Методы вычислений 16.09.22

#include <iostream>
#include <iomanip>
#include <vector>
#include <cmath>
using namespace std;

typedef vector <double> vec;
typedef vector <vec> mat;

const double v = 10;

int n;
mat A;
vec x, b;

vec operator * (const mat& A, const vec& x)
{
    vec b(n + 1);

    for (int i = 0; i <= n; ++i)
        for (int j = 0; j <= n; ++j)
            b[i] += A[i][j] * x[j];

    return b;
}

vec Gauss(mat& A, vec& b)
{
    mat T(n + 1, vec(n + 1));

    for (int k = 0; k < n; ++k)
        for (int i = k + 1; i <= n; ++i)
        {
            T[i][k] = A[i][k] / A[k][k];
            b[i] -= T[i][k] * b[k];

            for (int j = k + 1; j <= n; ++j)
                A[i][j] -= T[i][k] * A[k][j];
        }

    vec x(n + 1);

    x[n] = b[n] / A[n][n];

    for (int k = n - 1; k >= 0; --k)
    {
        double sum = 0;

        for (int j = k + 1; j <= n; ++j)
            sum += A[k][j] * x[j];

        x[k] = (b[k] - sum) / A[k][k];
    }

    return x;
}

void print(mat& A)
{
    cout << "Матрица:\n";

    for (int i = 0; i <= n; ++i, cout << "\n")
        for (int j = 0; j <= n; ++j)
            cout << left << setw(10) << A[i][j];
}

void print(vec& a)
{
    cout << "Вектор: (";

    for (int i = 0; i < n; ++i)
        cout << a[i] << ", ";

    cout << a[n] << ")\n";
}

void print(mat& A, vec& b)
{
    cout << "СЛУ имеет вид:\n";

    for (int i = 0; i <= n; ++i, cout << "\n")
    {
        for (int j = 0; j < n; ++j)
            cout << A[i][j] << " * x_" << (j + 1) << " + ";

        cout << A[i][n] << " * x_" << (n + 1) << " = " << b[i];
    }
}

int main()
{
    setlocale(LC_ALL, "Russian");
    cout << fixed << setprecision(4);

    n = 10;

    A.resize(n + 1);

    for (int i = 0; i <= n; ++i)
        for (int j = 0; j <= n; ++j)
        {
            A[i].push_back(v + i);
            if (i != j) A[i][j] /= 100.0;
        }

    x.resize(n + 1);

    for (int i = 0; i <= n; ++i)
        x[i] = i;

    vec b = A * x;

    vec checkx = Gauss(A, b);

    print(checkx);

    return 0;
}