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lapytko · Sep 16, 2019 · f722dd7 · f722dd7
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diff --git a/Gauss.sln b/Gauss.sln
@@ -0,0 +1,25 @@
+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio 15
+VisualStudioVersion = 15.0.28010.2019
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "Gauss", "Gauss\Gauss.csproj", "{57C4D1F2-DD71-4987-9160-5E8260556484}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|Any CPU = Debug|Any CPU
+		Release|Any CPU = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{57C4D1F2-DD71-4987-9160-5E8260556484}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{57C4D1F2-DD71-4987-9160-5E8260556484}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{57C4D1F2-DD71-4987-9160-5E8260556484}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{57C4D1F2-DD71-4987-9160-5E8260556484}.Release|Any CPU.Build.0 = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+	GlobalSection(ExtensibilityGlobals) = postSolution
+		SolutionGuid = {70A69724-3978-4877-99D8-9E91272B1968}
+	EndGlobalSection
+EndGlobal
diff --git a/Gauss/Gauss.cs b/Gauss/Gauss.cs
@@ -0,0 +1,133 @@
+using System;
+using System.Collections;
+using System.Data;
+
+namespace Gauss {
+    public class GaussSolutionNotFound : Exception {
+        public GaussSolutionNotFound(string msg)
+            : base("Ðåøåíèå íå ìîæåò áûòü íàéäåíî: \r\n" + msg) {
+        }
+    }
+
+    public class LinearSystem {
+        private double[,] initial_a_matrix;
+        private double[,] a_matrix;  // ìàòðèöà A
+        private double[] x_vector;   // âåêòîð íåèçâåñòíûõ x
+        private double[] initial_b_vector;
+        private double[] b_vector;   // âåêòîð b
+        private double eps;          // ïîðÿäîê òî÷íîñòè äëÿ ñðàâíåíèÿ âåùåñòâåííûõ ÷èñåë 
+        private int size;            // ðàçìåðíîñòü çàäà÷è
+
+
+        public LinearSystem(double[,] a_matrix, double[] b_vector)
+            : this(a_matrix, b_vector, 0.0001) {
+        }
+        public LinearSystem(double[,] a_matrix, double[] b_vector, double eps) {
+            if (a_matrix == null || b_vector == null)
+                throw new ArgumentNullException("Îäèí èç ïàðàìåòðîâ ðàâåí null.");
+
+            int b_length = b_vector.Length;
+            int a_length = a_matrix.Length;
+            if (a_length != b_length * b_length)
+                throw new ArgumentException(@"Êîëè÷åñòâî ñòðîê è ñòîëáöîâ â ìàòðèöå A äîëæíî ñîâïàäàòü ñ êîëè÷åñòâîì ýëåìåíòðîâ â âåêòîðå B.");
+
+            this.initial_a_matrix = a_matrix;  // çàïîìèíàåì èñõîäíóþ ìàòðèöó
+            this.a_matrix = (double[,])a_matrix.Clone(); // ñ å¸ êîïèåé áóäåì ïðîèçâîäèòü âû÷èñëåíèÿ
+            this.initial_b_vector = b_vector;  // çàïîìèíàåì èñõîäíûé âåêòîð
+            this.b_vector = (double[])b_vector.Clone();  // ñ åãî êîïèåé áóäåì ïðîèçâîäèòü âû÷èñëåíèÿ
+            this.x_vector = new double[b_length];
+            this.size = b_length;
+            this.eps = eps;
+
+            GaussSolve();
+        }
+
+        public double[] XVector {
+            get {
+                return x_vector;
+            }
+        }
+
+        // èíèöèàëèçàöèÿ ìàññèâà èíäåêñîâ ñòîëáöîâ
+        private int[] InitIndex() {
+            int[] index = new int[size];
+            for (int i = 0; i < index.Length; ++i)
+                index[i] = i;
+            return index;
+        }
+
+        // ïîèñê ãëàâíîãî ýëåìåíòà â ìàòðèöå
+        private double FindR(int row, int[] index) {
+            int max_index = row;
+            double max = a_matrix[row, index[max_index]];
+            double max_abs = Math.Abs(max);
+            for (int cur_index = row + 1; cur_index < size; ++cur_index) {
+                double cur = a_matrix[row, index[cur_index]];
+                double cur_abs = Math.Abs(cur);
+                if (cur_abs > max_abs) {
+                    max_index = cur_index;
+                    max = cur;
+                    max_abs = cur_abs;
+                }
+            }
+
+            if (max_abs < eps) {
+                if (Math.Abs(b_vector[row]) > eps)
+                    throw new GaussSolutionNotFound("Ñèñòåìà óðàâíåíèé íåñîâìåñòíà.");
+                else
+                    throw new GaussSolutionNotFound("Ñèñòåìà óðàâíåíèé èìååò ìíîæåñòâî ðåøåíèé.");
+            }
+
+            // ìåíÿåì ìåñòàìè èíäåêñû ñòîëáöîâ
+            int temp = index[row];
+            index[row] = index[max_index];
+            index[max_index] = temp;
+
+            return max;
+        }
+
+        // ðåøåíèå ìåòîäîì Ãàóññà
+        private void GaussSolve() {
+            int[] index = InitIndex();
+            GaussForwardStroke(index);
+            GaussBackwardStroke(index);
+            GaussDiscrepancy();
+        }
+
+        // Ïðÿìîé õîä ìåòîäà Ãàóññà
+        private void GaussForwardStroke(int[] index) {
+            for (int i = 0; i < size; ++i) {
