probability utilities

Assets/Engine/Runtime/Utilities/Probability.cs

@@ -0,0 +1,74 @@
+using System;
+using System.Linq;
+using MathNet.Numerics.Distributions;
+using Random = System.Random;
+
+namespace EscapeRoomEngine.Engine.Runtime.Utilities
+{
+    [Serializable]
+    public struct NormalDistribution
+    {
+        public double mean, σ;
+
+        public static NormalDistribution Standard => new NormalDistribution { mean = 0, σ = 1 };
+
+        public NormalDistribution(double[] samples) : this()
+        {
+            mean = Probability.Mean(samples);
+            σ = Probability.StandardDeviation(samples, mean);
+        }
+
+        public double Sample() => σ * Probability.Normal() + mean;
+
+        public double Cumulative(double x) => new Normal(mean, σ).CumulativeDistribution(x);
+    }
+    
+    public static class Probability
+    {
+        private static readonly Random _random = new();
+
+        /// <summary>
+        /// Sample a random variable from the standard normal distribution.
+        /// For simplicity, the result is clamped between -3 and 3. This is accurate for 99.7% of all samples, by the three-σ rule.
+        /// </summary>
+        /// <remarks>The calculation of the random variable is done by a Box-Muller transform.</remarks>
+        public static double Normal()
+        {
+            double u1, u2, square;
+            
+            // get two random points inside the unit circle
+            do
+            {
+                u1 = 2 * _random.NextDouble() - 1;
+                u2 = 2 * _random.NextDouble() - 1;
+                square = u1 * u1 + u2 * u2;
+            } while (square >= 1f);
+
+            return u1 * Math.Sqrt(-2 * Math.Log(square) / square);
+        }
+
+        public static double Mean(double[] samples)
+        {
+            if (samples.Length == 0)
+            {
+                return 0;
+            }
+            
+            return samples.Sum() / samples.Length;
+        }
+
+        public static double StandardDeviation(double[] samples) => StandardDeviation(samples, Mean(samples));
+        public static double StandardDeviation(double[] samples, double mean)
+        {
+            var deviations = new double[samples.Length];
+
+            for (var i = 0; i < samples.Length; i++)
+            {
+                var d = samples[i] - mean;
+                deviations[i] = d * d;
+            }
+
+            return Math.Sqrt(Mean(deviations));
+        }
+    }
+}

Assets/Engine/Runtime/Utilities/Probability.cs.meta

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+fileFormatVersion: 2
+guid: cb71ef4d16a642f1aca0a2446e985311
+timeCreated: 1671052645

Assets/Engine/Runtime/Utilities/Utilities.cs

@@ -1,6 +1,5 @@
 using System;
 using System.Collections.Generic;
-using System.Linq;
 using UnityEngine;
 using Random = UnityEngine.Random;