probability utilities

App.config

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Assets/Engine/Runtime/Engine.asmdef

@@ -9,7 +9,8 @@
     "allowUnsafeCode": false,
     "overrideReferences": true,
     "precompiledReferences": [
-        "Realm.dll"
+        "Realm.dll",
+        "MathNet.Numerics.dll"
     ],
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     "defineConstraints": [],

Assets/Engine/Runtime/Measurements/PuzzleStorage.cs

@@ -1,5 +1,4 @@
-using System;
+using EscapeRoomEngine.Engine.Runtime.Modules;
-using EscapeRoomEngine.Engine.Runtime.Modules;
 using Realms;
 using UnityEngine;
 using Logger = EscapeRoomEngine.Engine.Runtime.Utilities.Logger;

Assets/Engine/Runtime/Modules/PuzzleState.cs

@@ -1,5 +1,4 @@
 using System;
-using EscapeRoomEngine.Engine.Runtime.Measurements;
 using EscapeRoomEngine.Engine.Runtime.Utilities;
 using NaughtyAttributes;
 using UnityEngine;

Assets/Engine/Runtime/UI/GameControl.cs

@@ -1,5 +1,4 @@
-using System;
+using EscapeRoomEngine.Engine.Runtime.Measurements;
-using EscapeRoomEngine.Engine.Runtime.Measurements;
 using EscapeRoomEngine.Engine.Runtime.Utilities;
 using NaughtyAttributes;
 using UnityEngine;

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));
+        }
+    }
+}

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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;
 

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Assets/NuGet/LICENSE

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+MIT License
+
+Copyright (c) 2018 Patrick McCarthy
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

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Assets/Test Assets/ProbabilityTest.cs

@@ -0,0 +1,75 @@
+using EscapeRoomEngine.Engine.Runtime.Utilities;
+using JetBrains.Annotations;
+using MathNet.Numerics.Distributions;
+using NaughtyAttributes;
+using UnityEngine;
+
+namespace Test_Assets
+{
+    public class ProbabilityTest : MonoBehaviour
+    {
+        public NormalDistribution distribution = NormalDistribution.Standard;
+        public int steps = 24;
+        public int n = 1000000;
+        public double sample;
+
+        [Button]
+        [UsedImplicitly]
+        public void ShowDistribution()
+        {
+            var samples = Samples();
+
+            var step = 6f / steps;
+            for (var i = -3f; i < 3f; i += step)
+            {
+                var count = 0;
+                for (var j = 0; j < n; j++)
+                {
+                    var sample = samples[j];
+                    if (sample >= i && sample < i + step)
+                    {
+                        count++;
+                    }
+                }
+
+                var row = "";
+                for (var j = 0; j < 1000f*count/n; j++)
+                {
+                    row += "*";
+                }
+                Debug.Log(row);
+            }
+        }
+
+        [Button]
+        [UsedImplicitly]
+        public void CalculateMean()
+        {
+            Debug.Log(Probability.Mean(Samples()));
+        }
+
+        [Button]
+        [UsedImplicitly]
+        public void CalculateStandardDeviation()
+        {
+            Debug.Log(Probability.StandardDeviation(Samples()));
+        }
+
+        [Button]
+        [UsedImplicitly]
+        public void SamplePercentile()
+        {
+            Debug.Log(distribution.Cumulative(sample));
+        }
+
+        private double[] Samples()
+        {
+            var samples = new double[n];
+            for (var i = 0; i < n; i++)
+            {
+                samples[i] = distribution.Sample();
+            }
+            return samples;
+        }
+    }
+}

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+      enabled: 0
+      settings:
+        DefaultValueInitialized: true
+  - first:
+      Windows Store Apps: WindowsStoreApps
+    second:
+      enabled: 0
+      settings: {}
+  userData: 
+  assetBundleName: 
+  assetBundleVariant: