// ЧМЫ5.cpp: определяет точку входа для консольного приложения.
//


#include <iostream>
#include <cmath>

using namespace std;

double f1(double x1, double x2) {
    return exp(x1*x2) + x1 - 6;
}

double f2(double x1, double x2) {
    return   x1*x1 - 6 * x2 - 1;
}

double f1_d1(double x1, double x2) {
    return x2*exp(x1*x2) + 1;
}

double f1_d2(double x1, double x2) {
    return x1*exp(x1*x2);
}

double f2_d1(double x1, double x2) {
    return 2 * x1;
}

double f2_d2(double x1, double x2) {
    return -6;
}

double x[2], x_prev[2];
double slau[2][3];

int slaufill() {
    slau[0][0] = f1_d1(x_prev[0],x_prev[1]);
    slau[0][1] = f1_d2(x_prev[0], x_prev[1]);
    slau[1][0] = f2_d1(x_prev[0], x_prev[1]);
    slau[1][1] = f2_d2(x_prev[0], x_prev[1]);
    slau[0][2] = -f1(x_prev[0], x_prev[1]);
    slau[1][2] = -f2(x_prev[0], x_prev[1]);
    return 0;
}

int slausolve_nextstep() {
    int i;
    double koef;
    koef = -slau[1][0] / slau[0][0];
    for (i = 0; i < 3; i++)
        slau[1][i] = slau[1][i] + slau[0][i] * koef;
    slau[1][2] = slau[1][2] / slau[1][1];
    slau[0][2] = (slau[0][2] - slau[0][1] * slau[1][2]) / slau[0][0];
    for (i = 0; i < 2; i++)
        x[i] = x_prev[i] + slau[i][2];
    return 0;
}

double maxdiff() {
    if (abs(x[0] - x_prev[0]) > abs(x[1] - x_prev[1]))
        return abs(x[0] - x_prev[0]);
    else
        return abs(x[1] - x_prev[1]);
}

int main() {
    double acc = 0.001;

    //Метод простых итераций:
    cout << "Metod prostih iteracii:" << endl;
    x_prev[0] = 2.5;
    x_prev[1] = 0.5;
    x[0] = sqrt(6 * log(6 - x_prev[0]) / x_prev[0] + 1);
    x[1] = (x_prev[0] * x_prev[0] - 1) / 6;
    while (maxdiff() > acc) {
        cout << "x1=" << x[0] << '\t' << "x1_prev=" << x_prev[0] << endl << endl;
        cout << "x2=" << x[1] << '\t' << "x2_prev=" << x_prev[1] << endl << endl;
        cout << "f1=" << f1(x[0], x[1]) << '\t' << "f2=" << f2(x[0], x[1]) << endl;
        x_prev[0] = x[0];
        x_prev[1] = x[1];
        x[0] = sqrt(6 * log(6 - x_prev[0]) / x_prev[0] + 1);
        x[1] = (x_prev[0] * x_prev[0] - 1) / 6;
        cout << "--------------------------" << endl << endl;
    }
    cout << "x1=" << x[0] << '\t' << "x1_prev=" << x_prev[0] << endl << endl;
    cout << "x2=" << x[1] << '\t' << "x2_prev=" << x_prev[1] << endl << endl;
    cout << round(f1(x[0], x[1])) << '\t' << round(f2(x[0], x[1])) << endl << endl;
    cout << "||||||||||||||||||||||||||" << endl << endl;


    cout << endl << endl << endl;


    //Метод Ньютона:
    cout << "Metod Newtona:" << endl;
    x_prev[0] = 3;
    x_prev[1] = 1;
    slaufill();
    slausolve_nextstep();
    while (maxdiff() > acc) {
        cout << "x1=" << x[0] << '\t' << "x1_prev=" << x_prev[0] << endl << endl;
        cout << "x2=" << x[1] << '\t' << "x2_prev=" << x_prev[1] << endl << endl;
        cout << "f1=" << f1(x[0], x[1]) << '\t' << "f2=" << f2(x[0], x[1]) << endl;
        x_prev[0] = x[0];
        x_prev[1] = x[1];
        slaufill();
        slausolve_nextstep();
        cout << "--------------------------" << endl << endl;
    }
    cout << "x1=" << x[0] << '\t' << "x1_prev=" << x_prev[0] << endl << endl;
    cout << "x2=" << x[1] << '\t' << "x2_prev=" << x_prev[1] << endl << endl;
    cout << round(f1(x[0], x[1])) << '\t' << round(f2(x[0], x[1])) << endl << endl;
    cout << "||||||||||||||||||||||||||" << endl << endl;
    char j;
    cin >> j;
    return 0;
}