// <copyright file="Categorical.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2014 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using IStation.Numerics.Random;
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using IStation.Numerics.Statistics;
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using IStation.Numerics.Threading;
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namespace IStation.Numerics.Distributions
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{
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/// <summary>
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/// Discrete Univariate Categorical distribution.
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/// For details about this distribution, see
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/// <a href="http://en.wikipedia.org/wiki/Categorical_distribution">Wikipedia - Categorical distribution</a>. This
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/// distribution is sometimes called the Discrete distribution.
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/// </summary>
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/// <remarks>
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/// The distribution is parameterized by a vector of ratios: in other words, the parameter
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/// does not have to be normalized and sum to 1. The reason is that some vectors can't be exactly normalized
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/// to sum to 1 in floating point representation.
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/// </remarks>
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/// <remarks>
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/// Support: 0..k where k = length(probability mass array)-1
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/// </remarks>
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public class Categorical : IDiscreteDistribution
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{
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System.Random _random;
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readonly double[] _pmfNormalized;
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readonly double[] _cdfUnnormalized;
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/// <summary>
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/// Initializes a new instance of the Categorical class.
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/// </summary>
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/// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
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/// as this is often impossible using floating point arithmetic.</param>
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/// <exception cref="ArgumentException">If any of the probabilities are negative or do not sum to one.</exception>
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public Categorical(double[] probabilityMass)
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: this(probabilityMass, SystemRandomSource.Default)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Categorical class.
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/// </summary>
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/// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
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/// as this is often impossible using floating point arithmetic.</param>
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/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
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/// <exception cref="ArgumentException">If any of the probabilities are negative or do not sum to one.</exception>
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public Categorical(double[] probabilityMass, System.Random randomSource)
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{
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if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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_random = randomSource ?? SystemRandomSource.Default;
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// Extract unnormalized cumulative distribution
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_cdfUnnormalized = new double[probabilityMass.Length];
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_cdfUnnormalized[0] = probabilityMass[0];
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for (int i = 1; i < probabilityMass.Length; i++)
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{
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_cdfUnnormalized[i] = _cdfUnnormalized[i - 1] + probabilityMass[i];
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}
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// Extract normalized probability mass
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var sum = _cdfUnnormalized[_cdfUnnormalized.Length - 1];
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_pmfNormalized = new double[probabilityMass.Length];
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for (int i = 0; i < probabilityMass.Length; i++)
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{
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_pmfNormalized[i] = probabilityMass[i]/sum;
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}
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}
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/// <summary>
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/// Initializes a new instance of the Categorical class from a <paramref name="histogram"/>. The distribution
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/// will not be automatically updated when the histogram changes. The categorical distribution will have
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/// one value for each bucket and a probability for that value proportional to the bucket count.
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/// </summary>
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/// <param name="histogram">The histogram from which to create the categorical variable.</param>
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public Categorical(Histogram histogram)
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{
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if (histogram == null)
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{
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throw new ArgumentNullException(nameof(histogram));
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}
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// The probability distribution vector.
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var p = new double[histogram.BucketCount];
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// Fill in the distribution vector.
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for (var i = 0; i < histogram.BucketCount; i++)
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{
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p[i] = histogram[i].Count;
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}
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_random = SystemRandomSource.Default;
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if (Control.CheckDistributionParameters && !IsValidProbabilityMass(p))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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// Extract unnormalized cumulative distribution
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_cdfUnnormalized = new double[p.Length];
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_cdfUnnormalized[0] = p[0];
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for (int i1 = 1; i1 < p.Length; i1++)
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{
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_cdfUnnormalized[i1] = _cdfUnnormalized[i1 - 1] + p[i1];
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}
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// Extract normalized probability mass
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var sum = _cdfUnnormalized[_cdfUnnormalized.Length - 1];
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_pmfNormalized = new double[p.Length];
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for (int i2 = 0; i2 < p.Length; i2++)
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{
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_pmfNormalized[i2] = p[i2]/sum;
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}
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}
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/// <summary>
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/// A string representation of the distribution.
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/// </summary>
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/// <returns>a string representation of the distribution.</returns>
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public override string ToString()
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{
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return $"Categorical(Dimension = {_pmfNormalized.Length})";
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}
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/// <summary>
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/// Checks whether the parameters of the distribution are valid.
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/// </summary>
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/// <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>
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/// <returns>If any of the probabilities are negative returns <c>false</c>, or if the sum of parameters is 0.0; otherwise <c>true</c></returns>
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public static bool IsValidProbabilityMass(double[] p)
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{
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var sum = 0.0;
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for (int i = 0; i < p.Length; i++)
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{
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double t = p[i];
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if (t < 0.0 || double.IsNaN(t))
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{
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return false;
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}
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sum += t;
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}
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return sum > 0.0;
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}
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/// <summary>
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/// Checks whether the parameters of the distribution are valid.
