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Jordan_Gauss/Jordan_Gauss.sln

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+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio Version 17
+VisualStudioVersion = 17.3.32804.467
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "Jordan_Gauss", "Jordan_Gauss\Jordan_Gauss.vcxproj", "{708C8740-9A13-4196-B3A6-54D86BF16D22}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|x64 = Debug|x64
+		Debug|x86 = Debug|x86
+		Release|x64 = Release|x64
+		Release|x86 = Release|x86
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{708C8740-9A13-4196-B3A6-54D86BF16D22}.Debug|x64.ActiveCfg = Debug|x64
+		{708C8740-9A13-4196-B3A6-54D86BF16D22}.Debug|x64.Build.0 = Debug|x64
+		{708C8740-9A13-4196-B3A6-54D86BF16D22}.Debug|x86.ActiveCfg = Debug|Win32
+		{708C8740-9A13-4196-B3A6-54D86BF16D22}.Debug|x86.Build.0 = Debug|Win32
+		{708C8740-9A13-4196-B3A6-54D86BF16D22}.Release|x64.ActiveCfg = Release|x64
+		{708C8740-9A13-4196-B3A6-54D86BF16D22}.Release|x64.Build.0 = Release|x64
+		{708C8740-9A13-4196-B3A6-54D86BF16D22}.Release|x86.ActiveCfg = Release|Win32
+		{708C8740-9A13-4196-B3A6-54D86BF16D22}.Release|x86.Build.0 = Release|Win32
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+	GlobalSection(ExtensibilityGlobals) = postSolution
+		SolutionGuid = {253A591D-9280-4E6D-8BA5-F848CDED7A9A}
+	EndGlobalSection
+EndGlobal

Jordan_Gauss/Jordan_Gauss/Jordan_Gauss.cpp

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+#include <iostream>
+#include <clocale>
+#include "Matrix.h"
+#include "Solver.h"
+#include "Vector.h"
+
+using namespace std;
+
+int main()
+{
+    setlocale(LC_ALL, "Russian");
+    size_t n;
+    cout << "Введите размерность вектора и квадратной матрицы: ";
+    cin >> n;
+
+    int a;
+    cout << "Выберите тип данных:\n 1. float\n 2. double\n";
+    cin >> a;
+
+    switch (a) {
+    case 1: {
+        solver<float>(n);
+        break; }
+    case 2: {
+        solver<double>(n);
+        break; }
+    }
+    return 0;
+}

Jordan_Gauss/Jordan_Gauss/Matrix.h

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+#pragma once
+#include<iostream>
+#include "Vector.h"
+
+using namespace std;
+
+template <typename T>
+class Matrix {
+    T** mas;
+    size_t size;
+public:
+    Matrix(size_t size)
+    {
+        this->size = size;
+        mas = new T * [size];
+
+        for (int i = 0; i < size; i++)
+            mas[i] = new T[size + 1];
+    }
+
+    Matrix(const Matrix<T>& m)
+    {
+        size = m.size;
+        mas = new T * [size];
+
+        for (int i = 0; i < size; i++)
+            mas[i] = new T[size + 1];
+
+        for (int i = 0; i < size; i++)
+            for (int j = 0; j < size + 1; j++)
+                mas[i][j] = m.mas[i][j];
+    }
+
+
+    void Set_Matrix()
+    {
+        for (int i = 0; i < size; i++)
+            for (int j = 0; j < size; j++)
+                cin >> mas[i][j];
+    }
+
+    T Get_Matrix(int i, int j)
+    {
+        return mas[i][j];
+    }
+
+    void extended_matrix(Vector<T> b)  //создание расширенной матрицы
+    {
+        for (int i = 0; i < size; i++)
+            mas[i][size] = b.Get_Vector(i);
+    }
+
+    void new_value_matrix(int i, int j, T new_val) //присвоить новое значение
+    {
+        mas[i][j] = new_val;
+    }
+
+    void swap_elem(int i1, int i2)
+    {
+        T w;
+        for (int j = 0; j < size + 1; j++)
+        {
+            w = mas[i1][j];
+            mas[i1][j] = mas[i2][j];
+            mas[i2][j] = w;
+        }
+    }
+
+    void print_matrix()
+    {
+        for (int i = 0; i < size; i++) {
+            for (int j = 0; j < size; j++)
+            {
+                cout <<  mas[i][j] << " ";
+            }
+            cout << "|" << mas[i][size] << "\n";
+        }
+        cout << "\n";
+    }
+
+    ~Matrix()
+    {
+        if (size > 0) {
+            for (int i = 0; i < size; i++)
+                delete[] mas[i];
+            delete[] mas;
+            size = 0;
+        }
+    }
+};

