mathnet-numerics/src/Numerics/Distributions/Multivariate/Multinomial.cs

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namespace MathNet.Numerics.Distributions
{
    using System;
    using System.Collections.Generic;
    using Properties;


    /// <summary>
    /// Implements the multinomial distribution. For details about this distribution, see 
    /// <a href="http://en.wikipedia.org/wiki/Multinomial_distribution">Wikipedia - Multinomial distribution</a>.
    /// </summary>
    /// <remarks><para>The distribution is parameterized by a vector of ratios: in other words, the parameter
    /// does not have to be normalized and sum to 1. The reason is that some vectors can't be exactly normalized
    /// to sum to 1 in floating point representation.</para>
    /// <para>The distribution will use the <see cref="System.Random"/> by default. 
    /// Users can set the random number generator by using the <see cref="RandomSource"/> property.</para>
    /// <para>The statistics classes will check all the incoming parameters whether they are in the allowed
    /// range. This might involve heavy computation. Optionally, by setting Control.CheckDistributionParameters
    /// to false, all parameter checks can be turned off.</para></remarks>
    public class Multinomial
    {
        /// <summary>
        /// Stores the normalized multinomial probabilities.
        /// </summary>
        private double[] _p;

        /// <summary>
        /// The number of trials.
        /// </summary>
        private int _n;

        /// <summary>
        /// The distribution's random number generator.
        /// </summary>
        private Random _random;

        /// <summary>
        /// Initializes a new instance of the Multinomial class.
        /// </summary>
        /// <param name="p">An array of nonnegative ratios: this array does not need to be normalized 
        /// as this is often impossible using floating point arithmetic.</param>
        /// <param name="n">The number of trials.</param>
        /// <exception cref="ArgumentOutOfRangeException">If any of the probabilities are negative or do not sum to one.</exception>
        /// <exception cref="ArgumentOutOfRangeException">If <paramref name="n"/> is negative.</exception>
        public Multinomial(double[] p, int n)
        {
            SetParameters(p, n);
            RandomSource = new System.Random();
        }

        /* TODO
        /// <summary>
        /// Generate a multinomial distribution from histogram <paramref name="h"/>. The distribution will
        /// not be automatically updated when the histogram changes.
        /// </summary>
        public Multinomial(Histogram h)
        {
            // The probability distribution vector.
            _p = new double[h.BinCount];

            // Fill in the distribution vector.
            for (int i = 0; i < h.BinCount; i++)
            {
                _p[i] = h[i];
            }

            RandomNumberGenerator = new System.Random();
        }*/

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        public override string ToString()
        {
            return "Multinomial(Dimension = " + _p.Length + ", Number of Trails = " + _n + ")";
        }

        /// <summary>
        /// Checks whether the parameters of the distribution are valid. 
        /// </summary>
        /// <param name="p">An array of nonnegative ratios: this array does not need to be normalized 
        /// as this is often impossible using floating point arithmetic.</param>
        /// <param name="n">The number of trials.</param>
        /// <returns>If any of the probabilities are negative returns false, 
        /// if the sum of parameters is 0.0, or if the number of trials is negative; otherwise true</returns>
        private static bool IsValidParameterSet(double[] p, int n)
        {
            double sum = 0.0;
            for (int i = 0; i < p.Length; i++)
            {
                if (p[i] < 0.0 || Double.IsNaN(p[i]))
                {
                    return false;
                }
                else
                {
                    sum += p[i];
                }
            }

            if (sum == 0.0)
            {
                return false;
            }

            if (n < 0)
            {
                return false;
            }

            return true;
        }

        /// <summary>
        /// Sets the parameters of the distribution after checking their validity.
        /// </summary>
        /// <param name="p">An array of nonnegative ratios: this array does not need to be normalized 
        /// as this is often impossible using floating point arithmetic.</param>
        /// <param name="n">The number of trials.</param>
        /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
        private void SetParameters(double[] p, int n)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(p, n))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            _p = (double[])p.Clone();
            _n = n;
        }

        /// <summary>
        /// Gets or sets the proportion of ratios.
        /// </summary>
        public double[] P
        {
            get
            {
                return (double[]) _p.Clone();
            }

            set
            {
                SetParameters(value, _n);
            }
        }

        /// <summary>
        /// Gets or sets the number of trials.
        /// </summary>
        public int N
        {
            get
            {
                return _n;
            }

            set
            {
                SetParameters(_p, value);
            }
        }

        /// <summary>
        /// Gets or sets the random number generator which is used to draw random samples.
        /// </summary>
        public Random RandomSource
        {
            get
            {
                return _random;
            }

            set
            {
                if (value == null)
                {
                    throw new ArgumentNullException();
                }

                _random = value;
            }
        }

        /// <summary>
        /// Samples one multinomial distributed random variable.
        /// </summary>
        /// <returns>the counts for each of the different possible values.</returns>
        public int[] Sample()
        {
            return Sample(RandomSource, _p, _n);
        }

        /// <summary>
        /// Samples a sequence multinomially distributed random variables.
        /// </summary>
        /// <returns>a sequence of counts for each of the different possible values.</returns>
        public IEnumerable<int[]> Samples()
        {
            while (true)
            {
                yield return Sample(RandomSource, _p, _n);
            }
        }

        /// <summary>
        /// Samples one multinomial distributed random variable.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="p">An array of nonnegative ratios: this array does not need to be normalized 
        /// as this is often impossible using floating point arithmetic.</param>
        /// <param name="n">The number of trials.</param>
        /// <returns>the counts for each of the different possible values.</returns>
        public static int[] Sample(System.Random rnd, double[] p, int n)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(p, n))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            // The cumulative density of p.
            double[] cp = Categorical.UnnormalizedCDF(p);
            // The variable that stores the counts.
            int[] ret = new int[p.Length];

            for (int i = 0; i < n; i++)
            {
                ret[Categorical.DoSample(rnd, cp)]++;
            }

            return ret;
        }

        /// <summary>
        /// Samples a multinomially distributed random variable.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="p">An array of nonnegative ratios: this array does not need to be normalized 
        /// as this is often impossible using floating point arithmetic.</param>
        /// <param name="n">The number of variables needed.</param>
        /// <returns>a sequence of counts for each of the different possible values.</returns>
        public static IEnumerable<int[]> Samples(System.Random rnd, double[] p, int n)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(p, n))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            // The cumulative density of p.
            double[] cp = Categorical.UnnormalizedCDF(p);

            while (true)
            {
                // The variable that stores the counts.
                int[] ret = new int[p.Length];

                for (int i = 0; i < n; i++)
                {
                    ret[Categorical.DoSample(rnd, cp)]++;
                }

                yield return ret;
            }
        }
    }
}