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/// </summary>
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/// <param name="cdf">An array of nonnegative ratios: this array does not need to be normalized as this is often impossible using floating point arithmetic.</param>
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/// <returns>If any of the probabilities are negative returns <c>false</c>, or if the sum of parameters is 0.0; otherwise <c>true</c></returns>
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public static bool IsValidCumulativeDistribution(double[] cdf)
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{
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var last = 0.0;
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for (int i = 0; i < cdf.Length; i++)
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{
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double t = cdf[i];
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if (t < 0.0 || double.IsNaN(t) || t < last)
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{
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return false;
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}
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last = t;
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}
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return last > 0.0;
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}
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/// <summary>
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/// Gets the probability mass vector (non-negative ratios) of the multinomial.
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/// </summary>
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/// <remarks>Sometimes the normalized probability vector cannot be represented exactly in a floating point representation.</remarks>
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public double[] P => (double[])_pmfNormalized.Clone();
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/// <summary>
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/// Gets or sets the random number generator which is used to draw random samples.
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/// </summary>
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public System.Random RandomSource
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{
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get => _random;
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set => _random = value ?? SystemRandomSource.Default;
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}
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/// <summary>
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/// Gets the mean of the distribution.
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/// </summary>
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public double Mean
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{
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get
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{
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// Mean = E[X] = Sum(x * p(x), x=0..N-1)
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// where f(x) is the probability mass function, and N is the number of categories.
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var sum = 0.0;
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for (int i = 0; i < _pmfNormalized.Length; i++)
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{
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sum += i*_pmfNormalized[i];
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}
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return sum;
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}
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}
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/// <summary>
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/// Gets the standard deviation of the distribution.
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/// </summary>
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public double StdDev => Math.Sqrt(Variance);
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/// <summary>
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/// Gets the variance of the distribution.
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/// </summary>
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public double Variance
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{
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get
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{
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// Variance = E[(X-E[X])^2] = E[X^2] - (E[X])^2 = Sum(p(x) * (x - E[X])^2), x=0..N-1)
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var m = Mean;
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var sum = 0.0;
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for (int i = 0; i < _pmfNormalized.Length; i++)
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{
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var r = i - m;
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sum += r*r*_pmfNormalized[i];
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}
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return sum;
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}
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}
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/// <summary>
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/// Gets the entropy of the distribution.
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/// </summary>
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public double Entropy
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{
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get { return -_pmfNormalized.Sum(p => p*Math.Log(p)); }
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}
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/// <summary>
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/// Gets the skewness of the distribution.
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/// </summary>
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/// <remarks>Throws a <see cref="NotSupportedException"/>.</remarks>
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public double Skewness => throw new NotSupportedException();
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/// <summary>
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/// Gets the smallest element in the domain of the distributions which can be represented by an integer.
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/// </summary>
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public int Minimum => 0;
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/// <summary>
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/// Gets the largest element in the domain of the distributions which can be represented by an integer.
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/// </summary>
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public int Maximum => _pmfNormalized.Length - 1;
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/// <summary>
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/// Gets he mode of the distribution.
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/// </summary>
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/// <remarks>Throws a <see cref="NotSupportedException"/>.</remarks>
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public int Mode => throw new NotSupportedException();
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/// <summary>
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/// Gets the median of the distribution.
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/// </summary>
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public double Median => InverseCumulativeDistribution(0.5);
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/// <summary>
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/// Computes the probability mass (PMF) at k, i.e. P(X = k).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
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/// <returns>the probability mass at location <paramref name="k"/>.</returns>
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public double Probability(int k)
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{
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if (k < 0)
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{
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return 0.0;
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}
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if (k >= _pmfNormalized.Length)
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{
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return 0.0;
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}
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return _pmfNormalized[k];
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}
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/// <summary>
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/// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
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/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
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public double ProbabilityLn(int k)
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{
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if (k < 0)
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{
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return 0.0;
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}
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if (k >= _pmfNormalized.Length)
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{
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return 0.0;
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}
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return Math.Log(_pmfNormalized[k]);
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}
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/// <summary>
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/// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
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/// </summary>
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/// <param name="x">The location at which to compute the cumulative distribution function.</param>
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/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
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public double CumulativeDistribution(double x)
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{
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if (x < 0.0)
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{
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return 0.0;
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}
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if (x >= _cdfUnnormalized.Length)
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{
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return 1.0;
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}
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return _cdfUnnormalized[(int)Math.Floor(x)]/_cdfUnnormalized[_cdfUnnormalized.Length - 1];
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}
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/// <summary>
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/// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
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/// at the given probability.
