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Calculate PI using Monte Carlo

Simple walkthrough that demonstrates how to estimate the value of PI using Monte Carlo simulation. A few holes need to be filled in and then you can run & parallelize the sample!

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open System

/// Calculates whether a point is within the unit circle
let insideCircle (x:float, y:float) = 
  // TASK #1: Implement the test! 
  false

/// Generates random X, Y values between 0 and 1
let randomPoints max = seq {
  let rnd = new Random()
  for i in 0 .. max do
    yield rnd.NextDouble(), rnd.NextDouble() }

/// Generate specified number of random points and
/// calculate PI using Monte Carlo simulation
let monteCarloPI size = 
  // TASK #2: Generate specified number of random
  // points and test how many are inside circle
  // (...)
  let inside = 0 
  // Estimate the value of PI
  float inside / float size * 4.0

// Test the Monte Carlo PI calculation
#time
monteCarloPI 1000000

// Run the calculation 10 times and calculate average
// Change to 'Array.Parallel.map' to parallelize!
[| for i in 0 .. 10 -> 1000000 |]
|> Array.map monteCarloPI
|> Array.average
namespace System
val insideCircle : x:float * y:float -> bool

Full name: Script.insideCircle


 Calculates whether a point is within the unit circle
val x : float
Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>
val y : float
val randomPoints : max:int -> seq<float * float>

Full name: Script.randomPoints


 Generates random X, Y values between 0 and 1
val max : int
Multiple items
val seq : sequence:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Core.Operators.seq

--------------------
type seq<'T> = Collections.Generic.IEnumerable<'T>

Full name: Microsoft.FSharp.Collections.seq<_>
val rnd : Random
Multiple items
type Random =
  new : unit -> Random + 1 overload
  member Next : unit -> int + 2 overloads
  member NextBytes : buffer:byte[] -> unit
  member NextDouble : unit -> float

Full name: System.Random

--------------------
Random() : unit
Random(Seed: int) : unit
val i : int
Random.NextDouble() : float
val monteCarloPI : size:int -> float

Full name: Script.monteCarloPI


 Generate specified number of random points and
 calculate PI using Monte Carlo simulation
val size : int
val inside : int
type Array =
  member Clone : unit -> obj
  member CopyTo : array:Array * index:int -> unit + 1 overload
  member GetEnumerator : unit -> IEnumerator
  member GetLength : dimension:int -> int
  member GetLongLength : dimension:int -> int64
  member GetLowerBound : dimension:int -> int
  member GetUpperBound : dimension:int -> int
  member GetValue : [<ParamArray>] indices:int[] -> obj + 7 overloads
  member Initialize : unit -> unit
  member IsFixedSize : bool
  ...

Full name: System.Array
val map : mapping:('T -> 'U) -> array:'T [] -> 'U []

Full name: Microsoft.FSharp.Collections.Array.map
val average : array:'T [] -> 'T (requires member ( + ) and member DivideByInt and member get_Zero)

Full name: Microsoft.FSharp.Collections.Array.average
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More information

Link:http://fssnip.net/cr
Posted:3 years ago
Author:Tomas Petricek
Tags: try f# , monte carlo , simulation , math , pi