Data Analysis Mathematics Linear Algebra Statistics
New Version 7.0!  QuickStart Samples

# Quasi-Random Sequences QuickStart Sample (Visual Basic)

Illustrates how to generate quasi-random sequences like FaurÃ© and Sobol sequences using classes in the Extreme.Statistics.Random namespace in Visual Basic.

```Imports System.Collections.Generic

Imports Extreme.Mathematics
Imports Extreme.Mathematics.Random

Namespace Extreme.Numerics.QuickStart.VB
' Illustrates the use of quasi-random sequences by computing
' a multi-dimensional integral.
Module QuasiRandomSequences

Sub Main()
' This QuickStart Sample demonstrates the use of
' quasi-random sequences by computing
' a multi-dimensional integral.

' We will use one million points.
Dim length As Integer = 1000000
' The number of dimensions:
Dim dimension As Integer = 5

' We will evaluate the function
'
'    Product(i = 1 -> # dimensions) |4 x(i) - 2|
'
' over the hypercube 0 <= x(i) <= 1. The value of this integral
' is exactly 1.

' Create the sequence
Dim sequence = QuasiRandom.HaltonSequence(dimension, length)

' Compute the integral by summing over all points
Console.WriteLine("# iter.  Estimate")
Dim sum As Double = 0.0
Dim i As Integer = 0
For Each point As Vector(Of Double) In sequence
If i Mod 100000 = 0 Then
Console.WriteLine("{0,6}  {1,8:F4}", i, sum / i)
End If

' Evaluate the integrand
Dim functionValue As Double = 1.0
For j As Integer = 0 To dimension - 1
functionValue *= Math.Abs(4.0 * point(j) - 2.0)
Next
sum += functionValue
i = i + 1
Next
Console.WriteLine("Final estimate: {0,8:F4}", sum / length)
Console.WriteLine("Exact value: 1.0000")

' Sobol sequences require more data And more initialization.
' Fortunately, different sequences of the same dimension
' can share much of the work And storage. The
' SobolSequenceGenerator class should be used in this case

Dim skip As Integer = 1000
Dim sobol As SobolSequenceGenerator = New SobolSequenceGenerator(dimension, length + skip)
' Sobol sequences are more flexible: they let you skip
' a number of points at the start of the sequence.
' The cost of skipping points Is O(1).
i = 0
sum = 0.0
For Each point As Vector(Of Double) In sobol.Generate(length, skip)
If i Mod 100000 = 0 Then
Console.WriteLine("{0,6}  {1,8:F4}", i, sum / i)
End If

' Evaluate the integrand
Dim functionValue As Double = 1.0
For j As Integer = 0 To dimension - 1
functionValue *= Math.Abs(4.0 * point(j) - 2.0)
Next
sum = sum + functionValue
i = i + 1
Next
' Print the final result.
Console.WriteLine("Final estimate: {0,8:F4}", sum / length)
Console.WriteLine("Exact value: 1.0000")

Console.Write("Press any key to exit.")