Lab2_SSNE

#include <iostream>
#include <cmath>

using std::cout;
using std::cin;
using std::endl;


double function1(double x, double y); //1 функция системы
double function2(double x, double y); //2 функция системы
double derivative_func1_dx(double x, double y); //1 производная 1 функции по x
double derivative_func1_dy(double x, double y); //1 производная 1 функции по y
double derivative_func2_dx(double x, double y); //1 производная 2 функции по x
double derivative_func2_dy(double x, double y); //1 производная 2 функции по y
double fi_x(double x, double y); // функция fi1(x, y) - выраженный x из 2 уравнения
double fi_y(double x, double y); // функция fi2(x, y) - выраженный y из 1 уравнения
void newton(double x, double y, double eps); // метод Ньютона для системы нелинейных уравнений
void simple_iter(double x, double y, double eps); // метод простой итерации для системы нелинейных уравнений
void jacobian(double** a); //вычиление матрицы якоби

int main()
{
    unsigned short int pck = -1;
    bool check_task = false;
    cout << "Solving systems of nonlinear equations" << endl;
    cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
    cout << "Choose a method:\n1. Newton's method\n2. Simple iteration method\nEnter:";

    while (check_task == false)
    {
        cin >> pck;
        switch (pck)
        {
        case 1:
        {
            check_task = true;
            double a, b, eps;
            cout << "Newton Method" << endl;
            cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
            cout << "Enter a (approximate value of x): "; cin >> a;
            cout << "Enter b (approximate value of y): "; cin >> b;
            cout << "Enter eps: "; cin >> eps;

            newton(a, b, eps);

            break;
        }
        case 2:
        {
            check_task = true;
            double a, b, eps;
            cout << "Simple iteration method" << endl;
            cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
            cout << "Enter a (approximate value of x): "; cin >> a;
            cout << "Enter b (approximate value of y): "; cin >> b;
            cout << "Enter eps: "; cin >> eps;

            simple_iter(a, b, eps);

            break;
        }
        default: {cout << "#Error#\nEnter a number of method again: "; }
        }
    }
    return 0;
}

double function1(double x, double y)
{
    return sin(x) - y - 1.2 ;
}
double function2(double x, double y)
{
    return 0.15 + cos(y) - x;
}
double derivative_func1_dx(double x, double y)
{
    return cos(x);
}
double derivative_func2_dx(double x, double y)
{
    return -1;
}
double derivative_func1_dy(double x, double y)
{
    return -1;
}
double derivative_func2_dy(double x, double y)
{
    return sin(y);
}
double fi_x(double x, double y)
{
    return 0.15 + cos(y);
}
double fi_y(double x, double y)
{
    return sin(x) - 1.2;
}
void newton(double x, double y, double eps)
{
    double** mass_a = new double* [2];
    for (int i = 0; i < 2; i++)
        mass_a[i] = new double[2];
    double dx, dy, n;
    double* b = new double[2];
    unsigned int count = 0;
    do
    {
        mass_a[0][0] = derivative_func1_dx(x, y);
        mass_a[0][1] = derivative_func1_dy(x, y);
        mass_a[1][0] = derivative_func2_dx(x, y);
        mass_a[1][1] = derivative_func2_dy(x, y);
        jacobian(mass_a);
        dx = -mass_a[0][0] * function1(x, y) + (-mass_a[0][1] * function2(x, y));
        dy = -mass_a[1][0] * function1(x, y) + (-mass_a[1][1] * function2(x, y));
        x += dx;
        y += dy;
        b[0] = function1(x, y);
        b[1] = function2(x, y);
        n = sqrt(b[0] * b[0] + b[1] * b[1]);
        count++;
    } while (n >= eps);
    cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
    cout << "Solution of the system of equations: \n";
    cout << "System of equations: sin(x) - y = 1.2 | 0.15 + cos(y) - x = 0" << endl;
    cout << "X= " << x << "\nY= " << y << endl;
    cout << "Count of iterations= " << count << endl;
    cout << "Checking the resulting solution:" << endl;
    printf("Function 1 (x, y) = %2.12f\nFunction 2 (x, y) = %2.12f\n", function1(x, y), function2(x, y));
    cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;


    for (int i = 0; i < 2; i++)
    {
        delete[] mass_a[i];
    }
    delete[] b;
}
void jacobian(double** a)
{
    double det;
    det = (a[0][0] * a[1][1]) - (a[0][1] * a[1][0]);
    for (int i = 0; i < 2; i++)
    {
        for (int j = 0; j < 2; j++)
        {
            if (i == 0 and j == 0)a[i][j] = a[i + 1][j + 1] / det;
            else if (i != j)a[i][j] = -a[i][j] / det;
            else if (i == 1 and j == 1)a[i][j] = a[i - 1][j - 1] / det;
        }
    }
}
void simple_iter(double x, double y, double eps)
{
    double x_last, y_last;
    unsigned int count = 0;
    do
    {
        x_last = x;
        y_last = y;
        x = fi_x(x_last, y_last);
        y = fi_y(x_last, y_last);
        count++;
    } while (fabs(function1(x, y)) >= eps and fabs(function2(x, y)) >= eps);
    cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
    cout << "Solution of the system of equations: \n";
    cout << "System of equations: sin(x) - y = 1.2 | 0.15 + cos(y) - x = 0" << endl;
    cout << "X= " << x << "\nY= " << y << endl;
    cout << "Count of iterations= " << count << endl;
    cout << "Checking the resulting solution:" << endl;
    printf("Function 1 (x, y) = %2.12f\nFunction 2 (x, y) = %2.12f\n", function1(x, y), function2(x, y));
    cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" << endl;
}