Add SoftMax Function (#469)

Author: RicardoRibeiroRodrigues

Algorithms.Tests/Numeric/SoftMaxTests.cs

@@ -0,0 +1,48 @@
+using System;
+using Algorithms.Numeric;
+using NUnit.Framework;
+
+namespace Algorithms.Tests.Numeric;
+
+public static class SoftMaxTests
+{
+    [TestCase(new[] {5.0, 5.0}, new[] {0.5, 0.5})]
+    [TestCase(new[] {1.0, 2.0, 3.0}, new[] {0.09003057317038046, 0.24472847105479767, 0.6652409557748219})]
+    [TestCase(new[] {0.0}, new[] {1.0})]
+    public static void SoftMaxFunction(double[] input, double[] expected)
+    {
+        // Act
+        var result = SoftMax.Compute(input);
+
+        // Assert
+        Assert.That(result, Is.EqualTo(expected).Within(1e-9));
+    }
+
+    [Test]
+    public static void SoftMaxFunctionThrowsArgumentException()
+    {
+        // Arrange
+        var input = Array.Empty<double>();
+
+        // Assert
+        Assert.Throws<ArgumentException>(() => SoftMax.Compute(input));
+    }
+
+    [TestCase(new[] {1.0, 2.0, 3.0, 4.0, 5.0})]
+    [TestCase(new[] {0.0, 0.0, 0.0, 0.0, 0.0})]
+    [TestCase(new[] {5.0})]
+    public static void SoftMaxFunctionSumsToOne(double[] input)
+    {
+        // Act
+        var result = SoftMax.Compute(input);
+
+        var sum = 0.0;
+        foreach (var value in result)
+        {
+            sum += value;
+        }
+
+        // Assert
+        Assert.That(sum, Is.EqualTo(1.0).Within(1e-9));
+    }
+}

Algorithms/Numeric/SoftMax.cs

@@ -0,0 +1,45 @@
+using System;
+
+namespace Algorithms.Numeric;
+
+/// <summary>
+///     Implementation of the SoftMax function.
+///     Its a function that takes as input a vector of K real numbers, and normalizes
+///     it into a probability distribution consisting of K probabilities proportional
+///     to the exponentials of the input numbers. After softmax, the elements of the vector always sum up to 1.
+///     https://en.wikipedia.org/wiki/Softmax_function.
+/// </summary>
+public static class SoftMax
+{
+    /// <summary>
+    ///    Compute the SoftMax function.
+    ///    The SoftMax function is defined as:
+    ///    softmax(x_i) = exp(x_i) / sum(exp(x_j)) for j = 1 to n
+    ///    where x_i is the i-th element of the input vector.
+    ///    The elements of the output vector are the probabilities of the input vector, the output sums up to 1.
+    /// </summary>
+    /// <param name="input">The input vector of real numbers.</param>
+    /// <returns>The output vector of real numbers.</returns>
+    public static double[] Compute(double[] input)
+    {
+        if (input.Length == 0)
+        {
+            throw new ArgumentException("Array is empty.");
+        }
+
+        var exponentVector = new double[input.Length];
+        var sum = 0.0;
+        for (var index = 0; index < input.Length; index++)
+        {
+            exponentVector[index] = Math.Exp(input[index]);
+            sum += exponentVector[index];
+        }
+
+        for (var index = 0; index < input.Length; index++)
+        {
+            exponentVector[index] /= sum;
+        }
+
+        return exponentVector;
+    }
+}

README.md

@@ -95,6 +95,7 @@ find more than one implementation for the same objective but using different alg
     * [Automorphic Number](./Algorithms/Numeric/AutomorphicNumber.cs)
     * [Josephus Problem](./Algorithms/Numeric/JosephusProblem.cs)
     * [Newton's Square Root Calculation](./Algorithms/NewtonSquareRoot.cs)
+    * [SoftMax Function](./Algorithms/Numeric/SoftMax.cs)
   * [Searches](./Algorithms/Search)
     * [A-Star](./Algorithms/Search/AStar/)
     * [Binary Search](./Algorithms/Search/BinarySearcher.cs)