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/// ------------------------------------------------------
/// RandomOps - (Pseudo) Random Number Generator For C#
/// Copyright (C) 2003-2010 Magnus Erik Hvass Pedersen.
/// Please see the file license.txt for license details.
/// RandomOps on the internet: http://www.Hvass-Labs.org/
/// ------------------------------------------------------
using System;
using System.Diagnostics;
namespace RandomOps
{
/// <remarks>
/// Implements RNG for a hypersphere. The methods are taken from:
/// [1] Marsaglia, G. "Choosing a Point from the Surface of a Sphere."
/// Ann. Math. Stat. 43, 645-646, 1972.
/// [2] Muller, M. E. "A Note on a Method for Generating Points Uniformly
/// on n-Dimensional Spheres."
/// Comm. Assoc. Comput. Mach. 2, 19-20, Apr. 1959.
/// </remarks>
public abstract partial class Random
{
/// <summary>
/// Generate a uniform random point on the unit-radius 3-dimensional sphere.
/// Thread-safe if Disk() is thread-safe.
/// </summary>
public virtual double[] Sphere3()
{
double[] x = new double[3];
Sphere3(ref x);
return x;
}
/// <summary>
/// Generate a uniform random point on the unit-radius 3-dimensional sphere.
/// Thread-safe if Disk() is thread-safe.
/// </summary>
/// <param name="x">Array to hold the random point.</param>
public virtual void Sphere3(ref double[] x)
{
double v1, v2, s;
// Pick two uniform numbers in the unit-radius 2-dim ball.
Disk(out v1, out v2, out s);
double a = Math.Sqrt(1 - s);
x[0] = 2 * v1 * a;
x[1] = 2 * v2 * a;
x[2] = 1 - 2 * s;
}
/// <summary>
/// Generate a uniform random point on the unit-radius 4-dimensional sphere.
/// Thread-safe if Disk() is thread-safe.
/// </summary>
public virtual double[] Sphere4()
{
double[] x = new double[4];
Sphere4(ref x);
return x;
}
/// <summary>
/// Generate a uniform random point on the unit-radius 4-dimensional sphere.
/// Thread-safe if Disk() is thread-safe.
/// </summary>
/// <param name="x">Array to hold the random point.</param>
public virtual void Sphere4(ref double[] x)
{
double v1, v2, v3, v4, s1, s2;
// Pick uniform numbers in the unit-radius 2-dim ball.
Disk(out v1, out v2, out s1);
Disk(out v3, out v4, out s2);
double a = Math.Sqrt((1 - s1) / s2);
x[0] = v1;
x[1] = v2;
x[2] = v3 * a;
x[3] = v4 * a;
}
/// <summary>
/// Generate a uniform random point on the n-dimensional hypersphere.
/// Thread-safe if Gauss() is thread-safe.
/// </summary>
/// <param name="n">Dimensionality of hypersphere.</param>
/// <param name="r">Radius of hypersphere.</param>
public virtual double[] Sphere(int n, double r)
{
Debug.Assert(n > 0);
double[] x = new double[n];
Sphere(ref x, r);
return x;
}
/// <summary>
/// Generate a uniform random point on the n-dimensional hypersphere.
/// Thread-safe if Gauss() is thread-safe, and each thread supplies
/// its own array x.
/// </summary>
/// <param name="x">Array to hold the random point.</param>
/// <param name="r">Radius of hypersphere.</param>
public virtual void Sphere(ref double[] x, double r)
{
Debug.Assert(x != null);
int n = x.Length;
Debug.Assert(n > 0);
double sum = 0;
int i;
for (i = 0; i < n; i++)
{
// Draw a gaussian (aka. normal) random number.
double a = Gauss();
// Store the element.
x[i] = a;
// Accumulate sum of squared elements.
sum += a * a;
}
// Adjust elements to get a certain radius.
double rInv = r / Math.Sqrt(sum);
for (i = 0; i < n; i++)
{
x[i] *= rInv;
}
}
}
}
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