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// Learn more about F# at http://fsharp.org
open MathNet.Numerics.Distributions
[<EntryPoint>]
let main argv =
let yinit = 1.0 // initial population size
let r = 1.4 // maximum population growth rate
let k = 20.0 // carrying capacity
let thetasd = 0.1 // standard deviation for adding noise to the population
let t = int argv.[0] // number of years of growth to simulate
let seedType = argv.[1] // "fixed" or "random" for setting deterministic behavior
let funType = argv.[2] // "for", "recif", "recmatch", "unfold"
let reps = int argv.[3] // number of replications
let logmodFor t y r k thetasd seedType =
let random = System.Random()
let seed = if seedType = "fixed" then 2005 else random.Next()
let normalDist = Normal(0.0, thetasd, RandomSource = System.Random(seed))
let theta = Array.init (t - 1) (fun _ -> normalDist.Sample())
let ys: float array = Array.zeroCreate t
Array.set ys 0 y
for i in 1 .. (t - 1) do
Array.set ys i (ys.[i-1] * (r - r * (ys.[i-1] / k)) * exp(theta.[i-1]))
ys
let logmodRecIf t y r k thetasd seedType =
let random = System.Random()
let seed = if seedType = "fixed" then 2005 else random.Next()
let normalDist = Normal(0.0, thetasd, RandomSource = System.Random(seed))
let calc y = y * (r - r * (y / k)) * exp(normalDist.Sample())
let rec loop acc t =
if t = 1 then List.rev acc
else loop ((calc acc.Head) :: acc) (t - 1)
loop [y] t
let logmodRecMatch t y r k thetasd seedType =
let random = System.Random()
let seed = if seedType = "fixed" then 2005 else random.Next()
let normalDist = Normal(0.0, thetasd, RandomSource = System.Random(seed))
let calc y = y * (r - r * (y / k)) * exp(normalDist.Sample())
let rec loop acc t =
match t with
| 1 -> List.rev acc
| _ -> loop ((calc acc.Head) :: acc) (t - 1)
loop [y] t
let logmodUnfold t y r k thetasd seedType =
let random = System.Random()
let seed = if seedType = "fixed" then 2005 else random.Next()
let normalDist = Normal(0.0, thetasd, RandomSource = System.Random(seed))
let calc y =
let result = y * (r - r * (y / k)) * exp(normalDist.Sample())
Some (y, result)
Seq.unfold calc y |> Seq.take t |> List.ofSeq // need to change form of calc to use List.unfold b/c doesn't terminate as written
// printfn "for loop"
// logmodFor t yinit r k thetasd seedType |> printfn "%A"
// printfn "---"
// printfn "recursion (if)"
// logmodRecIf t yinit r k thetasd seedType |> printfn "%A"
// printfn "---"
// printfn "recursion (match)"
// logmodRecMatch t yinit r k thetasd seedType |> printfn "%A"
// printfn "---"
// printfn "unfold"
// logmodUnfold t yinit r k thetasd seedType |> printfn "%A"
let repeat n f =
let rec loop n acc =
match n with
| 0 -> acc
| _ -> loop (n - 1) (f() :: acc)
loop n []
if funType = "for" then
repeat reps (fun () -> logmodFor t yinit r k thetasd seedType) |> ignore
elif funType = "recif" then
repeat reps (fun () -> logmodRecIf t yinit r k thetasd seedType) |> ignore
elif funType = "recmatch" then
repeat reps (fun () -> logmodRecMatch t yinit r k thetasd seedType) |> ignore
elif funType = "unfold" then
repeat reps (fun () -> logmodUnfold t yinit r k thetasd seedType) |> ignore
else
invalidArg "funType" "must be one of for, recif, recmatch, unfold"
0 // return an integer exit code
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