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5f6e6d72 · Саидбаталов Дмитрий · 00b2832b · 5f6e6d72 · 5f6e6d72 · 5f6e6d72
Commit 5f6e6d72 authored Dec 26, 2020 by Саидбаталов Дмитрий
--- a/NM_Saidbatalov_LR5.sln
+++ b/NM_Saidbatalov_LR5.sln
+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio Version 16
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+MinimumVisualStudioVersion = 10.0.40219.1
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+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
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+		Debug|x86 = Debug|x86
+		Release|x64 = Release|x64
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+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
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+		{4585C8F4-9E57-4635-9D35-533B259EDFA5}.Release|x86.Build.0 = Release|Win32
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
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+		SolutionGuid = {5736620F-5D8C-4B63-9A66-2263CD5BE29F}
+	EndGlobalSection
+EndGlobal
--- a/NM_Saidbatalov_LR5/NM_Saidbatalov_LR5.cpp
+++ b/NM_Saidbatalov_LR5/NM_Saidbatalov_LR5.cpp
+#include <iostream>
+#include "SLAE.h"
+
+using namespace std;
+
+int main()
+{
+    setlocale(LC_ALL, "Russian");
+    int N = 800;
+    int l = 23;
+    int L = 2 * l;
+    double eps = pow(10, -5);
+
+    double** A1 = genStripMatrix(N, l, 1.1);
+    double** A2 = genStripMatrix(N, l, 2);
+    double** A3 = genStripMatrix(N, l, 10);
+   /* cout << "A" << endl;
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++)
+        {
+            cout << A1[i][j] << "\t";
+        }
+        cout << endl;
+    }*/
+    double* x1 = genVector(N);
+    double* x2 = genVector(N);
+    double* x3 = genVector(N);
+    double* b1 = getB(A1, x1, N);
+    double* b2 = getB(A2, x3, N);
+    double* b3 = getB(A3, x3, N);
+
+    /*cout << endl << "x" << endl;
+    for (int i = 0; i < N; i++)
+    {
+        cout << x1[i] << endl;
+    }
+
+    cout << endl << "b" << endl;
+    for (int i = 0; i < N; i++)
+    {
+        cout << b1[i] << endl;
+    }*/
+
+    SLAE sl_1 = symmetrization(A1, b1, N, l);
+    SLAE sl_2 = symmetrization(A2, b2, N, l);
+    SLAE sl_3 = symmetrization(A3, b3, N, l);
+
+    /*cout << endl << "A*" << endl;
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j <= 2 * l; j++)
+        {
+            cout << sl_1.A[i][j] << "\t";
+        }
+        cout << endl;
+    }*/
+
+    /*cout << endl << "b*" << endl;
+    for (int i = 0; i < N; i++)
+    {
+        cout << sl_1.b[i] << endl;
+    }*/
+
+    double* x_0_1 = new double[N];
+    double* x_0_2 = new double[N];
+    double* x_0_3 = new double[N];
+
+    auto x_dist = std::uniform_real_distribution<>(-1., 1.);
+    auto rng = std::default_random_engine();
+
+    for (int i = 0; i < N; i++)
+    {
+        x_0_1[i] = x_dist(rng);
+        x_0_2[i] = x_dist(rng);
+        x_0_3[i] = x_dist(rng);
+    }
+
+    double norm_1 = 0.;
+    double norm_2 = 0.;
+    double norm_3 = 0.;
+
+    double* solve_1;
+    double* solve_2;
+    double* solve_3;
+
+    solve_1 = Jacobi(sl_1, x_0_1, N, L, eps);
+    solve_2 = Jacobi(sl_2, x_0_2, N, L, eps);
+    solve_3 = Jacobi(sl_3, x_0_3, N, L, eps);
+
+    for (int h = 0; h < N; h++)
+    {
+        if (fabs(solve_1[h] - x1[h]) > norm_1)
+            norm_1 = fabs(solve_1[h] - x1[h]);
+        if (fabs(solve_2[h] - x2[h]) > norm_2)
+            norm_2 = fabs(solve_2[h] - x2[h]);
+        if (fabs(solve_3[h] - x3[h]) > norm_3)
+            norm_3 = fabs(solve_3[h] - x3[h]);
+    }
+    cout << "---------------------------------------------------------------" << endl;
+    cout << "Задача 2" << endl;
+    cout << "Решение СЛАУ 1 методом Якоби:" << endl;
+    cout << "Погрешность:" << norm_1 << endl;
+    cout << "Количество итераций:" << solve_1[N] << endl;
+    //////////////////////////////////////////////////////////
+    cout << endl << "Решение СЛАУ 2 методом Якоби:" << endl;
