Add Minkowski distance algorithm (#497)

Author: Paulofalcao2002

Algorithms.Tests/LinearAlgebra/Distances/MinkowskiTests.cs

@@ -0,0 +1,28 @@
+using NUnit.Framework;
+using Algorithms.LinearAlgebra.Distances;
+using FluentAssertions;
+using System;
+
+namespace Algorithms.Tests.LinearAlgebra.Distances;
+
+public class MinkowskiTests
+{
+    [TestCase(new[] { 2.0, 3.0 }, new[] { -1.0, 5.0 }, 1, 5.0)] // Simulate Manhattan condition
+    [TestCase(new[] { 7.0, 4.0, 3.0 }, new[] { 17.0, 6.0, 2.0 }, 2, 10.247)] // Simulate Euclidean condition
+    [TestCase(new[] { 1.0, 2.0, 3.0, 4.0 }, new[] { 1.75, 2.25, -3.0, 0.5 }, 20, 6.0)] // Simulate Chebyshev condition
+    [TestCase(new[] { 1.0, 1.0, 9.0 }, new[] { 2.0, 2.0, -5.2 }, 3, 14.2)]
+    [TestCase(new[] { 1.0, 2.0, 3.0 }, new[] { 1.0, 2.0, 3.0 }, 5, 0.0)]
+    public void DistanceTest(double[] point1, double[] point2, int order, double expectedDistance)
+    {
+        Minkowski.Distance(point1, point2, order).Should().BeApproximately(expectedDistance, 0.01);
+    }
+
+    [TestCase(new[] { 2.0, 3.0 }, new[] { -1.0 }, 2)]
+    [TestCase(new[] { 1.0 }, new[] { 1.0, 2.0, 3.0 }, 1)]
+    [TestCase(new[] { 1.0, 1.0 }, new[] { 2.0, 2.0 }, 0)]
+    public void DistanceThrowsArgumentExceptionOnInvalidInput(double[] point1, double[] point2, int order)
+    {
+        Action action = () => Minkowski.Distance(point1, point2, order);
+        action.Should().Throw<ArgumentException>();
+    }
+}

Algorithms/LinearAlgebra/Distances/Minkowski.cs

@@ -0,0 +1,37 @@
+using System;
+using System.Linq;
+
+namespace Algorithms.LinearAlgebra.Distances;
+
+/// <summary>
+/// Implementation of Minkowski distance.
+/// It is the sum of the lengths of the projections of the line segment between the points onto the
+/// coordinate axes, raised to the power of the order and then taking the p-th root.
+/// For the case of order = 1, the Minkowski distance degenerates to the Manhattan distance,
+/// for order = 2, the usual Euclidean distance is obtained and for order = infinity, the Chebyshev distance is obtained.
+/// </summary>
+public static class Minkowski
+{
+    /// <summary>
+    /// Calculate Minkowski distance for two N-Dimensional points.
+    /// </summary>
+    /// <param name="point1">First N-Dimensional point.</param>
+    /// <param name="point2">Second N-Dimensional point.</param>
+    /// <param name="order">Order of the Minkowski distance.</param>
+    /// <returns>Calculated Minkowski distance.</returns>
+    public static double Distance(double[] point1, double[] point2, int order)
+    {
+        if (order < 1)
+        {
+            throw new ArgumentException("The order must be greater than or equal to 1.");
+        }
+
+        if (point1.Length != point2.Length)
+        {
+            throw new ArgumentException("Both points should have the same dimensionality");
+        }
+
+        // distance = (|x1-y1|^p + |x2-y2|^p + ... + |xn-yn|^p)^(1/p)
+        return Math.Pow(point1.Zip(point2, (x1, x2) => Math.Pow(Math.Abs(x1 - x2), order)).Sum(), 1.0 / order);
+    }
+}

README.md

@@ -61,6 +61,7 @@ find more than one implementation for the same objective but using different alg
       * [Chebyshev](./Algorithms/LinearAlgebra/Distances/Chebyshev.cs)
       * [Euclidean](./Algorithms/LinearAlgebra/Distances/Euclidean.cs)
       * [Manhattan](./Algorithms/LinearAlgebra/Distances/Manhattan.cs)
+      * [Minkowski](./Algorithms/LinearAlgebra/Distances/Minkowski.cs)
     * [Eigenvalue](./Algorithms/LinearAlgebra/Eigenvalue)
       * [Power Iteration](./Algorithms/LinearAlgebra/Eigenvalue/PowerIteration.cs)
   * [Modular Arithmetic](./Algorithms/ModularArithmetic)