Matrix Multiplication

MatrixMultiplication/MatrixMultiplication.Tests/MatrixMultiplication.Tests.csproj

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+<Project Sdk="Microsoft.NET.Sdk">
+
+    <PropertyGroup>
+        <TargetFramework>net6.0</TargetFramework>
+        <Nullable>enable</Nullable>
+
+        <IsPackable>false</IsPackable>
+    </PropertyGroup>
+
+    <ItemGroup>
+        <PackageReference Include="Microsoft.NET.Test.Sdk" Version="16.11.0" />
+        <PackageReference Include="NUnit" Version="3.13.2" />
+        <PackageReference Include="NUnit3TestAdapter" Version="4.0.0" />
+        <PackageReference Include="coverlet.collector" Version="3.1.0" />
+    </ItemGroup>
+
+    <ItemGroup>
+      <ProjectReference Include="..\MatrixMultiplication\MatrixMultiplication.csproj" />
+    </ItemGroup>
+
+</Project>

MatrixMultiplication/MatrixMultiplication.Tests/MatrixMultiplicationTests.cs

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+using System.IO;
+using NUnit.Framework;
+
+namespace MatrixMultiplication.Tests;
+
+public class Tests
+{
+    [Test]
+    public void FileIsReadCorrectly()
+    {
+        using var file1 = new StreamWriter(File.Create("matrix1.txt"));
+        using var file2 = new StreamWriter(File.Create("matrix2.txt"));
+        file1.WriteLine("10 4 5");
+        file1.WriteLine("8 9 1");
+        file2.WriteLine("2 9");       
+        file2.WriteLine("1 7");
+        file2.WriteLine("4 19");
+        file1.Close();
+        file2.Close();
+        var matrix1 = new DenseMatrix("matrix1.txt");
+        var matrix2 = new DenseMatrix("matrix2.txt");
+        Assert.AreEqual(matrix1.Matrix, new[,] { { 10, 4, 5 }, { 8, 9, 1 } });
+        Assert.AreEqual(matrix2.Matrix, new[,] { { 2, 9 }, { 1, 7 }, {4, 19} });
+    }
+
+    [Test]
+    public void SerialCalculationsAreCorrect()
+    {
+        var correctResult = new[,] { { 44, 213 }, { 29, 154 } };
+        var matrix1 = new DenseMatrix(new[,] { { 10, 4, 5 }, { 8, 9, 1 } }, "matrix1.txt");
+        var matrix2 = new DenseMatrix(new[,] { { 2, 9 }, { 1, 7 }, {4, 19} }, "matrix2.txt");
+        var result = DenseMatrix.MultiplySerially(matrix1, matrix2);
+        Assert.AreEqual(correctResult, result.Matrix);
+    }
+
+    [Test]
+    public void SerialCalculationsAndConcurrentCalculationsAreEqual()
+    {
+        for (int i = 0; i < 10; i++)
+        {
+            DenseMatrix.MatrixGenerator("matrix1.txt", (9, 10));
+            DenseMatrix.MatrixGenerator("matrix2.txt", (10, 8));
+            var matrix1 = new DenseMatrix("matrix1.txt");
+            var matrix2 = new DenseMatrix("matrix2.txt");
+            var result1 = DenseMatrix.MultiplyConcurrently(matrix1, matrix2);
+            var result2 = DenseMatrix.MultiplySerially(matrix1, matrix2);
+            Assert.AreEqual(result1.Matrix, result2.Matrix);
+        }
+    }
+
+    [Test]
+    public void SerialAndConcurrentCalculationsCanMultiply1X1Matrices()
+    {
+        var matrix1 = new DenseMatrix(new[,] { { 9 } }, "matrix1.txt");
+        var matrix2 = new DenseMatrix(new[,] { { 100 } }, "matrix2.txt");
+        var result1 = DenseMatrix.MultiplyConcurrently(matrix1, matrix2);
+        var result2 = DenseMatrix.MultiplySerially(matrix1, matrix2);
+        Assert.AreEqual(result1.Matrix, new[,] { {900} });
+        Assert.AreEqual(result1.Matrix, result2.Matrix);
+    }
+
+    [Test]
+    public void SerialAndConcurrentCalculationsCanMultiplyVectors()
+    {
+        DenseMatrix.MatrixGenerator("matrix1.txt", (1, 900));
+        DenseMatrix.MatrixGenerator("matrix2.txt", (900, 1));
+        var matrix1 = new DenseMatrix("matrix1.txt");
+        var matrix2 = new DenseMatrix("matrix2.txt");
+        var result1 = DenseMatrix.MultiplyConcurrently(matrix1, matrix2);
+        var result2 = DenseMatrix.MultiplySerially(matrix1, matrix2);
+        Assert.AreEqual(result1.Matrix, result2.Matrix);
+    }
+}