+    cout << "Погрешность:" << norm_2 << endl;
+    cout << "Количество итераций:" << solve_2[N] << endl;
+    ///////////////////////////////////////////////////////////
+    cout << endl << "Решение СЛАУ 3 методом Якоби:" << endl;
+    cout << "Погрешность:" << norm_3 << endl;
+    cout << "Количество итераций:" << solve_3[N] << endl;
+    cout << "---------------------------------------------------------------" << endl;
+    norm_1 = 0.;
+    norm_2 = 0.;
+    norm_3 = 0.;
+
+    double w = 1.0;
+    solve_1 = SOR(sl_1, x_0_1, N, L, eps, w);
+    solve_2 = SOR(sl_2, x_0_2, N, L, eps, w);
+    solve_3 = SOR(sl_3, x_0_3, N, L, eps, w);
+
+    for (int h = 0; h < N; h++)
+    {
+        if (fabs(solve_1[h] - x1[h]) > norm_1)
+            norm_1 = fabs(solve_1[h] - x1[h]);
+        if (fabs(solve_2[h] - x2[h]) > norm_2)
+            norm_2 = fabs(solve_2[h] - x2[h]);
+        if (fabs(solve_3[h] - x3[h]) > norm_3)
+            norm_3 = fabs(solve_3[h] - x3[h]);
+    }
+    cout << "---------------------------------------------------------------" << endl;
+    cout << "Задача 3. w =" << w << endl;
+    cout << "Решение СЛАУ 1 методом SOR:" << endl;
+    cout << "Погрешность:" << norm_1 << endl;
+    cout << "Количество итераций:" << solve_1[N] << endl;
+    ////////////////////////////////////////////////////////
+    cout << endl << "Решение СЛАУ 2 методом SOR:" << endl;
+    cout << "Погрешность:" << norm_2 << endl;
+    cout << "Количество итераций:" << solve_2[N] << endl;
+    /////////////////////////////////////////////////////////
+    cout << endl << "Решение СЛАУ 3 методом SOR:" << endl;
+    cout << "Погрешность:" << norm_3 << endl;
+    cout << "Количество итераций:" << solve_3[N] << endl;
+    cout << "---------------------------------------------------------------" << endl;
+
+    norm_1 = 0.;
+    norm_2 = 0.;
+    norm_3 = 0.;
+
+    solve_1 = CGM(sl_1, x_0_1, N, L, eps);
+    solve_2 = CGM(sl_2, x_0_2, N, L, eps);
+    solve_3 = CGM(sl_3, x_0_3, N, L, eps);
+
+    for (int h = 0; h < N; h++)
+    {
+        if (fabs(solve_1[h] - x1[h]) > norm_1)
+            norm_1 = fabs(solve_1[h] - x1[h]);
+        if (fabs(solve_2[h] - x2[h]) > norm_2)
+            norm_2 = fabs(solve_2[h] - x2[h]);
+        if (fabs(solve_3[h] - x3[h]) > norm_3)
+            norm_3 = fabs(solve_3[h] - x3[h]);
+    }
+    cout << "---------------------------------------------------------------" << endl;
+    cout << "Задача 4" << endl;
+    cout << "Решение СЛАУ 1 методом CGM:" << endl;
+    cout << "Погрешность:" << norm_1 << endl;
+    cout << "Количество итераций:" << solve_1[N] << endl;
+    ////////////////////////////////////////////////////////
+    cout << endl << "Решение СЛАУ 2 методом CGM:" << endl;
+    cout << "Погрешность:" << norm_2 << endl;
+    cout << "Количество итераций:" << solve_2[N] << endl;
+    /////////////////////////////////////////////////////////
+    cout << endl << "Решение СЛАУ 3 методом CGM:" << endl;
+    cout << "Погрешность:" << norm_3 << endl;
+    cout << "Количество итераций:" << solve_3[N] << endl;
+    cout << "---------------------------------------------------------------" << endl;
+
+    norm_1 = 0.;
+    norm_2 = 0.;
+    norm_3 = 0.;
+
+    int m = 4;
+    //solve_1 = PCGM(sl_1, x_0_1, N, 2 * l, eps, m);
+    solve_2 = PCGM(sl_2, x_0_2, N, L, eps, m);
+    solve_3 = PCGM(sl_3, x_0_3, N, L, eps, m);
+
+    for (int h = 0; h < N; h++)
+    {
+        //if (fabs(solve_1[h] - x1[h]) > norm_1)
+        //    norm_1 = fabs(solve_1[h] - x1[h]);
+        if (fabs(solve_2[h] - x2[h]) > norm_2)
+            norm_2 = fabs(solve_2[h] - x2[h]);
+        if (fabs(solve_3[h] - x3[h]) > norm_3)
+            norm_3 = fabs(solve_3[h] - x3[h]);
+    }
+    cout << "Количество шагов метода Якоби: m = " << m << endl;
+    //cout << "Решение СЛАУ 1 методом PCGM:" << endl;
+    //cout << "Погрешность:" << norm_1 << endl;
+    //cout << "Количество итераций:" << solve_1[N] << endl;
