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Add "simple gauss jordan elimination" example
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‎NumericalCalculation/BasicWithCSharp/BasicWithCSharp.sln‎

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@@ -9,6 +9,8 @@ Project("{8BB2217D-0F2D-49D1-97BC-3654ED321F3B}") = "LossOfTrailingDigits", "Los
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EndProject
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Project("{8BB2217D-0F2D-49D1-97BC-3654ED321F3B}") = "CancellationOfSignificantDigits", "CancellationOfSignificantDigits\CancellationOfSignificantDigits.xproj", "{29AECCDE-8736-4B28-A0E3-5B3F36751283}"
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EndProject
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Project("{8BB2217D-0F2D-49D1-97BC-3654ED321F3B}") = "SimpleGaussJordanElimination", "SimpleGaussJordanElimination\SimpleGaussJordanElimination.xproj", "{9BD9D6EF-BF88-444C-9485-A9A72C15D375}"
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EndProject
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Global
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GlobalSection(SolutionConfigurationPlatforms) = preSolution
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Debug|Any CPU = Debug|Any CPU
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{29AECCDE-8736-4B28-A0E3-5B3F36751283}.Debug|Any CPU.Build.0 = Debug|Any CPU
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{29AECCDE-8736-4B28-A0E3-5B3F36751283}.Release|Any CPU.ActiveCfg = Release|Any CPU
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{29AECCDE-8736-4B28-A0E3-5B3F36751283}.Release|Any CPU.Build.0 = Release|Any CPU
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{9BD9D6EF-BF88-444C-9485-A9A72C15D375}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
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{9BD9D6EF-BF88-444C-9485-A9A72C15D375}.Debug|Any CPU.Build.0 = Debug|Any CPU
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{9BD9D6EF-BF88-444C-9485-A9A72C15D375}.Release|Any CPU.ActiveCfg = Release|Any CPU
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{9BD9D6EF-BF88-444C-9485-A9A72C15D375}.Release|Any CPU.Build.0 = Release|Any CPU
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EndGlobalSection
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GlobalSection(SolutionProperties) = preSolution
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HideSolutionNode = FALSE

‎NumericalCalculation/BasicWithCSharp/SimpleGaussJordanElimination/Properties/launchSettings.json‎

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{
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"profiles": {
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"SimpleGaussJordanElimination": {
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"commandName": "Project",
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"commandLineArgs": "> result.txt"
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}
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}
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}

‎NumericalCalculation/BasicWithCSharp/SimpleGaussJordanElimination/SimpleGaussJordanElimination.cs‎

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using System;
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namespace SimpleGaussJordanElimination
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{
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public class SimpleGaussJordanElimination
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{
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public static void Main(string[] args)
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{
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Solve();
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}
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static void WriteEquations(double[,] leftMatrix, double[] rightVector)
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{
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var rowCount = rightVector.Length;
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if (rowCount != leftMatrix.GetLength(0))
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{
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throw new ArgumentException();
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}
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for (int i = 0; i < rowCount; i++)
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{
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for (int j = 0; j < leftMatrix.GetLength(1); j++)
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{
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Console.Write($"{leftMatrix[i, j],8:F4} ");
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}
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Console.WriteLine($" | {rightVector[i],8:F4}");
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}
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}
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static void Solve()
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{
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const int Dimension = 4;
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double[,] matrixA = new double[Dimension, Dimension]
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{
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{ 2, 3, 1, 4 },
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{ 4, 1, -3, -2 },
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{ -1, 2, 2, 1 },
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{ 3, -4, 4, 3 },
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};
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double[] vectorB = new double[Dimension]
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{
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10,
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0,
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4,
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6
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};
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double[] solutionX;
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Console.WriteLine("初期状態");
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WriteEquations(matrixA, vectorB);
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Console.WriteLine();
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// 前進消去
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for (int i = 0; i < Dimension - 1; i++)
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{
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for (int j = i + 1; j < Dimension; j++)
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{
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var s = matrixA[j, i] / matrixA[i, i];
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for (int k = i; k < Dimension; k++)
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{
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matrixA[j, k] -= matrixA[i, k] * s;
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}
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vectorB[j] -= vectorB[i] * s;
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}
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}
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Console.WriteLine("前進消去後");
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WriteEquations(matrixA, vectorB);
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Console.WriteLine();
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// 後退消去
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for (int i = Dimension - 1; i >= 0; i--)
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{
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vectorB[i] /= matrixA[i, i];
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matrixA[i, i] = 1; // matrixA[i, i] /= matrixA[i, i]
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for (int j = i - 1; j >= 0; j--)
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{
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var s = matrixA[j, i]; // s = matrixA[j, i] / matrixA[i, i]
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matrixA[j, i] = 0; // matrixA[j, i] -= s
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vectorB[j] -= vectorB[i] * s;
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}
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}
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Console.WriteLine("後退消去後");
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WriteEquations(matrixA, vectorB);
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Console.WriteLine();
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// solutionX = new double[Dimension];
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// for (int i = 0; i < Dimension; i++)
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// {
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// solutionX[i] = vectorB[i] / matrixA[i, i];
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// }
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solutionX = vectorB;
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Console.WriteLine("解");
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Console.WriteLine(string.Join("\n", System.Linq.Enumerable.Select(solutionX, x => $"{x,8:F4}")));
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}
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}
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}