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/// </summary>
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/// <param name="probability">A real number between 0 and 1.</param>
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/// <returns>An integer between 0 and the size of the categorical (exclusive), that corresponds to the inverse CDF for the given probability.</returns>
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public int InverseCumulativeDistribution(double probability)
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{
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if (probability < 0.0 || probability > 1.0 || double.IsNaN(probability))
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{
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throw new ArgumentOutOfRangeException(nameof(probability));
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}
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var denormalizedProbability = probability*_cdfUnnormalized[_cdfUnnormalized.Length - 1];
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int idx = Array.BinarySearch(_cdfUnnormalized, denormalizedProbability);
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if (idx < 0)
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{
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idx = ~idx;
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}
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return idx;
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}
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/// <summary>
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/// Computes the probability mass (PMF) at k, i.e. P(X = k).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
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/// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
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/// as this is often impossible using floating point arithmetic.</param>
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/// <returns>the probability mass at location <paramref name="k"/>.</returns>
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public static double PMF(double[] probabilityMass, int k)
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{
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if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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if (k < 0)
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{
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return 0.0;
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}
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if (k >= probabilityMass.Length)
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{
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return 0.0;
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}
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return probabilityMass[k]/probabilityMass.Sum();
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}
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/// <summary>
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/// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
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/// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
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/// as this is often impossible using floating point arithmetic.</param>
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/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
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public static double PMFLn(double[] probabilityMass, int k)
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{
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return Math.Log(PMF(probabilityMass, k));
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}
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/// <summary>
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/// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
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/// </summary>
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/// <param name="x">The location at which to compute the cumulative distribution function.</param>
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/// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
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/// as this is often impossible using floating point arithmetic.</param>
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/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
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/// <seealso cref="CumulativeDistribution"/>
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public static double CDF(double[] probabilityMass, double x)
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{
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if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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if (x < 0.0)
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{
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return 0.0;
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}
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if (x >= probabilityMass.Length)
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{
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return 1.0;
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}
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var cdfUnnormalized = ProbabilityMassToCumulativeDistribution(probabilityMass);
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return cdfUnnormalized[(int)Math.Floor(x)]/cdfUnnormalized[cdfUnnormalized.Length - 1];
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}
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/// <summary>
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/// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
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/// at the given probability.
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/// </summary>
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/// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
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/// as this is often impossible using floating point arithmetic.</param>
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/// <param name="probability">A real number between 0 and 1.</param>
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/// <returns>An integer between 0 and the size of the categorical (exclusive), that corresponds to the inverse CDF for the given probability.</returns>
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public static int InvCDF(double[] probabilityMass, double probability)
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{
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if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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if (probability < 0.0 || probability > 1.0 || double.IsNaN(probability))
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{
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throw new ArgumentOutOfRangeException(nameof(probability));
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}
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var cdfUnnormalized = ProbabilityMassToCumulativeDistribution(probabilityMass);
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var denormalizedProbability = probability*cdfUnnormalized[cdfUnnormalized.Length - 1];
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int idx = Array.BinarySearch(cdfUnnormalized, denormalizedProbability);
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if (idx < 0)
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{
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idx = ~idx;
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}
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return idx;
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}
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/// <summary>
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/// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
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/// at the given probability.
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/// </summary>
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/// <param name="cdfUnnormalized">An array corresponding to a CDF for a categorical distribution. Not assumed to be normalized.</param>
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/// <param name="probability">A real number between 0 and 1.</param>
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/// <returns>An integer between 0 and the size of the categorical (exclusive), that corresponds to the inverse CDF for the given probability.</returns>
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public static int InvCDFWithCumulativeDistribution(double[] cdfUnnormalized, double probability)
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{
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if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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if (probability < 0.0 || probability > 1.0 || double.IsNaN(probability))
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{
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throw new ArgumentOutOfRangeException(nameof(probability));
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}
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var denormalizedProbability = probability*cdfUnnormalized[cdfUnnormalized.Length - 1];
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int idx = Array.BinarySearch(cdfUnnormalized, denormalizedProbability);
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if (idx < 0)
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{
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idx = ~idx;
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}
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return idx;
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}
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/// <summary>
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/// Computes the cumulative distribution function. This method performs no parameter checking.
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/// If the probability mass was normalized, the resulting cumulative distribution is normalized as well (up to numerical errors).
