// <copyright file="Distance.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) 2009-2013 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 IStation.Numerics.LinearAlgebra;
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using IStation.Numerics.Providers.LinearAlgebra;
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using IStation.Numerics.Statistics;
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namespace IStation.Numerics
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{
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/// <summary>
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/// Metrics to measure the distance between two structures.
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/// </summary>
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public static class Distance
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{
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/// <summary>
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/// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
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/// </summary>
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public static double SAD<T>(Vector<T> a, Vector<T> b) where T : struct, IEquatable<T>, IFormattable
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{
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return (a - b).L1Norm();
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}
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/// <summary>
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/// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
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/// </summary>
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public static double SAD(double[] a, double[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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double sum = 0d;
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for (var i = 0; i < a.Length; i++)
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{
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sum += Math.Abs(a[i] - b[i]);
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}
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return sum;
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}
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/// <summary>
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/// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
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/// </summary>
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public static float SAD(float[] a, float[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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float sum = 0f;
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for (var i = 0; i < a.Length; i++)
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{
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sum += Math.Abs(a[i] - b[i]);
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}
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return sum;
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}
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/// <summary>
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/// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
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/// </summary>
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public static double MAE<T>(Vector<T> a, Vector<T> b) where T : struct, IEquatable<T>, IFormattable
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{
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return (a - b).L1Norm()/a.Count;
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}
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/// <summary>
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/// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
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/// </summary>
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public static double MAE(double[] a, double[] b)
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{
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return SAD(a, b)/a.Length;
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}
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/// <summary>
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/// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
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/// </summary>
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public static float MAE(float[] a, float[] b)
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{
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return SAD(a, b)/a.Length;
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}
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/// <summary>
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/// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
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/// </summary>
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public static double SSD<T>(Vector<T> a, Vector<T> b) where T : struct, IEquatable<T>, IFormattable
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{
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var norm = (a - b).L2Norm();
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return norm*norm;
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}
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/// <summary>
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/// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
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/// </summary>
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public static double SSD(double[] a, double[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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var diff = new double[a.Length];
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LinearAlgebraControl.Provider.SubtractArrays(a, b, diff);
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return LinearAlgebraControl.Provider.DotProduct(diff, diff);
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}
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/// <summary>
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/// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
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/// </summary>
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public static float SSD(float[] a, float[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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var diff = new float[a.Length];
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LinearAlgebraControl.Provider.SubtractArrays(a, b, diff);
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return LinearAlgebraControl.Provider.DotProduct(diff, diff);
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}
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/// <summary>
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/// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
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/// </summary>
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public static double MSE<T>(Vector<T> a, Vector<T> b) where T : struct, IEquatable<T>, IFormattable
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{
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var norm = (a - b).L2Norm();
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return norm*norm/a.Count;
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}
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/// <summary>
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/// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
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/// </summary>
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public static double MSE(double[] a, double[] b)
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{
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return SSD(a, b)/a.Length;
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}
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/// <summary>
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/// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
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/// </summary>
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public static float MSE(float[] a, float[] b)
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{
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return SSD(a, b)/a.Length;
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}
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/// <summary>
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/// Euclidean Distance, i.e. the L2-norm of the difference.
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/// </summary>
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public static double Euclidean<T>(Vector<T> a, Vector<T> b) where T : struct, IEquatable<T>, IFormattable
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{
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return (a - b).L2Norm();
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}
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/// <summary>
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/// Euclidean Distance, i.e. the L2-norm of the difference.
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/// </summary>
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public static double Euclidean(double[] a, double[] b)
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{
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return Math.Sqrt(SSD(a, b));
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}
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/// <summary>
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/// Euclidean Distance, i.e. the L2-norm of the difference.
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/// </summary>
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public static float Euclidean(float[] a, float[] b)
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{
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return (float) Math.Sqrt(SSD(a, b));
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}
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/// <summary>
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/// Manhattan Distance, i.e. the L1-norm of the difference.
