Add Find root method "Bryoden".

src/FSharp/FindRoots.fs

@@ -66,6 +66,10 @@ module FindRoots =
         | true, root -> Some root
         | false, _ -> None
 
+    let broyden maxIterations accuracy guess (f:double[]->double[]) =
+        match Broyden.TryFindRoot(tobcl f, guess, accuracy, maxIterations) with
+        | true, root -> Some root
+        | false, _ -> None
 
     // simple usage
 

src/FSharpUnitTests/FindRootsTests.fs

@@ -9,6 +9,13 @@ module FindRootsTests =
 
     let f x = (x - 3.0)*(x - 4.0)
     let df x = 2.0*x - 7.0
+    let g (xa:float[]) = 
+        let x = xa.[0];
+        let T = xa.[1];
+        let k = 0.12 * Math.Exp(12581.0 * (T - 298.0) / (298.0 * T));
+        let fx = 120.0 * x - 75.0 * k * (1.0 - x);
+        let fT = -x * (873.0 - T) + 11.0 * (T - 300.0);
+        [|fx; fT|]
 
     [<Test>]
     let ``Bisection should find both roots of (x - 3) * (x - 4)``() =
@@ -35,9 +42,19 @@ module FindRootsTests =
         (f, df) ||> FindRoots.newtonRaphsonRobust 100 20 1e-14 -5.0 3.5 |> should equal (Some 3.0)
         (f, df) ||> FindRoots.newtonRaphsonRobust 100 20 1e-14 3.2 5.0 |> should equal (Some 4.0)
 
+    [<Test>]
+    let ``Bryoden should find both roots of (x - 3) * (x - 4) and Twoeq2``() =
+        f |> (fun g (x:float[]) -> [|g x.[0]|]) |> FindRoots.broyden 100 1e-14 [|1.0;|] |> should equal (Some [|3.0|])
+        f |> (fun g (x:float[]) -> [|g x.[0]|]) |> FindRoots.broyden 100 1e-14 [|9.0;|] |> should equal (Some [|4.0|])
+        g |> FindRoots.broyden 100 1e-6 [|1.0; 400.0;|] |> (fun x ->
+            match x with
+            | Some x -> should (equalWithin 1e-1) [|0.9638680512795; 346.16369814640|]
+            | None ->   failwith "The element in array is not equal.") |> ignore
+
     [<Test>]
     let ``Simple method should find both roots of (x - 3) * (x - 4)``() =
         f |> FindRoots.ofFunction -5.0 3.5 |> Option.get |> should (equalWithin 1e-8) 3.0
         f |> FindRoots.ofFunction 3.2 5.0 |> Option.get |> should (equalWithin 1e-8) 4.0
         (f, df) ||> FindRoots.ofFunctionDerivative -5.0 3.5 |> Option.get |> should (equalWithin 1e-8) 3.0
         (f, df) ||> FindRoots.ofFunctionDerivative 3.2 5.0 |> Option.get |> should (equalWithin 1e-8) 4.0
+