Data Analysis Mathematics Linear Algebra Statistics
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# Quasi-Random Sequences QuickStart Sample (C#)

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

```using System;

namespace Extreme.Statistics.Quickstart.CSharp
{
using Extreme.Mathematics;
using Extreme.Mathematics.Random;

/// <summary>
/// Illustrates the use of quasi-random sequences by computing
/// a multi-dimensional integral.
/// </summary>
public class QuasiRandomSequences
{
/// <summary>
/// The main entry point for the application.
/// </summary>
static void Main(string[] args)
{
// This QuickStart Sample demonstrates the use of
// quasi-random sequences by computing
// a multi-dimensional integral.

// We will use one million points.
int length = 1000000;
// The number of dimensions:
int dimension = 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:
var sequence = QuasiRandom.HaltonSequence(dimension, length);

Console.WriteLine("# iter.  Estimate");
// Compute the integral by summing over all points:
double sum = 0.0;

int i = 0;
foreach (var point in sequence)
{
if (i % 100000 == 0)
Console.WriteLine("{0,6}  {1,8:F4}", i, sum / i);

// Evaluate the integrand:
double functionValue = 1.0;
for(int j = 0; j < dimension; j++)
functionValue *= Math.Abs(4.0*point[j]-2.0);
sum += functionValue;
i++;
}
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:

int skip = 1000;
var sobol = 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;
foreach (var point in sobol.Generate(length, skip))
{
if (i % 100000 == 0)
Console.WriteLine("{0,6}  {1,8:F4}", i, sum / i);

// Evaluate the integrand:
double functionValue = 1.0;
for (int j = 0; j < dimension; j++)
functionValue *= Math.Abs(4.0 * point[j] - 2.0);
sum += functionValue;
i++;
}
// 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.");