+    ////////////////////////////////////////////////////////
+    cout << endl << "Решение СЛАУ 2 методом PCGM:" << endl;
+    cout << "Погрешность:" << norm_2 << endl;
+    cout << "Количество итераций:" << solve_2[N] << endl;
+    /////////////////////////////////////////////////////////
+    cout << endl << "Решение СЛАУ 3 методом PCGM:" << endl;
+    cout << "Погрешность:" << norm_3 << endl;
+    cout << "Количество итераций:" << solve_3[N] << endl;
+    cout << "---------------------------------------------------------------" << endl;
+
+    for (int i = 0; i < N; i++)
+    {
+        delete[] A1[i];
+        delete[] A2[i];
+        delete[] A3[i];
+        delete[] sl_1.A[i];
+        delete[] sl_2.A[i];
+        delete[] sl_3.A[i];
+    }
+
+    delete[] A1;
+    delete[] A2;
+    delete[] A3;
+    delete[] sl_1.A;
+    delete[] sl_2.A;
+    delete[] sl_3.A;
+    delete[] sl_1.b;
+    delete[] sl_2.b;
+    delete[] sl_3.b;
+    delete[] x1;
+    delete[] x2;
+    delete[] x3;
+    delete[] b1;
+    delete[] b2;
+    delete[] b3;
+    delete[] x_0_1;
+    delete[] x_0_2;
+    delete[] x_0_3;
+    delete[] solve_1;
+    delete[] solve_2;
+    delete[] solve_3;
+}
+
--- a/NM_Saidbatalov_LR5/NM_Saidbatalov_LR5.vcxproj
+++ b/NM_Saidbatalov_LR5/NM_Saidbatalov_LR5.vcxproj
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\ No newline at end of file
--- a/NM_Saidbatalov_LR5/NM_Saidbatalov_LR5.vcxproj.filters
+++ b/NM_Saidbatalov_LR5/NM_Saidbatalov_LR5.vcxproj.filters
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\ No newline at end of file
--- a/NM_Saidbatalov_LR5/SLAE.cpp
+++ b/NM_Saidbatalov_LR5/SLAE.cpp
+#include "SLAE.h"
+
+double** genStripMatrix(int n, int l, double q)
+{
+    double** A = new double* [n];
+	for (int i = 0; i < n; i++)
+	{
+		A[i] = new double[n];
+		for (int j = 0; j < n; j++)
+		{
+			A[i][j] = 0.;
+		}
+	}
+	auto x_dist = std::uniform_real_distribution<>(-1., 1.);
+	auto rng = std::default_random_engine();
+
+	for (int i = 0; i < n; i++)
+	{
+		int left;
+		int right;
+		if (0 > i - l)
+			left = 0;
+		else left = i - l;
+		if (i + l < n)
+			right = i + l + 1;
+		else
+			right = n;
+		for (int j = left; j < right; j++)
+		{
+			if (i == j) continue;
+			A[i][j] = x_dist(rng);
+			A[i][i] += fabs(A[i][j]);
+			A[i][i] *= q;
+		}
+	}
+
+    return A;
+}
+
+double* genVector(int n)
+{
+	auto x_dist = std::uniform_real_distribution<>(-1., 1.);
+	auto rng = std::default_random_engine();
+
+	double* x = new double[n];
+	for (int i = 0; i < n; i++)
+	{
+		x[i] = x_dist(rng);
+	}
+	return x;
+}
+
+double* getB(double** A, double* x, int n)
+{
+	double* b = new double[n];
+	for (int i = 0; i < n; i++)
+	{
+		b[i] = 0.;
+		for (int j = 0; j < n; j++)
+		{
+			b[i] += A[i][j] * x[j];
+		}
+	}
+	return b;
+}
+
+SLAE symmetrization(double** A, double* b, int n, int l)
+{
+	SLAE slae;
+	double** _A = new double* [n];
+	double* _b = new double[n];
+	for (int i = 0; i < n; i++)
+	{
+		_A[i] = new double[n];
+	}
+
+	for (int i = 0; i < n; i++)
+	{
+		for (int j = 0; j < n; j++)
+		{
+			_A[i][j] = 0.;
+			for (int k = 0; k < n; k++)
+			{
+				_A[i][j] += A[k][i] * A[k][j];
+			}
+			//std::cout << _A[i][j] << "\t";
+		}
+		//std::cout << std::endl;
+	}
+	slae.A = new double* [n];
+	for (int i = 0; i < n; i++)
+	{
+		slae.A[i] = new double[2 * l + 1];
+	}
+
+	///////////////////////////////     ,    
+
+	int L = 0;
+	for (int k = 2 * l; k >= 0; k--)
+	{
+		for (int i = 0; i < L; i++)
+		{
+			slae.A[i][k] = 0.0;
+		}
+		for (int i = L; i < n; i++)
+		{
+			slae.A[i][k] = _A[i - L][i];
+		}
+		L++;
+	}
+
+	for (int i = 0; i < n; i++)
+	{
+		_b[i] = 0.;
+		for (int j = 0; j < n; j++)
+		{
+			_b[i] += A[j][i] * b[j];
+		}
+	}
+
+	///////////////////////////////
+	slae.b = _b;
+	return slae;
+}
+
+double* Jacobi(SLAE sl, double* x, int n, int L, double eps)
+{
+	double* x_k = new double[n + 1];
+	double* temp = new double[n];
+	int it = 0;
+	double norm;
+	for (int i = 0; i < n; i++)
+	{
+		x_k[i] = x[i];