111 lines
3.6 KiB
C#
111 lines
3.6 KiB
C#
using System;
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using System.Linq;
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using MathNet.Numerics.Distributions;
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using UnityEngine;
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using Random = System.Random;
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namespace EscapeRoomEngine.Engine.Runtime.Utilities
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{
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/// <summary>
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/// The representation of a normal distribution with a certain mean μ and standard deviation σ.
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/// </summary>
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[Serializable]
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public struct NormalDistribution
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{
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/// <summary>
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/// The mean of this distribution.
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/// </summary>
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public float μ;
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/// <summary>
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/// The standard deviation of this distribution.
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/// </summary>
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public float σ;
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/// <summary>
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/// Generate a standard normal distribution.
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/// </summary>
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public static NormalDistribution Standard => new() { μ = 0, σ = 1 };
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public NormalDistribution(float[] samples) : this()
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{
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μ = Probability.Mean(samples);
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σ = samples.Length == 0 ? 1.0f : Probability.StandardDeviation(samples, μ);
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}
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/// <summary>
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/// Sample a random value from this distribution.
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/// </summary>
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public float Sample() => σ * Probability.Normal() + μ;
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/// <summary>
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/// Sample the CDF of this distribution.
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/// </summary>
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public float Cumulative(float x) => (float)new Normal(μ, σ).CumulativeDistribution(x);
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/// <summary>
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/// Sample the inverse CDF of this distribution.
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/// </summary>
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public float InverseCumulative(float x) => (float)new Normal(μ, σ).InverseCumulativeDistribution(x);
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}
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/// <summary>
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/// This class is used for probability calculations.
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/// </summary>
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public static class Probability
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{
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private static readonly Random _random = new();
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/// <summary>
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/// Sample a random variable from the standard normal distribution.
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/// For simplicity, the result is clamped between -3 and 3. This is accurate for 99.7% of all samples, by the three-σ rule.
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/// </summary>
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/// <remarks>The calculation of the random variable is done by a Box-Muller transform.</remarks>
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public static float Normal()
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{
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float u1, u2, square;
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// get two random points inside the unit circle
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do
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{
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u1 = 2 * (float)_random.NextDouble() - 1;
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u2 = 2 * (float)_random.NextDouble() - 1;
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square = u1 * u1 + u2 * u2;
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} while (square >= 1f);
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return u1 * Mathf.Sqrt(-2 * Mathf.Log(square) / square);
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}
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/// <summary>
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/// Calculate the mean of a list of samples.
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/// </summary>
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public static float Mean(float[] samples)
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{
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if (samples.Length == 0)
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{
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return 0;
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}
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return samples.Sum() / samples.Length;
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}
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/// <summary>
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/// Calculate the standard deviation of a list of samples.
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/// </summary>
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public static float StandardDeviation(float[] samples) => StandardDeviation(samples, Mean(samples));
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/// <summary>
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/// Calculate the standard deviation of a list of samples without recalculating the mean.
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/// </summary>
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public static float StandardDeviation(float[] samples, float mean)
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{
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var deviations = new float[samples.Length];
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for (var i = 0; i < samples.Length; i++)
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{
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var d = samples[i] - mean;
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deviations[i] = d * d;
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}
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return Mathf.Sqrt(Mean(deviations));
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}
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}
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} |