Numerical integration: Difference between revisions

=={{header|F Sharp}}==

<lang fsharp>

// 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")

</lang>