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/// </summary>
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public static double Manhattan<T>(Vector<T> a, Vector<T> b) where T : struct, IEquatable<T>, IFormattable
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{
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return (a - b).L1Norm();
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}
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/// <summary>
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/// Manhattan Distance, i.e. the L1-norm of the difference.
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/// </summary>
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public static double Manhattan(double[] a, double[] b)
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{
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return SAD(a, b);
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}
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/// <summary>
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/// Manhattan Distance, i.e. the L1-norm of the difference.
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/// </summary>
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public static float Manhattan(float[] a, float[] b)
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{
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return SAD(a, b);
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}
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/// <summary>
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/// Chebyshev Distance, i.e. the Infinity-norm of the difference.
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/// </summary>
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public static double Chebyshev<T>(Vector<T> a, Vector<T> b) where T : struct, IEquatable<T>, IFormattable
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{
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return (a - b).InfinityNorm();
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}
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/// <summary>
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/// Chebyshev Distance, i.e. the Infinity-norm of the difference.
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/// </summary>
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public static double Chebyshev(double[] a, double[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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double max = Math.Abs(a[0] - b[0]);
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for (int i = 1; i < a.Length; i++)
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{
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var next = Math.Abs(a[i] - b[i]);
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if (next > max)
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{
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max = next;
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}
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}
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return max;
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}
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/// <summary>
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/// Chebyshev Distance, i.e. the Infinity-norm of the difference.
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/// </summary>
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public static float Chebyshev(float[] a, float[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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float max = Math.Abs(a[0] - b[0]);
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for (int i = 1; i < a.Length; i++)
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{
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var next = Math.Abs(a[i] - b[i]);
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if (next > max)
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{
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max = next;
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}
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}
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return max;
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}
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/// <summary>
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/// Minkowski Distance, i.e. the generalized p-norm of the difference.
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/// </summary>
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public static double Minkowski<T>(double p, Vector<T> a, Vector<T> b) where T : struct, IEquatable<T>, IFormattable
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{
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return (a - b).Norm(p);
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}
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/// <summary>
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/// Minkowski Distance, i.e. the generalized p-norm of the difference.
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/// </summary>
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public static double Minkowski(double p, double[] a, double[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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if (p < 0d)
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{
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throw new ArgumentOutOfRangeException(nameof(p));
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}
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if (p == 1d)
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{
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return Manhattan(a, b);
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}
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if (p == 2d)
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{
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return Euclidean(a, b);
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}
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if (double.IsPositiveInfinity(p))
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{
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return Chebyshev(a, b);
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}
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double sum = 0d;
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for (var i = 0; i < a.Length; i++)
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{
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sum += Math.Pow(Math.Abs(a[i] - b[i]), p);
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}
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return Math.Pow(sum, 1.0 / p);
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}
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/// <summary>
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/// Minkowski Distance, i.e. the generalized p-norm of the difference.
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/// </summary>
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public static float Minkowski(double p, float[] a, float[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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if (p < 0d)
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{
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throw new ArgumentOutOfRangeException(nameof(p));
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}
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if (p == 1d)
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{
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return Manhattan(a, b);
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}
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if (p == 2d)
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{
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return Euclidean(a, b);
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}
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if (double.IsPositiveInfinity(p))
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{
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return Chebyshev(a, b);
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}
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double sum = 0d;
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for (var i = 0; i < a.Length; i++)
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{
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sum += Math.Pow(Math.Abs(a[i] - b[i]), p);
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}
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return (float) Math.Pow(sum, 1.0/p);
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}
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/// <summary>
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/// Canberra Distance, a weighted version of the L1-norm of the difference.
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/// </summary>
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public static double Canberra(double[] a, double[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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double sum = 0d;
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for (var i = 0; i < a.Length; i++)
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{
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sum += Math.Abs(a[i] - b[i]) / (Math.Abs(a[i]) + Math.Abs(b[i]));
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}
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return sum;
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}
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/// <summary>
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/// Canberra Distance, a weighted version of the L1-norm of the difference.
