Poisson.cs


using System;
// using System.Collections.Generic;
// using System.Diagnostics;
// using System.Reflection;
// using System.Text;
// using System.Windows;
// using System.Windows.Media.Animation;
// using System.ComponentModel;
// using System.Globalization;

namespace Poisson {
    public static class Poisson {
        private static uint m_z = 1;
        private static uint m_w = 1;
        public static uint GetUint() {
            m_z = 36969 * (m_z & 65535) + (m_z >> 16);
            m_w = 18000 * (m_w & 65535) + (m_w >> 16);
            return (m_z << 16) + m_w;
        }

        public static double GetUniform() {
            // 0 <= u < 2^32
            uint u = GetUint();
            // The magic number below is 1/(2^32 + 2).
            // The result is strictly between 0 and 1.
            return (u + 1.0) * 2.328306435454494e-10;
        }
        public static int GetPoisson(double lambda) {
            return (lambda < 30.0) ? PoissonSmall(lambda) : PoissonLarge(lambda);
        }

        private static int PoissonSmall(double lambda) {
            // Algorithm due to Donald Knuth, 1969.
            double p = 1.0, L = Math.Exp(-lambda);
            int k = 0;
            do {
                k++;
                p *= GetUniform();
            }
            while (p > L);
            return k - 1;
        }

        private static int PoissonLarge(double lambda) {
            // "Rejection method PA" from "The Computer Generation of 
            // Poisson Random Variables" by A. C. Atkinson,
            // Journal of the Royal Statistical Society Series C 
            // (Applied Statistics) Vol. 28, No. 1. (1979)
            // The article is on pages 29-35. 
            // The algorithm given here is on page 32.

            double c = 0.767 - 3.36 / lambda;
            double beta = Math.PI / Math.Sqrt(3.0 * lambda);
            double alpha = beta * lambda;
            double k = Math.Log(c) - lambda - Math.Log(beta);

            for (; ; )
            {
                double u = GetUniform();
                double x = (alpha - Math.Log((1.0 - u) / u)) / beta;
                int n = (int)Math.Floor(x + 0.5);
                if (n < 0)
                    continue;
                double v = GetUniform();
                double y = alpha - beta * x;
                double temp = 1.0 + Math.Exp(y);
                double lhs = y + Math.Log(v / (temp * temp));
                double rhs = k + n * Math.Log(lambda) - LogFactorial(n);
                if (lhs <= rhs)
                    return n;
            }
        }
        static double LogFactorial(int n) {
            if (n < 0) {
                throw new ArgumentOutOfRangeException();
            } else if (n > 254) {
                double x = n + 1;
                return (x - 0.5) * Math.Log(x) - x + 0.5 * Math.Log(2 * Math.PI) + 1.0 / (12.0 * x);
            } else {
                double[] lf =
                {
            0.000000000000000,
            0.000000000000000,
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            1156.170837573242400,
        };
                return lf[n];
            }
        }
    }
}