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/// </summary>
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/// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
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/// as this is often impossible using floating point arithmetic.</param>
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/// <returns>An array representing the unnormalized cumulative distribution function.</returns>
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internal static double[] ProbabilityMassToCumulativeDistribution(double[] probabilityMass)
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{
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var cdfUnnormalized = new double[probabilityMass.Length];
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cdfUnnormalized[0] = probabilityMass[0];
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for (int i = 1; i < probabilityMass.Length; i++)
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{
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cdfUnnormalized[i] = cdfUnnormalized[i - 1] + probabilityMass[i];
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}
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return cdfUnnormalized;
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}
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/// <summary>
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/// Returns one trials from the categorical distribution.
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/// </summary>
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/// <param name="rnd">The random number generator to use.</param>
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/// <param name="cdfUnnormalized">The (unnormalized) cumulative distribution of the probability distribution.</param>
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/// <returns>One sample from the categorical distribution implied by <paramref name="cdfUnnormalized"/>.</returns>
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internal static int SampleUnchecked(System.Random rnd, double[] cdfUnnormalized)
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{
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// TODO : use binary search to speed up this procedure.
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double u = rnd.NextDouble()*cdfUnnormalized[cdfUnnormalized.Length - 1];
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var idx = 0;
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if (u == 0.0d)
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{
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// skip zero-probability categories
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while (0.0d == cdfUnnormalized[idx])
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{
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idx++;
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}
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}
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while (u > cdfUnnormalized[idx])
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{
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idx++;
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}
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return idx;
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}
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static void SamplesUnchecked(System.Random rnd, int[] values, double[] cdfUnnormalized)
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{
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// TODO : use binary search to speed up this procedure.
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double[] uniform = rnd.NextDoubles(values.Length);
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double w = cdfUnnormalized[cdfUnnormalized.Length - 1];
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CommonParallel.For(0, values.Length, 4096, (a, b) =>
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{
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for (int i = a; i < b; i++)
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{
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var u = uniform[i]*w;
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var idx = 0;
|
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if (u == 0.0d)
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{
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// skip zero-probability categories
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while (0.0d == cdfUnnormalized[idx])
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{
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idx++;
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}
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}
|
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while (u > cdfUnnormalized[idx])
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{
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idx++;
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}
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values[i] = idx;
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}
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});
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}
|
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static IEnumerable<int> SamplesUnchecked(System.Random rnd, double[] cdfUnnormalized)
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{
|
while (true)
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{
|
yield return SampleUnchecked(rnd, cdfUnnormalized);
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}
|
}
|
|
/// <summary>
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/// Samples a Binomially distributed random variable.
|
/// </summary>
|
/// <returns>The number of successful trials.</returns>
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public int Sample()
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{
|
return SampleUnchecked(_random, _cdfUnnormalized);
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}
|
|
/// <summary>
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/// Fills an array with samples generated from the distribution.
|
/// </summary>
|
public void Samples(int[] values)
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{
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SamplesUnchecked(_random, values, _cdfUnnormalized);
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}
|
|
/// <summary>
|
/// Samples an array of Bernoulli distributed random variables.
|
/// </summary>
|
/// <returns>a sequence of successful trial counts.</returns>
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public IEnumerable<int> Samples()
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{
|
return SamplesUnchecked(_random, _cdfUnnormalized);
|
}
|
|
/// <summary>
|
/// Samples one categorical distributed random variable; also known as the Discrete distribution.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="probabilityMass">An array of nonnegative ratios. Not assumed to be normalized.</param>
|
/// <returns>One random integer between 0 and the size of the categorical (exclusive).</returns>
|
public static int Sample(System.Random rnd, double[] probabilityMass)
|
{
|
if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
var cdf = ProbabilityMassToCumulativeDistribution(probabilityMass);
|
return SampleUnchecked(rnd, cdf);
|
}
|
|
/// <summary>
|
/// Samples a categorically distributed random variable.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="probabilityMass">An array of nonnegative ratios. Not assumed to be normalized.</param>
|
/// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
|
public static IEnumerable<int> Samples(System.Random rnd, double[] probabilityMass)
|
{
|
if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
var cdf = ProbabilityMassToCumulativeDistribution(probabilityMass);
|
return SamplesUnchecked(rnd, cdf);
|
}
|
|
/// <summary>
|
/// Fills an array with samples generated from the distribution.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="values">The array to fill with the samples.</param>
|
/// <param name="probabilityMass">An array of nonnegative ratios. Not assumed to be normalized.</param>
|
/// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
|
public static void Samples(System.Random rnd, int[] values, double[] probabilityMass)
|
{
|
if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
var cdf = ProbabilityMassToCumulativeDistribution(probabilityMass);
|
SamplesUnchecked(rnd, values, cdf);
|
}
|
|
/// <summary>
|
/// Samples one categorical distributed random variable; also known as the Discrete distribution.