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/// </summary>
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public static float Canberra(float[] a, float[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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float sum = 0f;
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for (var i = 0; i < a.Length; i++)
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{
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sum += Math.Abs(a[i] - b[i]) / (Math.Abs(a[i]) + Math.Abs(b[i]));
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}
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return sum;
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}
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/// <summary>
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/// Cosine Distance, representing the angular distance while ignoring the scale.
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/// </summary>
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public static double Cosine(double[] a, double[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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var ab = LinearAlgebraControl.Provider.DotProduct(a, b);
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var a2 = LinearAlgebraControl.Provider.DotProduct(a, a);
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var b2 = LinearAlgebraControl.Provider.DotProduct(b, b);
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return 1d - ab/Math.Sqrt(a2*b2);
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}
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/// <summary>
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/// Cosine Distance, representing the angular distance while ignoring the scale.
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/// </summary>
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public static float Cosine(float[] a, float[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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var ab = LinearAlgebraControl.Provider.DotProduct(a, b);
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var a2 = LinearAlgebraControl.Provider.DotProduct(a, a);
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var b2 = LinearAlgebraControl.Provider.DotProduct(b, b);
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return (float)(1d - ab/Math.Sqrt(a2*b2));
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}
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/// <summary>
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/// Hamming Distance, i.e. the number of positions that have different values in the vectors.
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/// </summary>
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public static double Hamming(double[] a, double[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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int count = 0;
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for (int i = 0; i < a.Length; i++)
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{
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if (a[i] != b[i])
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{
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count++;
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}
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}
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return count;
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}
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/// <summary>
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/// Hamming Distance, i.e. the number of positions that have different values in the vectors.
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/// </summary>
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public static float Hamming(float[] a, float[] b)
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{
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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int count = 0;
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for (int i = 0; i < a.Length; i++)
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{
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if (a[i] != b[i])
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{
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count++;
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}
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}
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return count;
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}
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/// <summary>
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/// Pearson's distance, i.e. 1 - the person correlation coefficient.
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/// </summary>
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public static double Pearson(IEnumerable<double> a, IEnumerable<double> b)
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{
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return 1.0 - Correlation.Pearson(a, b);
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}
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/// <summary>
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/// Jaccard distance, i.e. 1 - the Jaccard index.
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/// </summary>
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/// <exception cref="ArgumentNullException">Thrown if a or b are null.</exception>
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/// <exception cref="ArgumentException">Throw if a and b are of different lengths.</exception>
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/// <returns>Jaccard distance.</returns>
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public static double Jaccard(double[] a, double[] b)
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{
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int intersection = 0, union = 0;
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (b == null)
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{
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throw new ArgumentNullException(nameof(b));
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}
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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if (a.Length == 0 && b.Length == 0)
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{
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return 0;
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}
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for (int x = 0, len = a.Length; x < len; x++)
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{
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if (a[x] != 0 && b[x] != 0)
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{
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if (a[x] == b[x])
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{
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intersection++;
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}
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union++;
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}
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}
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return 1.0 - ((double)intersection / (double)union);
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}
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/// <summary>
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/// Jaccard distance, i.e. 1 - the Jaccard index.
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/// </summary>
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/// <exception cref="ArgumentNullException">Thrown if a or b are null.</exception>
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/// <exception cref="ArgumentException">Throw if a and b are of different lengths.</exception>
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/// <returns>Jaccard distance.</returns>
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public static double Jaccard(float[] a, float[] b)
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{
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int intersection = 0, union = 0;
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (b == null)
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{
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throw new ArgumentNullException(nameof(b));
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}
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if (a.Length != b.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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if (a.Length == 0 && b.Length == 0)
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{
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return 0;
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}
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for (int x = 0, len = a.Length; x < len; x++)
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{
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if (a[x] != 0 && b[x] != 0)
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{
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if (a[x] == b[x])
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{
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intersection++;
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}
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union++;
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}
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}
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return 1.0 - ((float)intersection / (float)union);
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}
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}
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}
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