32 | PM> Install-Package FsRandom25 |
> fsi tools\build.fsx --debug39 |
\`\`(0, 1)\`\`, \`\`[0, 1)\`\`, \`\`(0, 1]\`\`, and \`\`[0, 1]\`\`.
79 | * **Random module** manipulates random numbers.
80 | * **Statistics module** provides a variety of statistical distributions such like `uniform`, `normal` and `gamma`.
81 | * **Seq module** provides functions for generating random number sequences.
82 | * **Array module** and **Array2D module** provide functions for array operations like `createRandom`, `sample`, `sampleWithReplacement`, and `shuffle`.
83 | * **List module** provides functions for generating random lists.
84 | * **String module** provides functions for generating random strings.
85 | * **Utility module** provides utility functions.
86 |
87 | ### Pseudo-Random Number Generators
88 |
89 | You can choose an algorithm of pseudo-random numbger generator:
90 |
91 | * **xorshift** implements [Xorshift](http://en.wikipedia.org/wiki/Xorshift) algorithm.
92 | * **systemrandom** leverages System.Random and its subclasses as a random number generators.
93 | This PRNG is not purely functional because the state of the PRNG is controled in the classes.
94 | * **mersenne** in MersenneTwister module implements 64-bit version of [Mersenne Twister](http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html) algorithm.
95 | * **sfmt** in SimdOrientedFastMersenneTwister module implements [SFMT](http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/index.html) algorithm.
96 | *)
97 |
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/docs/numerical-examples.fsx:
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1 | (*** hide ***)
2 | #I "../Build/lib/net45"
3 | #r "FsRandom.dll"
4 | open FsRandom
5 |
6 | let state = createState xorshift (123456789u, 362436069u, 521288629u, 88675123u)
7 |
8 | (**
9 |
10 | Numerical Examples
11 | ==================
12 |
13 | This page illustrates how FsRandom is applicable to scientific computations.
14 | For statistics, the Statistics module is useful:
15 | *)
16 |
17 | open FsRandom.Statistics
18 |
19 | (**
20 |
21 | Estimating pi, the ratio of a circle's circumference to its diameter
22 | --------------------------------------------------------------------
23 |
24 | Suppose there is a circle of radius 1 is inside a square with side length 2.
25 | The area of the circle is \\(\pi\\) and the area of the square is 4.
26 | If you put \\(N\\) random points on the square, roughly \\(\displaystyle\frac{\pi}{4}N\\) points are inside the circle.
27 | In other words, if you find \\(M\\) points out of \\(N\\) are inside the circle,
28 | \\(\displaystyle\frac{M}{N}\\) approximates \\(\displaystyle\frac{\pi}{4}\\).
29 |
30 |
32 | 
69 |
70 |
71 |
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/examples/ApproximateBayesianComputation.fsx:
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1 | #if INTERACTIVE
2 | #I "../Build"
3 | #r "FsRandom.dll"
4 | #endif
5 |
6 | open FsRandom
7 | open FsRandom.Statistics
8 |
9 | let seed = 123456789u, 362436069u, 521288629u, 88675123u
10 | let state = createState xorshift seed
11 |
12 | type HiddenSystem = A | B
13 | let switch = function A -> B | B -> A
14 | let observe correctly = function
15 | | A -> if correctly then 'A' else 'B'
16 | | B -> if correctly then 'B' else 'A'
17 | let model (theta, gamma, length) = random {
18 | let state = ref A
19 | let builder = System.Text.StringBuilder ()
20 | for index = 1 to length do
21 | let! switchState = Utility.flipCoin theta
22 | if switchState then state := switch !state
23 | let! correctly = Utility.flipCoin gamma
24 | builder.Append (observe correctly !state) |> ignore
25 | return builder.ToString ()
26 | }
27 |
28 | let observed = "AAAABAABBAAAAAABAAAA"
29 | let prior = uniform (0.0, 1.0) // try `beta (6.0, 13.0)` for better acceptance ratio
30 | let gamma = 0.8
31 |
32 | let w (data:string) =
33 | Seq.windowed 2 data
34 | |> Seq.filter (fun c -> c.[0] <> c.[1]) // switch
35 | |> Seq.length
36 | let rho simulated = abs (w observed - w simulated)
37 |
38 | /// Datail to output
39 | type SimulationDetail = {
40 | Theta : float
41 | SimulatedData : string
42 | SummaryStatistic : int
43 | Distance : int
44 | Accepted : bool
45 | }
46 | let simulate epsilon = random {
47 | let! theta = prior
48 | let! simulated = model (theta, gamma, String.length observed)
49 | let distance = rho simulated
50 | return {
51 | Theta = theta
52 | SimulatedData = simulated
53 | SummaryStatistic = w simulated
54 | Distance = distance
55 | Accepted = distance <= epsilon
56 | }
57 | }
58 |
59 | let n = 25
60 | let epsilon = 2
61 | printfn "epsilon = %d" epsilon
62 | printfn "index theta simulated data summary rho outcome"
63 | Seq.ofRandom (simulate epsilon) state
64 | |> Seq.take n
65 | |> Seq.iteri (fun index detail ->
66 | printfn "%5d %.3f %s %7d %3d %7s"
67 | <| index + 1
68 | <| detail.Theta
69 | <| detail.SimulatedData
70 | <| detail.SummaryStatistic
71 | <| detail.Distance
72 | <| if detail.Accepted then "accepted" else "rejected"
73 | )
74 |
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/examples/Benchmark.fsx:
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1 | #if INTERACTIVE
2 | #I "../Build"
3 | #r "FsRandom.dll"
4 | #endif
5 |
6 | open System
7 | open FsRandom
8 |
9 | type BenchmarkOption = {
10 | Iterate : int
11 | Size : int
12 | Round : int
13 | Trim : float
14 | }
15 | let option =
16 | #if INTERACTIVE
17 | // recursion iteration with fsharpi (Mac/Linux) is very slow.
18 | // Too large Iterate does not return so long.
19 | let defaultOption = { Iterate = 100000; Size = 100000; Round = 20; Trim = 0.2 }
20 | let args = fsi.CommandLineArgs
21 | #else
22 | let defaultOption = { Iterate = 5000000; Size = 100000; Round = 20; Trim = 0.2 }
23 | let args = Environment.GetCommandLineArgs ()
24 | #endif
25 | let rec loop acc = function
26 | | [] -> acc
27 | | "--iterate" :: n :: rest -> loop { acc with Iterate = int n } rest
28 | | "--size" :: n :: rest -> loop { acc with Size = int n } rest
29 | | "--round" :: r :: rest -> loop { acc with Round = int r } rest
30 | | "--trim" :: t :: rest -> loop { acc with Trim = float t } rest
31 | | s :: _ ->
32 | eprintfn "unknown option: %s" s
33 | let programName = System.IO.Path.GetFileName (args.[0])
34 | eprintfn "usage: %s [--iterate int] [--size int] [--round int] [--trim p]" programName
35 | exit 1
36 | let args = (List.ofArray args).Tail
37 | loop defaultOption args
38 |
39 | let time f x =
40 | let stopwatch = System.Diagnostics.Stopwatch ()
41 | stopwatch.Start ()
42 | f x |> ignore
43 | stopwatch.Stop ()
44 | stopwatch.Elapsed
45 | let trimmedMean p (s:seq