Data commit

Task/Numerical-integration/F-Sharp/numerical-integration.fs

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+// integration methods
+let left f dx x = f x * dx
+let right f dx x = f (x + dx) * dx
+let mid f dx x = f (x + dx / 2.0) * dx
+let trapez f dx x = (f x + f (x + dx)) * dx / 2.0
+let simpson f dx x = (f x + 4.0 * f (x + dx / 2.0) + f (x + dx)) * dx / 6.0
+
+// common integration function
+let integrate a b f n method =
+    let dx = (b - a) / float n
+    [0..n-1] |> Seq.map (fun i -> a + float i * dx) |> Seq.sumBy (method f dx)
+
+// test cases
+let methods = [ left; right; mid; trapez; simpson ]
+let cases = [
+    (fun x -> x * x * x), 0.0, 1.0,    100
+    (fun x -> 1.0 / x),   1.0, 100.0,  1000
+    (fun x -> x),         0.0, 5000.0, 5000000
+    (fun x -> x),         0.0, 6000.0, 6000000
+]
+
+// execute and output
+Seq.allPairs cases methods
+|> Seq.map (fun ((f, a, b, n), method) -> integrate a b f n method)
+|> Seq.iter (printfn "%f")