let VectorTests =
             (Vector.scan (fun acc x -> acc + x) smallv |> should approximately_vector_equal 14 (new DenseVector( [|0.3;0.6;0.9;1.2;1.5|] ) :> Vector<float>) )
         spec "Vector.scanBack"
             (Vector.scanBack (fun x acc -> acc + x) smallv |> should approximately_vector_equal 14 (new DenseVector( [|1.5;1.2;0.9;0.6;0.3|] ) :> Vector<float>) )
-        spec "Vector.reduce_left"
+        spec "Vector.reduce"
             (Vector.reduce (fun acc x -> acc ** x) smallv |> should approximately_equal 14 0.990295218585507)
-        spec "Vector.reduce_right"
+        spec "Vector.reduceBack"
             (Vector.reduceBack (fun x acc -> x ** acc) smallv |> should approximately_equal 14 0.488911287726319)
     ]
 
@@ -108,7 +110,9 @@ let MatrixTests =
     
     specs "Matrix" [
         spec "Matrix.fold"
-            (Matrix.fold (fun a b -> a + b) 0.0 smallM |> should equal 1.2)
+            (Matrix.fold (fun a b -> a - b) 0.0 smallM |> should equal -1.2)
+        spec "Matrix.foldBack"
+            (Matrix.foldBack (fun a b -> a - b) 0.0 smallM |> should equal 0.0)
         spec "Matrix.foldi"
             (Matrix.foldi (fun i j acc x -> acc + x + float (i+j)) 0.0 smallM |> should equal 5.2)
         spec "Matrix.toArray2"