Jordan_Gauss/Jordan_Gauss/Solver.h

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+#pragma once
+#include <iostream>
+#include "Vector.h"
+#include "Matrix.h"
+
+using namespace std;
+
+bool check_null(float x)
+{
+    float eps = 10e-6f;
+    if (abs(x) < eps) return true;
+    return false;
+}
+bool check_null(double x)
+{
+    double eps = 10e-16;
+    if (abs(x) < eps) return true;
+    return false;
+}
+
+template <typename T>
+void print_res(int size, Matrix<T> A)
+{
+    T* res = new T[size];
+    for (int i = 0; i < size; i++)
+        res[i] = 0;
+
+    bool flag = true;
+
+    for (int i = 0; i < size; i++)
+    {
+        if (A.Get_Matrix(i, i) == 1)
+        {
+            for (int j = 0; j < size; j++)
+                if (j != i)
+                    res[i] -= A.Get_Matrix(i, j);
+            res[i] += A.Get_Matrix(i, size);
+            if (check_null(res[i])) res[i] = 0;
+        }
+        else
+            if (check_null(A.Get_Matrix(i, i)))
+            {
+                if (check_null(A.Get_Matrix(i, size))) //если переменная xi является свободной, присваиваем значение 1
+                {
+                    res[i] = 1;
+                    cout << "Свободной переменной является x" << i + 1 << endl;
+                }
+                else
+                {
+                    cout << "Нет решения, так как матрица несовместна\n";
+                    flag = false;
+                    break;
+                }
+            }
+    }
+    if (flag)
+    {
+        for (int i = 0; i < size; i++)
+            cout << "x" << i + 1 << " = " << res[i] << endl;
+    }
+
+}
+
+template <typename T>
+void solver(size_t size)
+{
+    Matrix <T>A(size);
+    cout << "Введите матрицу построчно: \n";
+    A.Set_Matrix();
+
+    Vector <T>b(size);
+    cout << "Введите вектор: \n";
+    b.Set_Vector();
+
+    A.extended_matrix(b);
+
+    int max_index;
+    for (int k = 0; k < size; k++)
+    {
+        max_index = k;
+        for (int i = k + 1; i < size; i++)
+        {
+            if (abs(A.Get_Matrix(max_index, k)) > abs(A.Get_Matrix(i, k)))
+                max_index = k;
+            else max_index = i;
+        }
+
+        if (check_null(A.Get_Matrix(max_index, k))) //если макс элемент равен нулю, то переходим на следующий столбец
+            break;
+
+        T del;
+        for (int i = 0; i < size; i++)
+        {
+            del = A.Get_Matrix(i, k) / A.Get_Matrix(max_index, k);
+            for (int j = 0; j < size + 1; j++)
+            {
+                if (i != max_index)
+                {
+                    if (check_null(A.Get_Matrix(i, j) - A.Get_Matrix(max_index, j) * del))
+                        A.new_value_matrix(i, j, 0);
+                    else A.new_value_matrix(i, j, A.Get_Matrix(i, j) - A.Get_Matrix(max_index, j) * del);
+                    if (j == k)
+                        A.new_value_matrix(i, j, 0);
+                }
+            }
+            del = A.Get_Matrix(max_index, k);
+            for (int j = 0; j < size + 1; j++)
+                A.new_value_matrix(max_index, j, A.Get_Matrix(max_index, j) / del);
+        }
+        if (max_index != k)
+            A.swap_elem(max_index, k);
+        A.print_matrix();
+    }
+    print_res(size, A);
+}

Jordan_Gauss/Jordan_Gauss/Vector.h

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+#pragma once
+#include <iostream>
+
+using namespace std;
+
+template <typename T>
+class Vector {
+    size_t size;
+    T* mas;
+public:
+    Vector(size_t size)
+    {
+        this->size = size;
+        mas = new T[size];
+        for (int i = 0; i < size; i++)
+            mas[i] = 0;
+    }
+
+    Vector(const Vector<T>& v)
+    {
+        size = v.size;
+        mas = new T[size];
+        for (int i = 0; i < size; i++)
+            mas[i] = v.mas[i];
+    }
+
+    void Set_Vector()
+    {
+        for (int i = 0; i < size; i++)
+            cin >> mas[i];
+        cout << "\n";
+    }
+
+    T Get_Vector(const int ind)
+    {
+        return mas[ind];
+    }
+
+    ~Vector()
+    {
+        delete[]mas;
+        size = 0;
+    }
+};