|
/// </summary>
|
/// <param name="probabilityMass">An array of nonnegative ratios. Not assumed to be normalized.</param>
|
/// <returns>One random integer between 0 and the size of the categorical (exclusive).</returns>
|
public static int Sample(double[] probabilityMass)
|
{
|
if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
var cdf = ProbabilityMassToCumulativeDistribution(probabilityMass);
|
return SampleUnchecked(SystemRandomSource.Default, cdf);
|
}
|
|
/// <summary>
|
/// Samples a categorically distributed random variable.
|
/// </summary>
|
/// <param name="probabilityMass">An array of nonnegative ratios. Not assumed to be normalized.</param>
|
/// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
|
public static IEnumerable<int> Samples(double[] probabilityMass)
|
{
|
if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
var cdf = ProbabilityMassToCumulativeDistribution(probabilityMass);
|
return SamplesUnchecked(SystemRandomSource.Default, cdf);
|
}
|
|
/// <summary>
|
/// Fills an array with samples generated from the distribution.
|
/// </summary>
|
/// <param name="values">The array to fill with the samples.</param>
|
/// <param name="probabilityMass">An array of nonnegative ratios. Not assumed to be normalized.</param>
|
/// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
|
public static void Samples(int[] values, double[] probabilityMass)
|
{
|
if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
var cdf = ProbabilityMassToCumulativeDistribution(probabilityMass);
|
SamplesUnchecked(SystemRandomSource.Default, values, cdf);
|
}
|
|
/// <summary>
|
/// Samples one categorical distributed random variable; also known as the Discrete distribution.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="cdfUnnormalized">An array of the cumulative distribution. Not assumed to be normalized.</param>
|
/// <returns>One random integer between 0 and the size of the categorical (exclusive).</returns>
|
public static int SampleWithCumulativeDistribution(System.Random rnd, double[] cdfUnnormalized)
|
{
|
if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SampleUnchecked(rnd, cdfUnnormalized);
|
}
|
|
/// <summary>
|
/// Samples a categorically distributed random variable.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="cdfUnnormalized">An array of the cumulative distribution. Not assumed to be normalized.</param>
|
/// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
|
public static IEnumerable<int> SamplesWithCumulativeDistribution(System.Random rnd, double[] cdfUnnormalized)
|
{
|
if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SamplesUnchecked(rnd, cdfUnnormalized);
|
}
|
|
/// <summary>
|
/// Fills an array with samples generated from the distribution.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="values">The array to fill with the samples.</param>
|
/// <param name="cdfUnnormalized">An array of the cumulative distribution. Not assumed to be normalized.</param>
|
/// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
|
public static void SamplesWithCumulativeDistribution(System.Random rnd, int[] values, double[] cdfUnnormalized)
|
{
|
if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
SamplesUnchecked(rnd, values, cdfUnnormalized);
|
}
|
|
/// <summary>
|
/// Samples one categorical distributed random variable; also known as the Discrete distribution.
|
/// </summary>
|
/// <param name="cdfUnnormalized">An array of the cumulative distribution. Not assumed to be normalized.</param>
|
/// <returns>One random integer between 0 and the size of the categorical (exclusive).</returns>
|
public static int SampleWithCumulativeDistribution(double[] cdfUnnormalized)
|
{
|
if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SampleUnchecked(SystemRandomSource.Default, cdfUnnormalized);
|
}
|
|
/// <summary>
|
/// Samples a categorically distributed random variable.
|
/// </summary>
|
/// <param name="cdfUnnormalized">An array of the cumulative distribution. Not assumed to be normalized.</param>
|
/// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
|
public static IEnumerable<int> SamplesWithCumulativeDistribution(double[] cdfUnnormalized)
|
{
|
if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SamplesUnchecked(SystemRandomSource.Default, cdfUnnormalized);
|
}
|
|
/// <summary>
|
/// Fills an array with samples generated from the distribution.
|
/// </summary>
|
/// <param name="values">The array to fill with the samples.</param>
|
/// <param name="cdfUnnormalized">An array of the cumulative distribution. Not assumed to be normalized.</param>
|
/// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
|
public static void SamplesWithCumulativeDistribution(int[] values, double[] cdfUnnormalized)
|
{
|
if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
SamplesUnchecked(SystemRandomSource.Default, values, cdfUnnormalized);
|
}
|
}
|
}
|
