Added additional outputs to the running covariance matrix, uncertainty analysis results. Minor improvements to numerical derivative hessian and step size calculation. Refactored the vegas class to use better variable names. Improved the MCMC diagnostics class.

Author: HadenSmith

4.8.1/Numerics/Data/Statistics/RunningCovarianceMatrix.cs

@@ -32,6 +32,8 @@
 using System;
 using System.Collections.Generic;
 using System.Linq;
+using System.Reflection;
+using System.Runtime.Remoting.Messaging;
 
 namespace Numerics.Data.Statistics
 {
@@ -74,6 +76,44 @@ public RunningCovarianceMatrix(int size)
         /// </summary>
         public Matrix Covariance { get; private set; }
 
+        /// <summary>
+        /// The sample covariance matrix corrected by the sample size with the degrees of freedom adjustment.
+        /// </summary>
+        public Matrix SampleCovariance => (1d / (N - 1)) * Covariance;
+
+        /// <summary>
+        /// The population covariance matrix corrected by the total sample size.
+        /// </summary>
+        public Matrix PopulationCovariance => (1d / N) * Covariance;
+
+        /// <summary>
+        /// The sample correlation matrix.
+        /// </summary>
+        public Matrix SampleCorrelation
+        { 
+            get
+            {
+                var D = Matrix.Diagonal(SampleCovariance);
+                D.Sqrt();
+                var invSqrtD = !D;
+                return (invSqrtD * SampleCovariance) * invSqrtD;
+            }       
+        }
+
+        /// <summary>
+        /// The population correlation matrix.
+        /// </summary>
+        public Matrix PopulationCorrelation
+        {
+            get
+            {
+                var D = Matrix.Diagonal(PopulationCovariance);
+                D.Sqrt();
+                var invSqrtD = !D;
+                return (invSqrtD * PopulationCovariance) * invSqrtD;
+            }
+        }
+
         /// <summary>
         /// Add a new vector to the running statistics. 
         /// </summary>

4.8.1/Numerics/Data/Time Series/Support/Series.cs

@@ -116,6 +116,9 @@ object IList.this[int index]
         /// <inheritdoc/>
         public virtual void Add(SeriesOrdinate<TIndex, TValue> item)
         {
+            if (item == null)
+                throw new ArgumentNullException(nameof(item));
+
             _seriesOrdinates.Add(item);
             if (SuppressCollectionChanged == false) { CollectionChanged?.Invoke(this, new NotifyCollectionChangedEventArgs(NotifyCollectionChangedAction.Add, item, _seriesOrdinates.Count - 1)); }
         }
@@ -132,6 +135,9 @@ public int Add(object item)
         /// <inheritdoc/>
         public virtual void Insert(int index, SeriesOrdinate<TIndex, TValue> item)
         {
+            if (item == null)
+                throw new ArgumentNullException(nameof(item));
+
             _seriesOrdinates.Insert(index, item);
             if (SuppressCollectionChanged == false) { CollectionChanged?.Invoke(this, new NotifyCollectionChangedEventArgs(NotifyCollectionChangedAction.Add, item, index)); }
         }

4.8.1/Numerics/Data/Time Series/Support/SeriesOrdinate.cs

@@ -116,10 +116,12 @@ public virtual TValue Value
         /// <returns>True of the two SeriesOrdinate objects are equal and false otherwise.</returns>
         public static bool operator ==(SeriesOrdinate<TIndex, TValue> left, SeriesOrdinate<TIndex, TValue> right)
         {
-            if (object.Equals(left, right) == false) { return false; }
-            if (!EqualityComparer<TIndex>.Default.Equals(left.Index, right.Index)) { return false; }
-            if (!EqualityComparer<TValue>.Default.Equals(left.Value, right.Value)) { return false; }
-            return true;
+            if (ReferenceEquals(left, null) && ReferenceEquals(right, null))
+                return true;
+            if (ReferenceEquals(left, null) || ReferenceEquals(right, null))
+                return false;
+            return EqualityComparer<TIndex>.Default.Equals(left.Index, right.Index) &&
+                   EqualityComparer<TValue>.Default.Equals(left.Value, right.Value);
         }
 
         /// <summary>