Статья Автор: Бережной Олег
матмоды 1

#include <iostream>
#include <vector>
#include <cmath>
#include <iomanip>
#include <algorithm>

using namespace std;

const double EPS = 1e-10;

vector<double> solveGauss(vector<vector<double>> A, vector<double> b) {
    int n = A.size();

    for (int k = 0; k < n; ++k) {
       
        int maxRow = k;
        for (int i = k + 1; i < n; ++i) {
            if (abs(A[i][k]) > abs(A[maxRow][k])) {
                maxRow = i;
            }
        }

     
        swap(A[k], A[maxRow]);
        swap(b[k], b[maxRow]);

       
        if (abs(A[k][k]) < EPS) {
            cerr << "Ошибка: Матрица вырождена или почти вырождена." << endl;
            return vector<double>(n, NAN);
        }

        
        for (int i = k + 1; i < n; ++i) {
            double factor = A[i][k] / A[k][k];
            b[i] -= factor * b[k];
            for (int j = k; j < n; ++j) {
                A[i][j] -= factor * A[k][j];
            }
        }
    }

    
    vector<double> x(n);
    for (int i = n - 1; i >= 0; --i) {
        x[i] = b[i];
        for (int j = i + 1; j < n; ++j) {
            x[i] -= A[i][j] * x[j];
        }
        x[i] /= A[i][i];
    }

    return x;
}

int main() {
    
    const int n = 3;

    
    vector<vector<double>> A = {
        {1.53, 1.61, 1.43},
        {2.35, 2.31, 2.07},
        {3.83, 3.73, 3.45}
    };

    
    vector<double> b = {5.13, 3.69, 5.98};

    cout << "Решение СЛАУ методом Гаусса" << endl;
    cout << "Система:" << endl;
    cout << fixed << setprecision(2);
    for (int i = 0; i < n; ++i) {
        cout << A[i][0] << "*x + " << A[i][1] << "*y + " << A[i][2] << "*z = " << b[i] << endl;
    }

  
    vector<double> x = solveGauss(A, b);

   
    if (isnan(x[0])) {
        return 1;
    }

    
    cout << endl;
    cout << setprecision(6);
    cout << "Решение:" << endl;
    cout << "x = " << x[0] << endl;
    cout << "y = " << x[1] << endl;
    cout << "z = " << x[2] << endl;

    
    cout << "\nПроверка (A * x):" << endl;
    for (int i = 0; i < n; ++i) {
        double residual = 0.0;
        for (int j = 0; j < n; ++j) {
            residual += A[i][j] * x[j];
        }
        cout << "Уравнение " << (i+1) << ": вычислено = " << residual
             << ", ожидалось = " << b[i]
             << ", разница = " << abs(residual - b[i]) << endl;
    }

    return 0;
}
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