+                double r = FindR(i, index);
+                for (int j = 0; j < size; ++j)
+                    a_matrix[i, j] /= r;
+                b_vector[i] /= r;
+                for (int k = i + 1; k < size; ++k) {
+                    double p = a_matrix[k, index[i]];
+                    for (int j = i; j < size; ++j)
+                        a_matrix[k, index[j]] -= a_matrix[i, index[j]] * p;
+                    b_vector[k] -= b_vector[i] * p;
+                    a_matrix[k, index[i]] = 0.0;
+                }
+            }
+        }
+
+        // Îáðàòíûé õîä ìåòîäà Ãàóññà
+        private void GaussBackwardStroke(int[] index) {
+            for (int i = size - 1; i >= 0; --i) {
+                double x_i = b_vector[i];
+                for (int j = i + 1; j < size; ++j)
+                    x_i -= x_vector[index[j]] * a_matrix[i, index[j]];
+                x_vector[index[i]] = x_i;
+            }
+        }
+
+        // x - ðåøåíèå óðàâíåíèÿ, ïîëó÷åííîå ìåòîäîì Ãàóññà
+        private void GaussDiscrepancy() {
+            for (int i = 0; i < size; ++i) {
+                double actual_b_i = 0.0;    
+                for (int j = 0; j < size; ++j)
+                    actual_b_i += initial_a_matrix[i, j] * x_vector[j];
+            }
+        }
+    }
+}
diff --git a/Gauss/Gauss.csproj b/Gauss/Gauss.csproj
@@ -0,0 +1,90 @@
+<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003" ToolsVersion="15.0">
+  <PropertyGroup>
+    <Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
+    <Platform Condition=" '$(Platform)' == '' ">AnyCPU</Platform>
+    <ProductVersion>8.0.50727</ProductVersion>
+    <SchemaVersion>2.0</SchemaVersion>
+    <ProjectGuid>{57C4D1F2-DD71-4987-9160-5E8260556484}</ProjectGuid>
+    <OutputType>WinExe</OutputType>
+    <AppDesignerFolder>Properties</AppDesignerFolder>
+    <RootNamespace>Gauss</RootNamespace>
+    <AssemblyName>Gauss</AssemblyName>
+    <TargetFrameworkVersion>v4.6.1</TargetFrameworkVersion>
+    <FileUpgradeFlags>
+    </FileUpgradeFlags>
+    <UpgradeBackupLocation>
+    </UpgradeBackupLocation>
+    <OldToolsVersion>2.0</OldToolsVersion>
+    <TargetFrameworkProfile />
+  </PropertyGroup>
+  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|AnyCPU' ">
+    <DebugSymbols>true</DebugSymbols>
+    <DebugType>full</DebugType>
+    <Optimize>false</Optimize>
+    <OutputPath>bin\Debug\</OutputPath>
+    <DefineConstants>DEBUG;TRACE</DefineConstants>
+    <ErrorReport>prompt</ErrorReport>
+    <WarningLevel>4</WarningLevel>
+    <Prefer32Bit>false</Prefer32Bit>
+  </PropertyGroup>
+  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|AnyCPU' ">
+    <DebugType>pdbonly</DebugType>
+    <Optimize>true</Optimize>
+    <OutputPath>bin\Release\</OutputPath>
+    <DefineConstants>TRACE</DefineConstants>
+    <ErrorReport>prompt</ErrorReport>
+    <WarningLevel>4</WarningLevel>
+    <Prefer32Bit>false</Prefer32Bit>
+  </PropertyGroup>
+  <ItemGroup>
+    <Reference Include="System" />
+    <Reference Include="System.Data" />
+    <Reference Include="System.Deployment" />
+    <Reference Include="System.Drawing" />
+    <Reference Include="System.Windows.Forms" />
+    <Reference Include="System.Xml" />
+  </ItemGroup>
+  <ItemGroup>
+    <Compile Include="MainForm.cs">
+      <SubType>Form</SubType>
+    </Compile>
+    <Compile Include="MainForm.Designer.cs">
+      <DependentUpon>MainForm.cs</DependentUpon>
+    </Compile>
+    <Compile Include="Gauss.cs" />
+    <Compile Include="Program.cs" />
+    <Compile Include="Properties\AssemblyInfo.cs" />
+    <EmbeddedResource Include="MainForm.resx">
+      <SubType>Designer</SubType>
+      <DependentUpon>MainForm.cs</DependentUpon>
+    </EmbeddedResource>
+    <EmbeddedResource Include="Properties\Resources.resx">
+      <Generator>ResXFileCodeGenerator</Generator>
+      <SubType>Designer</SubType>
+      <LastGenOutput>Resources.Designer.cs</LastGenOutput>
+    </EmbeddedResource>
+    <None Include="app.config" />
+    <None Include="Properties\Settings.settings">
+      <Generator>SettingsSingleFileGenerator</Generator>
+      <LastGenOutput>Settings.Designer.cs</LastGenOutput>
+    </None>
+    <Compile Include="Properties\Resources.Designer.cs">
+      <AutoGen>True</AutoGen>
+      <DesignTime>True</DesignTime>
+      <DependentUpon>Resources.resx</DependentUpon>
+    </Compile>
+    <Compile Include="Properties\Settings.Designer.cs">
+      <AutoGen>True</AutoGen>
+      <DependentUpon>Settings.settings</DependentUpon>
+      <DesignTimeSharedInput>True</DesignTimeSharedInput>
+    </Compile>
+  </ItemGroup>
+  <Import Project="$(MSBuildBinPath)\Microsoft.CSharp.targets" />
+  <!-- To modify your build process, add your task inside one of the targets below and uncomment it. 
+       Other similar extension points exist, see Microsoft.Common.targets.
+  <Target Name="BeforeBuild">
+  </Target>
+  <Target Name="AfterBuild">
+  </Target>
+  -->
+</Project>