MatrixMultiplication/MatrixMultiplication.sln

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+
+Microsoft Visual Studio Solution File, Format Version 12.00
+Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "MatrixMultiplication", "MatrixMultiplication\MatrixMultiplication.csproj", "{12DC35BA-E0BB-4B8A-8DD4-B762EA24490A}"
+EndProject
+Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "MatrixMultiplication.Tests", "MatrixMultiplication.Tests\MatrixMultiplication.Tests.csproj", "{A5D3DA1C-4802-43C2-8C7E-29C49AAC7B4F}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|Any CPU = Debug|Any CPU
+		Release|Any CPU = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{12DC35BA-E0BB-4B8A-8DD4-B762EA24490A}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{12DC35BA-E0BB-4B8A-8DD4-B762EA24490A}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{12DC35BA-E0BB-4B8A-8DD4-B762EA24490A}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{12DC35BA-E0BB-4B8A-8DD4-B762EA24490A}.Release|Any CPU.Build.0 = Release|Any CPU
+		{A5D3DA1C-4802-43C2-8C7E-29C49AAC7B4F}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{A5D3DA1C-4802-43C2-8C7E-29C49AAC7B4F}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{A5D3DA1C-4802-43C2-8C7E-29C49AAC7B4F}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{A5D3DA1C-4802-43C2-8C7E-29C49AAC7B4F}.Release|Any CPU.Build.0 = Release|Any CPU
+	EndGlobalSection
+EndGlobal

MatrixMultiplication/MatrixMultiplication/Comparison.cs

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+namespace MatrixMultiplication;
+
+/// <summary>
+/// Tools for matrix multiplication comparison.
+/// </summary>
+public static class Comparison
+{
+    /// <summary>
+    /// Calculates standard deviation using time of matrix multiplications and number of multiplications.
+    /// </summary>
+    /// <param name="N"></param>
+    /// <param name="calculationTime"></param>
+    /// <returns></returns>
+    public static double CalculateDeviation(int N, long[] calculationTime)
+    {
+        var expectedValue = CalculateExpectedValue(N, calculationTime);
+        double variance = 0;
+        for (var i = 0; i < N; i++)
+        {
+            variance += Math.Pow(calculationTime[i] - expectedValue, 2) / N;
+        }
+
+        return Math.Sqrt(variance);
+    }
+
+    /// <summary>
+    /// Calculates expected value (which is arithmetic average in the context of matrix multiplication time).
+    /// </summary>
+    /// <param name="N">Number of multiplications.</param>
+    /// <param name="calculationTime">Array, which elements are time of matrix multiplications.</param>
+    /// <returns></returns>
+    public static long CalculateExpectedValue(int N, long[] calculationTime) => calculationTime.Sum() / N;
+}

MatrixMultiplication/MatrixMultiplication/Main.cs

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+using System.Diagnostics;
+using MatrixMultiplication;
+using Matrix = MatrixMultiplication.DenseMatrix;
+
+const int N = 10;
+
+Table.CreateTable("table.txt");
+
+for (var j = 1; j < 9; j++)
+{
+    long[] calculationTime = new long[N];
+    var size = j * 100;
+    for (var i = 0; i < N; i++)
+    {
+        Matrix.MatrixGenerator("matrix1.txt", (size, size));
+        Matrix.MatrixGenerator("matrix2.txt", (size, size));
+        var matrix1 = new Matrix("matrix1.txt");
+        var matrix2 = new Matrix("matrix2.txt");
+        var stopwatch = new Stopwatch();
+        stopwatch.Start();
+        Matrix.MultiplyConcurrently(matrix1, matrix2);
+        stopwatch.Stop();
+        calculationTime[i] = stopwatch.ElapsedMilliseconds;
+    }
+
+    var expectedValue1 = Comparison.CalculateExpectedValue(N, calculationTime);
+    var deviation1 = Comparison.CalculateDeviation(N, calculationTime);
+
+    for (var i = 0; i < N; i++)
+    {
+        Matrix.MatrixGenerator("matrix1.txt", (size, size));
+        Matrix.MatrixGenerator("matrix2.txt", (size, size));
+        var matrix1 = new Matrix("matrix1.txt");
+        var matrix2 = new Matrix("matrix2.txt");
+        var stopwatch = new Stopwatch();
+        stopwatch.Start();
+        Matrix.MultiplySerially(matrix1, matrix2);
+        stopwatch.Stop();
+        calculationTime[i] = stopwatch.ElapsedMilliseconds;
+    }
+
+    var expectedValue2 = Comparison.CalculateExpectedValue(N, calculationTime);
+    var deviation2 = Comparison.CalculateDeviation(N, calculationTime);
+
+    Table.WriteDataToTable("table.txt", (size, size), expectedValue1, deviation1, expectedValue2, deviation2);
+}