‎NumericalCalculation/BasicWithCSharp/SimpleGaussJordanElimination/SimpleGaussJordanElimination.xproj‎

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<?xml version="1.0" encoding="utf-8"?>
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<Project ToolsVersion="14.0" DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
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<PropertyGroup>
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<VisualStudioVersion Condition="'$(VisualStudioVersion)' == ''">14.0</VisualStudioVersion>
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<VSToolsPath Condition="'$(VSToolsPath)' == ''">$(MSBuildExtensionsPath32)\Microsoft\VisualStudio\v$(VisualStudioVersion)</VSToolsPath>
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</PropertyGroup>
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<Import Project="$(VSToolsPath)\DotNet\Microsoft.DotNet.Props" Condition="'$(VSToolsPath)' != ''" />
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<PropertyGroup Label="Globals">
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<ProjectGuid>9bd9d6ef-bf88-444c-9485-a9a72c15d375</ProjectGuid>
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<RootNamespace>SimpleGaussJordanElimination</RootNamespace>
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<BaseIntermediateOutputPath Condition="'$(BaseIntermediateOutputPath)'=='' ">.\obj</BaseIntermediateOutputPath>
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<OutputPath Condition="'$(OutputPath)'=='' ">.\bin\</OutputPath>
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<TargetFrameworkVersion>v4.5.2</TargetFrameworkVersion>
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</PropertyGroup>
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<PropertyGroup>
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<SchemaVersion>2.0</SchemaVersion>
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</PropertyGroup>
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<Import Project="$(VSToolsPath)\DotNet\Microsoft.DotNet.targets" Condition="'$(VSToolsPath)' != ''" />
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</Project>

‎NumericalCalculation/BasicWithCSharp/SimpleGaussJordanElimination/project.json‎

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{
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"version": "1.0.0-*",
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"buildOptions": {
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"emitEntryPoint": true
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},
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"dependencies": {
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"Microsoft.NETCore.App": {
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"type": "platform",
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"version": "1.0.1"
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}
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},
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"frameworks": {
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"netcoreapp1.0": {
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"imports": "dnxcore50"
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}
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}
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}

‎NumericalCalculation/BasicWithCSharp/SimpleGaussJordanElimination/result.txt‎

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初期状態
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2.0000 3.0000 1.0000 4.0000 | 10.0000
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4.0000 1.0000 -3.0000 -2.0000 | 0.0000
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-1.0000 2.0000 2.0000 1.0000 | 4.0000
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3.0000 -4.0000 4.0000 3.0000 | 6.0000
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前進消去後
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2.0000 3.0000 1.0000 4.0000 | 10.0000
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0.0000 -5.0000 -5.0000 -10.0000 | -20.0000
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0.0000 0.0000 -1.0000 -4.0000 | -5.0000
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0.0000 0.0000 0.0000 -30.0000 | -30.0000
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後退消去後
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1.0000 0.0000 0.0000 0.0000 | 1.0000
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0.0000 1.0000 0.0000 0.0000 | 1.0000
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0.0000 0.0000 1.0000 0.0000 | 1.0000
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0.0000 0.0000 0.0000 1.0000 | 1.0000
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解
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1.0000
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1.0000
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1.0000
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1.0000

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